Abstract

The prefrontal cortex (PFC) is central to flexible, goal-directed cognition, and understanding its representational code is an important problem in cognitive neuroscience. In humans, multivariate pattern analysis (MVPA) of fMRI blood oxygenation level-dependent (BOLD) measurements has emerged as an important approach for studying neural representations. Many previous studies have implicitly assumed that MVPA of fMRI BOLD is just as effective in decoding information encoded in PFC neural activity as it is in visual cortex. However, MVPA studies of PFC have had mixed success. Here we estimate the base rate of decoding information from PFC BOLD activity patterns from a meta-analysis of published MVPA studies. We show that PFC has a significantly lower base rate (55.4%) than visual areas in occipital (66.6%) and temporal (71.0%) cortices and one that is close to chance levels. Our results have implications for the design and interpretation of MVPA studies of PFC and raise important questions about its functional organization.

INTRODUCTION

The prefrontal cortex (PFC) supports flexible, goal-directed behavior. Patients with frontal lobe lesions struggle to coherently organize their behavior around a goal and show reduced flexibility in changing circumstances (Anderson, Damasio, Jones, & Tranel, 1991; Shallice & Burgess, 1991; Luria, 1966). Theories of PFC function emphasize its role in representing task-relevant variables such as rules, goals, rewards, action choices, and so forth during task performance (Badre, 2008; Hazy, Frank, & O'Reilly, 2007; Rougier, Noelle, Braver, Cohen, & O'Reilly, 2005; Duncan, 2001; Miller & Cohen, 2001; Funahashi, Bruce, & Goldman-Rakic, 1989; Fuster & Alexander, 1971). These task representations are hypothesized to serve as a source of top–down, contextual signals that bias processing in other brain regions, thus achieving cognitive control. Understanding the nature of these PFC representations remains a key open problem in the study of cognitive control, learning, generalization, multitasking, and decision-making (Botvinick, Weinstein, Solway, & Barto, 2015; Botvinick & Cohen, 2014; Feng, Schwemmer, Gershman, & Cohen, 2014; Badre & Frank, 2012; Frank & Badre, 2012).

Much of our knowledge of PFC representations derives from single-neuron electrophysiology conducted in highly trained nonhuman primates. Such studies have consistently revealed rich coding of a variety of task-relevant information in the firing rate of individual PFC neurons (Mansouri, Tanaka, & Buckley, 2009; Wallis, Anderson, & Miller, 2001; White & Wise, 1999; Rainer, Asaad, & Miller, 1998; Sakagami & Niki, 1994), the activity patterns of ensembles of neurons (Saez, Rigotti, Ostojic, Fusi, & Salzman, 2015; Rigotti et al., 2013; Stokes et al., 2013; Meyers, Freedman, Kreiman, Miller, & Poggio, 2008; Sigala, Kusunoki, Nimmo-Smith, Gaffan, & Duncan, 2008), and the oscillatory synchronization of local field potentials (Buschman, Denovellis, Diogo, Bullock, & Miller, 2012).

In humans, blood oxygenation level-dependent (BOLD) measures from fMRI were traditionally seen as lacking the sensitivity and spatial resolution for the study of neural information coding (Nevado, Young, & Panzeri, 2004). In the past decade, however, this view has been challenged by the development of multivariate pattern analysis (MVPA) methods that employ machine learning pattern classifiers to decode the information content of spatially distributed BOLD activity patterns (Chatham & Badre, in press; Haynes, 2015; Tong & Pratte, 2012; Haynes & Rees, 2006; Kriegeskorte, Goebel, & Bandettini, 2006; Norman, Polyn, Detre, & Haxby, 2006; Haxby et al., 2001). MVPA has been applied to fMRI data from all over the brain, and PFC is no exception. Several studies have reported statistically reliable classification of task rule and other task-relevant variables from regions within PFC (Waskom & Wagner, 2017; Reverberi, Görgen, & Haynes, 2012a; Cole, Etzel, Zacks, Schneider, & Braver, 2011; Woolgar, Hampshire, Thompson, & Duncan, 2011; Woolgar, Thompson, Bor, & Duncan, 2011; Bode & Haynes, 2009).

Nevertheless, there is an impression among researchers with experience using MVPA that decoding information from PFC BOLD patterns is particularly difficult. Typical group mean classification accuracies reported in fMRI studies of PFC decoding often hover just above chance levels, for example, values of 53%, 55%, and 55% reported in Nelissen, Stokes, Nobre, and Rushworth (2013), Woolgar, Thompson, et al. (2011), and Bode and Haynes (2009) for two-way classifications, even for task features like rules that are known to be robustly represented by the activity of PFC neurons in nonhuman primates (Ott, Jacob, & Nieder, 2014; Eiselt & Nieder, 2013; Stokes et al., 2013; Vallentin, Bongard, & Nieder, 2012; Sigala et al., 2008; Muhammad, Wallis, & Miller, 2006; Wallis et al., 2001).

Decoding accuracies are themselves not standardized measures of effect size (Hebart & Baker, 2017). However, consistently low decoding accuracies across studies hint at a low base rate for decoding information from PFC BOLD patterns. The base rate is the decoding accuracy one may expect to obtain (or the probability of success) when decoding specific information hypothesized to be encoded in the activity of neurons in a given region using methods typically employed in the literature. A low base rate in PFC may result, in part, from methodological choices, and in that case, it would be useful to know what these choices are. Alternatively, a low base rate would raise the possibility that PFC BOLD signal itself does not adequately capture the information encoded in the spiking activity of prefrontal neurons. Indeed, the base rate for a brain region likely depends on interactions between the underlying microanatomy, neurovascular coupling and the signal-to-noise ratio (SNR). The finding of a low base rate would raise interesting questions about why and how PFC coding differs in its type and organization from other parts of the brain with higher base rates.

A low base rate would also have implications for experimental design and inference. Note that low decoding accuracies can nevertheless be reliably different from chance (even reflecting a large effect), and therefore be meaningfully interpreted. However, detecting low decoding accuracies that are higher than chance levels would require that prefrontal MVPA studies collect sufficient data. Moreover, a systematically lower base rate in PFC would complicate the interpretation of comparisons with other brain regions or analyses using roving, whole-brain “searchlights” to discover local regions coding information in their activity patterns.

In this article, we carry out a systematic meta-analysis of published fMRI studies of PFC that employed MVPA. From this analysis, we estimate the base rate of decoding information from PFC BOLD patterns and compare it to base rates obtained from visual cortex and midtemporal regions. We also determine the distribution of classification accuracies obtained for “significant” and “null” effects in PFC and ask to what extent they overlap. Based on estimates of typical classification accuracies from these distributions, we also consider whether published studies typically collect sufficient data to detect small differences in decoding accuracy. Finally, we identify studies that have achieved better-than-average decoding accuracies and ask whether they are associated with particular subregions of PFC, task features, or analysis methods.

Collectively, our results show that the base rate of decoding information from PFC is just above chance levels, is systematically lower than other regions, and appears to be largely consistent across various methodological approaches. We conclude by considering the potential reasons for this low base rate of PFC classification.

METHODS

Literature Search and Study Inclusion

We conducted a comprehensive search of the literature to identify all published studies between the years of 2001 and 2016 that employed multivariate methods to decode information from fMRI BOLD patterns in PFC. In summary, we queried the PubMed database for articles whose abstracts contained at least one term related to (1) functional imaging, (2) multivoxel pattern analysis, and (3) frontal cortex. In addition, we explicitly excluded articles whose abstracts contained terms related to patient samples and nonhuman primates. A full list of terms employed for the search is shown in Figure 1.

Figure 1. 

Search terms employed for literature search. The final literature search was conducted on September 3, 2016. The search string was entered into Pubmed's advanced search (https://www.ncbi.nlm.nih.gov/pubmed/advanced), additionally restricting the year of publication to be 2001 through 2016.

Figure 1. 

Search terms employed for literature search. The final literature search was conducted on September 3, 2016. The search string was entered into Pubmed's advanced search (https://www.ncbi.nlm.nih.gov/pubmed/advanced), additionally restricting the year of publication to be 2001 through 2016.

This search resulted in a set of 462 studies that employed multivariate fMRI analysis, including classification analysis and representational similarity analysis. Across approaches, there was further variability in the metrics used to report the strength of decoding, including significance statistics, correlation coefficients, single-subject mean classification accuracies, group-level mean classification accuracies, etc. To allow for comparison and aggregation across studies, we focused on the largest subset of studies, those that employed a cross-validated classification approach for decoding and reported group-level summary classification accuracies. We define the cross-validated classification approach as one in which unseen and unlabeled BOLD patterns are assigned labels by a “classifier” trained on independent data, and the success of this classification is reported in terms of classification accuracies. We further restricted our data set to the studies that reported decoding analyses with two classes (i.e., those that had 50% as chance level). This left us with 76 studies, which are listed in Table 1.

Table 1. 

List of Studies Included in the Meta-analysis

Study IDa(76 Total)ReferenceNo. of ParticipantsNo. of AnalysesDecoded RuleAverage Decoding Accuracyb
Woolgar, Thompson, et al., 2011  17 12 Yes 0.548 
Hou & Liu, 2012  Yes 0.640 
Nelissen et al., 2013  10 Yes 0.525 
Bode & Haynes, 2009  14 Yes 0.588 
Cole et al., 2011  14 42 Yes 0.565 
Riggall & Postle, 2012  Yes 0.565 
Haynes et al., 2007  12 Yes 0.668 
10 Wang, Baucom, & Shinkareva, 2013  13 24 No 0.608 
11 Brodersen et al., 2012  16 24 No 0.565 
12 Dux et al., 2009  Yes 0.587 
13 Gallivan, McLean, Flanagan, & Culham, 2013  11 96 No 0.562 
16 Kuhl, Rissman, & Wagner, 2012  18 15 No 0.611 
18 Li, Ostwald, Giese, & Kourtzi, 2007  24 Yes 0.632 
20 Reverberi, Görgen, & Haynes, 2012b  14 Yes 0.535 
21 Reverberi et al., 2012a  13 Yes 0.560 
22 Schlegel et al., 2013  15 10 Yes 0.575 
23 Shinkareva, Malave, Just, & Mitchell, 2012  12 18 No 0.582 
24 Soon, Brass, Heinze, & Haynes, 2008  12 Yes 0.545 
25 Tamber-Rosenau, Esterman, Chiu, & Yantis, 2011  Yes 0.510 
26 Bode et al., 2011  11 Yes 0.520 
27 Momennejad & Haynes, 2012  11 Yes 0.600 
28 Woolgar, Hampshire, et al., 2011  12 18 Yes 0.586 
31 Yang et al., 2014  12 Yes 0.700 
32 Axelrod, Bar, Rees, & Yovel, 2015  15 No 0.547 
33 Said, Moore, Engell, Todorov, & Haxby, 2010  15 No 0.539 
37 Vickery, Chun, & Lee, 2011  22 31 No 0.587 
39 Tusche, Bode, & Haynes, 2010  16 10 No 0.757 
41 Tamber-Rosenau, Dux, Tombu, Asplund, & Marois, 2013  26 Yes 0.661 
42 Momennejad & Haynes, 2013  23 Yes 0.564 
43 Bulthé, De Smedt, & de Beeck, 2014  16 No 0.604 
46 Soto, Waldschmidt, Helie, & Ashby, 2013  24 42 Yes 0.604 
47 Gallivan, McLean, Valyear, & Culham, 2013  13 Yes 0.548 
48 Gallivan, McLean, Smith, & Culham, 2011  18 96 No 0.681 
49 Gallivan, McLean, Valyear, Pettypiece, & Culham, 2011  24 No 0.557 
50 Abrams et al., 2013  20 No 0.753 
52 Abrams et al., 2011  20 No 0.789 
53 Kaul, Rees, & Ishai, 2011  40 No 0.549 
54 Filimon, Rieth, Sereno, & Cottrell, 2015  16 Yes 0.757 
55 Behroozi & Daliri, 2015  No 0.620 
56 Gilbert, Swencionis, & Amodio, 2012  20 No 0.535 
57 Kuhl, Johnson, & Chun, 2013  26 11 Yes 0.563 
59 Lee, Janata, Frost, Hanke, & Granger, 2011  12 No 0.525 
60 Hampton & O'Doherty, 2007  18 Yes 0.603 
61 Rolls, Grabenhorst, & Franco, 2009  18 No 0.710 
62 Van der Laan, De Ridder, Viergever, & Smeets, 2012  20 No 0.600 
63 Ackerman & Courtney, 2012  26 Yes 0.567 
64 Clithero, Smith, Carter, & Huettel, 2011  20 No 0.616 
65 Liu, Hospadaruk, Zhu, & Gardner, 2011  Yes 0.586 
66 Ritter, Hebart, Wolbers, & Bingel, 2014  15 No 0.822 
67 Soon, He, Bode, & Haynes, 2013  34 Yes 0.550 
68 Sobhani, Fox, Kaplan, & Aziz-Zadeh, 2012  19 No 0.585 
69 Mahon & Caramazza, 2010  15 No 0.734 
70 Crittenden, Mitchell, & Duncan, 2016  18 20 Yes NR 
71 Gonzalez, Billington, & Burke, 2016  13 No 0.785 
72 Baggio et al., 2016  35 Yes 0.560 
73 Bursley, Nestor, Tarr, & Creswell, 2016  41 No 0.520 
74 Wisniewski, Goschke, & Haynes, 2016  35 Yes 0.560 
75 Kumar et al., 2016  17 No 0.540 
76 Muhle-Karbe, Duncan, De Baene, Mitchell, & Brass, 2017  27 Yes 0.572 
77 Liu, 2016  13 No 0.560 
78 Di Bono, Begliomini, Castiello, & Zorzi, 2015  19 12 No 0.646 
79 Shikauchi & Ishii, 2014  22 Yes 0.540 
80 Woolgar, Williams, & Rich, 2015  38 12 No 0.553 
81 Morawetz, Bode, Baudewig, Jacobs, & Heekeren, 2016  66 15 No 0.583 
82 Chan, Kucyi, & DeSouza, 2015  No 0.545 
83 Etzel, Cole, Zacks, Kay, & Braver, 2016  24 10 Yes 0.602 
84 Woolgar, Afshar, Williams, & Rich, 2015  22 Yes 0.600 
85 Kahnt, Weber, Haker, Robbins, & Tobler, 2015  53 No 0.587 
86 Cole, Ito, & Braver, 2016  21 16 No 0.599 
87 McNamee, Liljeholm, Zika, & O'Doherty, 2015  19 No 0.517 
88 Erez & Duncan, 2015  19 12 No 0.530 
89 Majerus et al., 2016  21 No 0.532 
90 Wisniewski, Reverberi, Tusche, & Haynes, 2014  19 No 0.624 
91 Krasovsky, Gilron, Yeshurun, & Mukamel, 2014  10 No 0.622 
92 Tusche, Smallwood, Bernhardt, & Singer, 2014  30 No 0.611 
93 Skerry & Saxe, 2014  21 20 No 0.534 
Study IDa(76 Total)ReferenceNo. of ParticipantsNo. of AnalysesDecoded RuleAverage Decoding Accuracyb
Woolgar, Thompson, et al., 2011  17 12 Yes 0.548 
Hou & Liu, 2012  Yes 0.640 
Nelissen et al., 2013  10 Yes 0.525 
Bode & Haynes, 2009  14 Yes 0.588 
Cole et al., 2011  14 42 Yes 0.565 
Riggall & Postle, 2012  Yes 0.565 
Haynes et al., 2007  12 Yes 0.668 
10 Wang, Baucom, & Shinkareva, 2013  13 24 No 0.608 
11 Brodersen et al., 2012  16 24 No 0.565 
12 Dux et al., 2009  Yes 0.587 
13 Gallivan, McLean, Flanagan, & Culham, 2013  11 96 No 0.562 
16 Kuhl, Rissman, & Wagner, 2012  18 15 No 0.611 
18 Li, Ostwald, Giese, & Kourtzi, 2007  24 Yes 0.632 
20 Reverberi, Görgen, & Haynes, 2012b  14 Yes 0.535 
21 Reverberi et al., 2012a  13 Yes 0.560 
22 Schlegel et al., 2013  15 10 Yes 0.575 
23 Shinkareva, Malave, Just, & Mitchell, 2012  12 18 No 0.582 
24 Soon, Brass, Heinze, & Haynes, 2008  12 Yes 0.545 
25 Tamber-Rosenau, Esterman, Chiu, & Yantis, 2011  Yes 0.510 
26 Bode et al., 2011  11 Yes 0.520 
27 Momennejad & Haynes, 2012  11 Yes 0.600 
28 Woolgar, Hampshire, et al., 2011  12 18 Yes 0.586 
31 Yang et al., 2014  12 Yes 0.700 
32 Axelrod, Bar, Rees, & Yovel, 2015  15 No 0.547 
33 Said, Moore, Engell, Todorov, & Haxby, 2010  15 No 0.539 
37 Vickery, Chun, & Lee, 2011  22 31 No 0.587 
39 Tusche, Bode, & Haynes, 2010  16 10 No 0.757 
41 Tamber-Rosenau, Dux, Tombu, Asplund, & Marois, 2013  26 Yes 0.661 
42 Momennejad & Haynes, 2013  23 Yes 0.564 
43 Bulthé, De Smedt, & de Beeck, 2014  16 No 0.604 
46 Soto, Waldschmidt, Helie, & Ashby, 2013  24 42 Yes 0.604 
47 Gallivan, McLean, Valyear, & Culham, 2013  13 Yes 0.548 
48 Gallivan, McLean, Smith, & Culham, 2011  18 96 No 0.681 
49 Gallivan, McLean, Valyear, Pettypiece, & Culham, 2011  24 No 0.557 
50 Abrams et al., 2013  20 No 0.753 
52 Abrams et al., 2011  20 No 0.789 
53 Kaul, Rees, & Ishai, 2011  40 No 0.549 
54 Filimon, Rieth, Sereno, & Cottrell, 2015  16 Yes 0.757 
55 Behroozi & Daliri, 2015  No 0.620 
56 Gilbert, Swencionis, & Amodio, 2012  20 No 0.535 
57 Kuhl, Johnson, & Chun, 2013  26 11 Yes 0.563 
59 Lee, Janata, Frost, Hanke, & Granger, 2011  12 No 0.525 
60 Hampton & O'Doherty, 2007  18 Yes 0.603 
61 Rolls, Grabenhorst, & Franco, 2009  18 No 0.710 
62 Van der Laan, De Ridder, Viergever, & Smeets, 2012  20 No 0.600 
63 Ackerman & Courtney, 2012  26 Yes 0.567 
64 Clithero, Smith, Carter, & Huettel, 2011  20 No 0.616 
65 Liu, Hospadaruk, Zhu, & Gardner, 2011  Yes 0.586 
66 Ritter, Hebart, Wolbers, & Bingel, 2014  15 No 0.822 
67 Soon, He, Bode, & Haynes, 2013  34 Yes 0.550 
68 Sobhani, Fox, Kaplan, & Aziz-Zadeh, 2012  19 No 0.585 
69 Mahon & Caramazza, 2010  15 No 0.734 
70 Crittenden, Mitchell, & Duncan, 2016  18 20 Yes NR 
71 Gonzalez, Billington, & Burke, 2016  13 No 0.785 
72 Baggio et al., 2016  35 Yes 0.560 
73 Bursley, Nestor, Tarr, & Creswell, 2016  41 No 0.520 
74 Wisniewski, Goschke, & Haynes, 2016  35 Yes 0.560 
75 Kumar et al., 2016  17 No 0.540 
76 Muhle-Karbe, Duncan, De Baene, Mitchell, & Brass, 2017  27 Yes 0.572 
77 Liu, 2016  13 No 0.560 
78 Di Bono, Begliomini, Castiello, & Zorzi, 2015  19 12 No 0.646 
79 Shikauchi & Ishii, 2014  22 Yes 0.540 
80 Woolgar, Williams, & Rich, 2015  38 12 No 0.553 
81 Morawetz, Bode, Baudewig, Jacobs, & Heekeren, 2016  66 15 No 0.583 
82 Chan, Kucyi, & DeSouza, 2015  No 0.545 
83 Etzel, Cole, Zacks, Kay, & Braver, 2016  24 10 Yes 0.602 
84 Woolgar, Afshar, Williams, & Rich, 2015  22 Yes 0.600 
85 Kahnt, Weber, Haker, Robbins, & Tobler, 2015  53 No 0.587 
86 Cole, Ito, & Braver, 2016  21 16 No 0.599 
87 McNamee, Liljeholm, Zika, & O'Doherty, 2015  19 No 0.517 
88 Erez & Duncan, 2015  19 12 No 0.530 
89 Majerus et al., 2016  21 No 0.532 
90 Wisniewski, Reverberi, Tusche, & Haynes, 2014  19 No 0.624 
91 Krasovsky, Gilron, Yeshurun, & Mukamel, 2014  10 No 0.622 
92 Tusche, Smallwood, Bernhardt, & Singer, 2014  30 No 0.611 
93 Skerry & Saxe, 2014  21 20 No 0.534 
a

Article ID (index no. assigned before exclusion) are used throughout the article and in our publically available database.

b

Mean decoding accuracy based on analyses reported as significant (NR = statistical significance of decoding accuracy was not clearly reported).

Within Study Extraction

Studies reported a variable number of decoding analyses, ranging from 1 to 96 per study. Some studies decoded the same information from different PFC regions, whereas other studies decoded different types of information from the same region. A few studies also applied the same analysis to data from different time points within a single trial. As a rule, we separately recorded all reported group-level summary classification accuracies. However, there were some exceptional cases in which it was either infeasible or undesirable to record all the reported classification accuracies. For example, analyses that attempt to classify stimulus information at each repetition time (TR) over a window of time would be likely to yield highly correlated classification accuracies due to the autocorrelation in fMRI BOLD signal. Therefore, in such cases, we only recorded the median decoding accuracy from the window, excluding baseline periods during which no decoding was expected, such as before stimulus onset. Another case concerns analyses conducted in both a single region and its constituent subregions, such as right, left, and bilateral dorsolateral PFC. We recorded only the subregions to reduce redundancy in our data set. Finally, in cases where the goal of an analysis was to test whether the number of included voxels influenced the result, we again only recorded the median accuracy achieved. Thus, in general, we sought to include independent classification attempts in PFC and, where classifications were nonindependent, to take the median. A large set of the studies, 27 of the 76, used a roving searchlight method to produce whole-brain decoding accuracy maps. All but four of these studies only reported the peak classification accuracy for different regions of the brain. These values may upwardly bias our base rate estimation but cannot be excluded because they form a significant chunk of reported accuracies given that searchlights are widely used. Importantly, this conservatively biases us against confirming our hypothesis that it is difficult to decode information from PFC BOLD patterns.

Another concern regarding the independence of observations relates to the intrinsic spatial smoothness of fMRI data sets. If decoding accuracies are obtained from two regions that are close enough to each other to show spatial correlation, the observations would not be independent. Given that articles do not report intrinsic spatial smoothness, we employed a threshold of 10 mm as the minimum separation required for decoding accuracies to be considered separate. We found no cases of two analyses from the same study, decoding the same information, focused on regions that were less that 10 mm apart. In addition, we conducted an analysis where we averaged all accuracies from a study if they were within the same AAL region. This did not affect our results.

To ensure that classification accuracy values were reliably recorded from each article, we conducted a validation procedure in which an independent investigator (blinded to the initially coded value and without authorship incentive) recoded the accuracy values from each article. In each case where the two values were different, the values were rechecked and corrected.

Estimating Distributions

To compare decoding accuracy across regions (frontal vs. occipital or midtemporal) and between significant and nonsignificant data, we estimated both distribution and density functions and measures of central tendency for the group mean data. Distribution plots were created by pooling accuracies across studies and applying kernel density estimation (using Scott's rule for bandwidth). To obtain 95% confidence intervals for distribution functions, density functions, and summary statistics (mean, median, etc.), we applied hierarchical bootstrapping, which accounts for the dependence among analyses from the same study. Analyses from the same study share features that may influence classification accuracy such as sample size, data quality, preprocessing methods, and so forth. Studies were first randomly sampled with replacement, and then group-level analyses were randomly sampled with replacement from these selected studies. Similar credible intervals were obtained by fitting Bayesian hierarchical Gaussian models to the data, though these models had to additionally assume a parametric family for the data. These confidence intervals capture error in our estimates due to sampling variability; however, they cannot account for a number of biases in the way decoding accuracies are obtained and reported. Null effects are often not reported (the so-called file drawer effect), the significant effects that are reported are often from the strong variants of a particular analysis (“researcher degrees of freedom” or, sometimes, “p-hacking”), thresholds used for determining significance in group classification are sometimes based on inappropriate assumptions of parametric distribution of accuracies, and searchlight analyses often report peak accuracy, which also has an inherent selection bias. Unfortunately, these biases are unavoidable in the current study. Therefore, we caution against overinterpreting these confidence intervals and provide them for descriptive rather than inferential purposes as they may not have the properties that one expects of true confidence intervals.

We excluded data from Study 70 for the estimation for the significant and nonsignificant distributions as the mean decoding accuracies were reported in a bar graph without a clear indication of which of these were significantly different from chance. Study 31 used 99.99% confidence intervals, with two accuracies of 63% and 64% within this interval. To be conservative, we excluded these accuracies in the estimation of the nonsignificant distribution.

Regression Analysis

A regression analysis was employed to examine how decoding accuracy across the studies in our database depended on brain region within frontal cortex, the type of information decoded, and the analysis methods used. The coding of these factors for the regression is described below.

Region

We examined classification performance as a function of brain region. Individual analyses reported location using a number of different atlases. Therefore, to compare accuracy in a single space, we mapped all reported locations to the AAL atlas. Analyses that were reported with centroid coordinates, from either an ROI or a roving searchlight, were assigned to AAL regions by coordinate-lookup in SPM12's AAL template image. Analyses that did not report coordinates employed ROIs coming from one of several common brain atlases including Brodmann (Eickhoff et al., 2005), Destrieux (Fischl et al., 2004), Desikan-Kellaney (Desikan et al., 2006), Oxford-Harvard (FSL). These analyses were assigned within AAL by a region-to-region correspondence table constructed by visually comparing the non-AAL atlases to the AAL atlas in MRICRON (Table 2).

Table 2. 

Original ROI to AAL ROI Correspondence Table

Original ROIaCorresponding AAL Region Assigned
Brodmann 
BA 8 left/right superior frontal gyrus, middle frontal gyrus, supplementary motor area, medial frontal gyrus 
BA 9 left/right middle frontal gyrus, superior frontal gyrus, medial frontal gyrus 
BA 10 left/right medial frontal gyrus, superior frontal gyrus 
BA 11 left/right middle frontal gyrus orbital part, superior frontal gyrus orbital part 
BA 12 left/right middle frontal gyrus orbital part, superior frontal gyrus orbital part 
BA 13 left/right middle frontal gyrus orbital part, superior frontal gyrus orbital part 
BA 14 left/right middle frontal gyrus orbital part, superior frontal gyrus orbital part 
BA 47 left/right inferior frontal gyrus pars orbitalis 
BA 45 left/right inferior frontal gyrus pars triangularis 
BA 44 left/right inferior frontal gyrus pars opercularis 
BA 46 left/right inferior frontal gyrus pars triangularis, middle frontal gyrus 
BA 24 left/right anterior cingulate gyrus, midcingulate area 
BA 32 left/right anterior cingulate gyrus, midcingulate area 
  
Oxford/Harvard 
DLPFC left/right middle frontal gyrus 
Dorsal premotor left/right precentral gyrus 
Ventral premotor left/right precentral gyrus 
SMA left/right supplementary motor area 
preSMA left/right supplementary motor area 
Ventrolateral PFC left/right inferior frontal gyrus pars triangularis, inferior frontal gyrus pars opercularis, inferior frontal gyrus pars orbitalis 
  
Desikan-Kellaney 
LPFC L left middle frontal gyrus, inferior frontal gyrus pars triangularis, inferior frontal gyrus pars opercularis 
LPFC R right middle frontal gyrus, inferior frontal gyrus pars triangularis, inferior frontal gyrus pars opercularis 
Bilateral LPFC left/right middle frontal gyrus, inferior frontal gyrus pars triangularis, inferior frontal gyrus pars opercularis 
Caudal anterior cingulate left/right midcingulate area 
Rostral anterior cingulate left/right anterior cingulate gyrus 
Pars opercularis left/right inferior frontal gyrus pars opercularis 
Pars triangularis left/right inferior frontal gyrus pars triangularis 
Pars orbitalis left/right inferior frontal gyrus pars orbitalis 
Lateral orbitofrontal left/right middle frontal gyrus orbital part, inferior frontal gyrus pars orbitalis 
Superior frontal left/right superior frontal gyrus 
Caudal middle frontal left/right middle frontal gyrus 
Rostral middle frontal left/right middle frontal gyrus 
Frontal pole left/right medial frontal gyrus, superior frontal gyrus 
Insula left/right insula 
  
Destrieux 
Premotor left/right precentral gyrus 
  
Unspecified 
SMA left/right supplementary motor area 
L Oper, R Oper left/right inferior frontal gyrus pars opercularis 
L Tria, R Tria left/right inferior frontal gyrus pars triangularis 
FO left/right inferior frontal gyrus pars opercularis 
MFC left/right midcingulate area, anterior cingulate gyrus 
SEF left/right supplementary motor area 
mPFC left/right medial frontal gyrus 
Insula left/right insula 
mSFG left/right medial frontal gyrus 
MFG left/right middle frontal gyrus 
lPFC left/right middle frontal gyrus 
Superior frontal sulcus left/right superior frontal gyrus 
FEF left/right precentral gyrus 
Cingulate left/right anterior cingulate gyrus, midcingulate area 
rACC left/right anterior cingulate gyrus 
ACC left/right anterior cingulate gyrus 
Medial prefrontal left/right medial frontal gyrus 
Anterior insula left/right insula 
Inferior frontal gyrus, IFG left/right inferior frontal gyrus pars triangularis 
DLPFC, dorsolateral PFC left/right middle frontal gyrus 
OFC left/right inferior frontal gyrus pars orbitalis, middle frontal gyrus orbital part, superior frontal gyrus orbital part 
mOFC left/right middle frontal gyrus orbital part 
lOFC left/right inferior frontal gyrus pars orbitalis 
PMC left/right precentral gyrus 
Medial frontopolar left/right medial frontal gyrus 
Original ROIaCorresponding AAL Region Assigned
Brodmann 
BA 8 left/right superior frontal gyrus, middle frontal gyrus, supplementary motor area, medial frontal gyrus 
BA 9 left/right middle frontal gyrus, superior frontal gyrus, medial frontal gyrus 
BA 10 left/right medial frontal gyrus, superior frontal gyrus 
BA 11 left/right middle frontal gyrus orbital part, superior frontal gyrus orbital part 
BA 12 left/right middle frontal gyrus orbital part, superior frontal gyrus orbital part 
BA 13 left/right middle frontal gyrus orbital part, superior frontal gyrus orbital part 
BA 14 left/right middle frontal gyrus orbital part, superior frontal gyrus orbital part 
BA 47 left/right inferior frontal gyrus pars orbitalis 
BA 45 left/right inferior frontal gyrus pars triangularis 
BA 44 left/right inferior frontal gyrus pars opercularis 
BA 46 left/right inferior frontal gyrus pars triangularis, middle frontal gyrus 
BA 24 left/right anterior cingulate gyrus, midcingulate area 
BA 32 left/right anterior cingulate gyrus, midcingulate area 
  
Oxford/Harvard 
DLPFC left/right middle frontal gyrus 
Dorsal premotor left/right precentral gyrus 
Ventral premotor left/right precentral gyrus 
SMA left/right supplementary motor area 
preSMA left/right supplementary motor area 
Ventrolateral PFC left/right inferior frontal gyrus pars triangularis, inferior frontal gyrus pars opercularis, inferior frontal gyrus pars orbitalis 
  
Desikan-Kellaney 
LPFC L left middle frontal gyrus, inferior frontal gyrus pars triangularis, inferior frontal gyrus pars opercularis 
LPFC R right middle frontal gyrus, inferior frontal gyrus pars triangularis, inferior frontal gyrus pars opercularis 
Bilateral LPFC left/right middle frontal gyrus, inferior frontal gyrus pars triangularis, inferior frontal gyrus pars opercularis 
Caudal anterior cingulate left/right midcingulate area 
Rostral anterior cingulate left/right anterior cingulate gyrus 
Pars opercularis left/right inferior frontal gyrus pars opercularis 
Pars triangularis left/right inferior frontal gyrus pars triangularis 
Pars orbitalis left/right inferior frontal gyrus pars orbitalis 
Lateral orbitofrontal left/right middle frontal gyrus orbital part, inferior frontal gyrus pars orbitalis 
Superior frontal left/right superior frontal gyrus 
Caudal middle frontal left/right middle frontal gyrus 
Rostral middle frontal left/right middle frontal gyrus 
Frontal pole left/right medial frontal gyrus, superior frontal gyrus 
Insula left/right insula 
  
Destrieux 
Premotor left/right precentral gyrus 
  
Unspecified 
SMA left/right supplementary motor area 
L Oper, R Oper left/right inferior frontal gyrus pars opercularis 
L Tria, R Tria left/right inferior frontal gyrus pars triangularis 
FO left/right inferior frontal gyrus pars opercularis 
MFC left/right midcingulate area, anterior cingulate gyrus 
SEF left/right supplementary motor area 
mPFC left/right medial frontal gyrus 
Insula left/right insula 
mSFG left/right medial frontal gyrus 
MFG left/right middle frontal gyrus 
lPFC left/right middle frontal gyrus 
Superior frontal sulcus left/right superior frontal gyrus 
FEF left/right precentral gyrus 
Cingulate left/right anterior cingulate gyrus, midcingulate area 
rACC left/right anterior cingulate gyrus 
ACC left/right anterior cingulate gyrus 
Medial prefrontal left/right medial frontal gyrus 
Anterior insula left/right insula 
Inferior frontal gyrus, IFG left/right inferior frontal gyrus pars triangularis 
DLPFC, dorsolateral PFC left/right middle frontal gyrus 
OFC left/right inferior frontal gyrus pars orbitalis, middle frontal gyrus orbital part, superior frontal gyrus orbital part 
mOFC left/right middle frontal gyrus orbital part 
lOFC left/right inferior frontal gyrus pars orbitalis 
PMC left/right precentral gyrus 
Medial frontopolar left/right medial frontal gyrus 
a

Original ROIs came from the Brodmann, Oxford/Harvard, Desikan-Kellaney, and Destrieux atlases or were unspecified. Unspecified ROIs were only reported by name in the article with no coordinate or reference atlas. These ROIs were assigned to AAL regions based on their appearance figures or their name's similarity to AAL region.

Within this region coding scheme, analyses with small ROIs or those that reported peak coordinates were each assigned to one AAL region, whereas analyses with larger ROIs were assigned to two or more AAL regions. Of all the analyses, 56%, 29%, and 15% were assigned to one, two, and three or more regions, respectively. In most cases where accuracies were assigned to two AAL regions, these were the left and right hemisphere counterparts of the same AAL region. Therefore, for the main regression, analyses that had been assigned to two AAL regions were assigned to a bilateral region regressor. The accuracies not assigned to a bilateral ROI or assigned to more than two regions were omitted from the main analysis to maintain mutual exclusivity, leaving 85% of the original data. These were included in further analyses.

Information Type

The type of information decoded in each analysis can be broadly categorized as either perceptual, response, rule, or value. We categorized an analysis as “perceptual” if trials were separated into classes so that they shared either a low-level perceptual feature such as color or a high-level feature such as object category. Importantly, trials or patterns from the same class would be associated with different actions. In contrast, we categorized an analysis as “response” if trials from the same class contained the same action but different perceptual features. We categorized an analysis as “rule” if trials from the same class shared the same abstract goal, task, or set of stimulus–response mappings. For example, one class of trials might require objects to be judged on their size, whereas the other class of trials might require judgments of shape. We categorized an analysis as “value” if different classes of trials were associated with different levels of subjective value. For example, classes of trials might be distinguished based on a participant's desire to purchase an object or whether they experienced a win or loss outcome.

Analysis Procedure

MVPAs varied along several dimensions at each step in the analysis pipeline from data collection and preprocessing to classification that could ultimately affect outcome. We recorded the following for each analysis at each step of the procedure: scanner strength, voxel size, ROI versus searchlight, number of participants, coregistration, smoothing, temporal averaging, response normalization, number of voxels, number of training patterns, and classifier used. Specific codes used and their definitions are elaborated below.

Coregistration/normalization: Coded as 0–1 and refers to whether the decoding analysis was conducted in native subject space or a standard space such as Montreal Neurological Institute. Studies that conducted decoding analyses in native space either reverse normalized atlas ROIs (e.g., AAL) to mask voxels or normalized the single-subject classification accuracy maps to a standard space to aggregate classification accuracy across participants. We labeled both cases as “native space” analyses because the classification was done before the smoothing induced by the normalization process.

Smoothing: Coded as 0–1 and refers to whether or not any smoothing kernel was applied to the fMRI data before the decoding analysis.

Temporal averaging: Coded as one of four types, referring to how multiple fMRI images are combined into a single pattern corresponding to an experimental event. Temporal averaging may improve SNRs but reduces the number of available training patterns.

  • 1. 

    No temporal averaging: Use every TR on every trial as a pattern.

  • 2. 

    Averaging across trials: Average across trials, but use separate pattern for each TR.

  • 3. 

    Averaging across TRs: Average across TRs, but use separate pattern for trial (or event).

  • 4. 

    Averaging across TRs and trials: Average data across both trials and TRs. This last category has the highest temporal compression, often yielding only a few training examples per class.

Response normalization: Coded into three levels: no normalization, temporal normalization, and spatial normalization. Temporal normalization de-means each voxel across time and divides by the standard deviation either within class or across all classes. Examples using this method are Studies 36, 25, and 4. Spatial normalization de-means each voxel using the average response of the surrounding voxels. An example using this method is Study 3.

Voxel size: The voxel dimensions were recorded for each study, and the volume was used in the regression analyses.

Voxel number: The number of voxels comprising each ROI or the roving searchlight was recorded. This number determines the dimensionality of the input to the classifier. We could not determine the number of voxels for the ROIs in 11 studies; most of these studies defined ROIs using univariate contrasts without reporting the voxel numbers either for each subject or at a group level.

Training set size: The number of patterns used to train the classifier was recorded, excluding the number held out as a test set during cross-validation. We could not determine the number of training patterns for two studies.

Classifiers: Coded as one of six types: Gaussian naive Bayes (gnb), logistic regression (logreg), linear discriminant analysis (lda), linear support vector machines (svm-lin), nonlinear support vector machines (svm-nonlin), and correlation-based (correlation).

Macaque Electrophysiology Studies

To complement our meta-analysis of fMRI decoding studies of PFC, we additionally obtained a small sample of decoding accuracies reported in electrophysiology studies of macaque PFC where ensemble decoding was carried out. To minimize bias, we restricted our search to studies of PFC cited in a recent review of macaque decoding studies. The decoding accuracies from this sample are listed in Table 6.

In-house fMRI Data Set

To complement our meta-analysis, we analyzed previously collected fMRI data from our laboratory on a cognitive control task requiring coding of rule and visual stimulus information. Rule information was indicated by a visual feature, so both types of information could be decoded from the same set of trials. This enabled comparison of decoding accuracies across frontal and visual cortex while controlling for differences in methods. This data set was also employed to estimate the BOLD SNRs and pattern reliabilities in frontal and visual cortex.

Participants

Twenty-one right-handed adults participated in the fMRI study. All had normal or corrected-to-normal vision and were screened for the presence of psychiatric or neurological conditions, the use of CNS-affecting drugs, and contraindications for MRI. All participants gave informed, written consent as approved by the Human Research Protections Office of Brown University, and they were compensated for their participation.

fMRI and Task Procedure

A Siemens 3T Trio Tim MRI system with a 32-channel head coil was used for whole-brain imaging. A T1-weighted multiecho MPRAGE anatomical image (TR = 2200 msec, echo time = 1.54, 3.36, 5.18, and 7.01 msec, flip angle = 7°, 144 sagittal slices, 1.2 × 1.2 × 1.2 mm) for visualization. Functional images were acquired, as participants carried out a cognitive control task (Figure 2) using a fat-saturated gradient-echo echo-planar sequence (TR = 2 sec, echo time = 28 msec, flip angle = 90°, 38 interleaved axial slices, 3 × 3 × 3 mm). Visual stimuli were projected onto a screen and viewed through a mirror attached to the head coil.

Figure 2. 

(A) Trial sequence: On each trial, a stimulus of particular color, shape, and pattern was displayed. The stimulus was displayed for 0.5 sec, followed by a 1.5-sec response window and a 16-sec intertrial interval. (B) Instructions: Before scanning, participants learned that a single stimulus feature (e.g., color) signified the “rule,” determining which of the other two stimulus features (e.g., shape or pattern) should guide the response. The “rule” feature had two levels (e.g., blue/red), whereas other two features had three levels. The feature signifying rule was counterbalanced across participants. Participants performed a total of 144–216 trials across 12–18 runs.

Figure 2. 

(A) Trial sequence: On each trial, a stimulus of particular color, shape, and pattern was displayed. The stimulus was displayed for 0.5 sec, followed by a 1.5-sec response window and a 16-sec intertrial interval. (B) Instructions: Before scanning, participants learned that a single stimulus feature (e.g., color) signified the “rule,” determining which of the other two stimulus features (e.g., shape or pattern) should guide the response. The “rule” feature had two levels (e.g., blue/red), whereas other two features had three levels. The feature signifying rule was counterbalanced across participants. Participants performed a total of 144–216 trials across 12–18 runs.

fMRI data were preprocessed in SPM8 (www.fil.ion.ucl.ac.uk/spm). Data were examined for artifacts, outliers, and excessive variance in the global signal (functions: tsdiffana, art_global, art_movie). All data were used for subsequent analysis. Functional images underwent slice timing correction, motion correction with rigid transformation, and normalization to the Montreal Neurological Institute stereotaxic space with default SPM8 parameters. Images were not smoothed before classification, SNR, or reliability analyses.

Multivariate Pattern Analyses

MVPAs were performed using PyMVPA (www.pymvpa.org/), using typical methodological choices. Voxels were selected from frontal and visual cortex using a univariate ANOVA with significance threshold of p = .05. Patterns were constructed by taking the voxel response 8 sec after the stimulus onset. A linear svm with a fixed penalty (C = 1) was used to classify patterns in a leave-one-run-out cross-validation scheme. We tested the significance of the classification using both a t test on the group level and permutation testing on individual participants. Variations on this typical MVPA were applied to explore whether decoding could be improved. We varied the preprocessing, feature selection, temporal averaging, and classifier. Although we do not detail the results here, we note that the group-level accuracy in both frontal and visual cortex were highly insensitive to these choices.

Signal-to-noise Ratio

We compared the raw and functional SNRs between frontal and visual cortex. For raw SNR, we used the mean signal in each voxel divided by the mean signal in a 5 × 5 × 5 mm box outside the brain. For functional SNR, we calculated a t statistic for each voxel; we subtracted the mean response during baseline from the mean response 6–8 sec after each stimulus presentation, and divided this difference by the pooled standard error. The SNR for each voxel was averaged within several regions from the frontal and visual cortex. For the frontal cortex, the frontal regions from the multiple-demand (MD) network were employed (imaging.mrc-cbu.cam.ac.uk/imaging/MDsystem): IFGop, opercular part of the inferior frontal gyrus; MFG, middle frontal gyrus; MFGorb, orbital part of the middle frontal gyrus; PrecG, precentral gyrus; ACC, anterior cingulate cortex. The MD regions were chosen as they reliably show univariate effects for various demand manipulations and have also been associated with rule coding. For visual cortex, the following AAL atlas regions were used: the cuneus, calcerine sulcus, inferior occipital cortex, middle occipital cortex, and superior occipital cortex.

Reliability

Reliabilities of multivoxel patterns in frontal and visual cortices were determined by computing the correlation between patterns estimated from separate halves of the data. One hundred random splits of the data were generated, and the correlation values from each split were averaged (after applying Fisher Z transformation).

RESULTS

Typical Decoding Performance in PFC Is Low

We leveraged our meta-analysis of published studies to approximately estimate the base rate of decoding information from PFC cortical BOLD patterns. To this end, we compiled all two-way, group-level mean classification accuracies reported across the 76 studies in our database. The resulting distribution is an estimate of the sampling distribution of group mean classification accuracies for decoding information from PFC BOLD patterns. The mean of this distribution was 57.4% (CI [56.0%, 59.0%]),1 though we observed a skew, so that more than 64.2% of the accuracies were below the mean. Therefore, we employed the median as a measure of the central tendency, arriving at a base rate of 55.4% (CI [54.0%, 57.0%]). For comparison, we also derived base rates for decoding visual information from occipital and temporal cortex BOLD patterns. These were computed from meta-analytic data previously compiled by Coutanche, Solomon, and Thompson-Schill (2016). Compared with PFC base rates, both the occipital and temporal cortex (median) base rates were markedly higher at 66.6% (CI [61.5%, 72%]) and 71.0% (CI [68.0%, 75.0%]), respectively (Figure 3).

Figure 3. 

Decoding accuracy distributions for frontal, occipital, and ventral temporal cortex. Cumulative distribution functions (A, C) and probability density functions (B, D) for visual decoding accuracies in occipital (red) and ventral temporal (orange) cortex compared with frontal decoding accuracies from all analyses (top, purple) and rule decoding analyses (bottom, aqua). Vertical lines indicate median values. Shaded areas reflect 95% confidence intervals obtained from a hierarchical bootstrapping procedure.

Figure 3. 

Decoding accuracy distributions for frontal, occipital, and ventral temporal cortex. Cumulative distribution functions (A, C) and probability density functions (B, D) for visual decoding accuracies in occipital (red) and ventral temporal (orange) cortex compared with frontal decoding accuracies from all analyses (top, purple) and rule decoding analyses (bottom, aqua). Vertical lines indicate median values. Shaded areas reflect 95% confidence intervals obtained from a hierarchical bootstrapping procedure.

MVPA studies of occipital and ventral temporal cortex focus exclusively on decoding information about visual stimulus attributes. This is because overwhelming evidence supports a strong prior for the hypothesis that the human occipital and ventral temporal cortices code for visual information. On the other hand, prefrontal MVPAs spanned attempts to decode a wide variety of information, reflecting a much less constrained hypothesis space for what information is represented in PFC. To control for this difference, we focused on a subset of 311 analyses in our database of prefrontal MVPA studies that attempted to decode “rule information.” Well-established deficits in rule-guided behavior have been linked to prefrontal dysfunction (Badre, Hoffman, Cooney, & D'Esposito, 2009; Petrides, 2005; Duncan, Emslie, Williams, Johnson, & Freer, 1996; Cohen & Servan-Schreiber, 1992; Milner, 1963) and have been attributed to a loss of the ability to represent rules in working memory (Miller & Cohen, 2001). Moreover, there is strong evidence from macaque electrophysiology that the prefrontal neurons code for task rules (Blackman et al., 2016; Ott et al., 2014; Eiselt & Nieder, 2013; Stokes et al., 2013; Vallentin et al., 2012; Sigala et al., 2008; Muhammad et al., 2006; Wallis et al., 2001). Therefore, it is reasonable to place a strong prior on the hypothesis that task rule information is coded in the activity of human prefrontal neurons. A base rate obtained from rule decoding studies should thus be more comparable to the studies in Coutanche et al.'s database. The median of the distribution of classification accuracies from rule decoding analyses was 57.1% (CI [56.0%, 60.0%]), again significantly lower than both the occipital and ventral temporal base rates.

These comparisons of base rates between visual and PFC were made across different studies, likely employing different scanning methods, analysis pipelines, sample sizes, and so forth, which may all affect decoding accuracies. To address this, we examined prefrontal and visual cortex decoding accuracies obtained in a single fMRI data set collected in our laboratory. fMRI data were collected while participants completed a cognitive control task that required encoding of both visual stimulus identity and visually cued rules. This enabled us to compare decoding accuracies across regions while controlling for all other variables. We obtained a decoding accuracy of 55.4% for a two-way classification of rule in frontal cortex, and 72.3% for a two-way classification of stimulus identity in visual cortex (Figure 4, Panel 4).

Figure 4. 

Comparing SNR, pattern reliability, decoding accuracy between frontal and visual cortex in our in-house fMRI data set. Raw SNR was estimated by computing a ratio of the activity measured in a brain ROI and the activity measured in a box outside the brain. Functional SNR was estimated as the mean t statistic for a stimulus versus baseline contrast. Pattern reliability was estimated as mean correlation between stimulus patterns from different halves of the data. Exact procedures for calculating each quantity can be found in the methods. Raw SNR was significantly higher in frontal cortex (t = 9.22, p < .001), whereas functional SNR and pattern reliability were significantly higher in visual cortex (t = 3.99, p < .001; t = 11.91, p < .001). Mean decoding accuracy was 55.4% for frontal cortex and 72.3% for visual cortex for two-way classification.

Figure 4. 

Comparing SNR, pattern reliability, decoding accuracy between frontal and visual cortex in our in-house fMRI data set. Raw SNR was estimated by computing a ratio of the activity measured in a brain ROI and the activity measured in a box outside the brain. Functional SNR was estimated as the mean t statistic for a stimulus versus baseline contrast. Pattern reliability was estimated as mean correlation between stimulus patterns from different halves of the data. Exact procedures for calculating each quantity can be found in the methods. Raw SNR was significantly higher in frontal cortex (t = 9.22, p < .001), whereas functional SNR and pattern reliability were significantly higher in visual cortex (t = 3.99, p < .001; t = 11.91, p < .001). Mean decoding accuracy was 55.4% for frontal cortex and 72.3% for visual cortex for two-way classification.

Finally, we leveraged our in-house data set to determine whether differences in SNR and pattern reliability mirrored differences in decoding accuracies. Although we found that raw SNR was actually higher in frontal cortex compared with visual cortex in our scanner (t = 9.22, p < .001), both functional SNR and pattern reliability were lower (t = 3.99, p < .001; t = 11.91, p < .001; Figure 4, Panels 1–3).

Collectively, these results demonstrate that the base rate for decoding information from human PFC BOLD patterns is low in comparison to two sensory regions of the brain, consistent with the impression that MVPA in human PFC is particularly difficult.

Overlaps between Decoding Accuracy Distributions for Null and Significant Effects

Our database of PFC decoding analyses included group mean classification accuracies of both significant (greater than chance) and null effects. This allowed us to separately compile literature-derived distributions of classification accuracies for (a) when information is successfully decoded from frontal BOLD activity patterns and (b) when no information is detected. These distributions should overlap minimally if the studies that produced the classification accuracies had high power and low false positive rates (Figure 5).

Figure 5. 

“Significant” versus “nonsignificant” decoding accuracy distributions. Cumulative distribution function (A) and probability density function (B) for frontal decoding accuracies reported as significant (blue) and nonsignificant (green). Dotted line in B reflects chance level (50%), and solid green line indicates 95th percentile of the (centered) nonsignificant distribution. 23.5% of decoding accuracies in the significant distribution fell below this “critical” value. Shaded areas reflect 95% confidence intervals obtained from a hierarchical bootstrapping procedure.

Figure 5. 

“Significant” versus “nonsignificant” decoding accuracy distributions. Cumulative distribution function (A) and probability density function (B) for frontal decoding accuracies reported as significant (blue) and nonsignificant (green). Dotted line in B reflects chance level (50%), and solid green line indicates 95th percentile of the (centered) nonsignificant distribution. 23.5% of decoding accuracies in the significant distribution fell below this “critical” value. Shaded areas reflect 95% confidence intervals obtained from a hierarchical bootstrapping procedure.

The median of the classification accuracy distribution of significant effects was 58.4% (CI [57.0%, 60.0%]). Note that the values in our “significant” distribution sample from an underlying “true” distribution of decoding accuracies thinned out at the left tail by the different significance thresholds used by specific studies. In other words, we are likely (conservatively) overestimating the center of this “true” distribution. The distribution for the null effects had a median of 51.5% (CI [51.0%, 52.0%). We computed the 95th percentile of this empirical “null distribution” analogous to the typical “critical value” used for null-hypothesis testing and obtained a value of 57.3% (CI [55.5%, 62.0%]). Note that these values sample a putative “true null” distribution thinned out at the right tail by the significant thresholds used in each analysis. Such thinning out would normally bias our estimates of central tendency and the critical value downward. On the other hand, the studies in our database employed different sample sizes and a variety of procedures for testing significance. If a proportion of these studies were underpowered, this would bias our estimates upward. In addition, it is also likely that our estimates are biased upward due to the so-called “file drawer effect” or systematic nonreporting of null findings and the practice of reporting only a subset of the analyses that were carried out (researcher degrees of freedom or, sometimes, p-hacking). To obtain a more conservative estimate of the critical value, we recentered the null distribution to 50%. With this approach, we obtained an estimate of 55.3% (CI [53.1%, 61.1%]) for the 95th percentile.

Despite these conservative adjustments, as shown in Figure 4, there was considerable overlap between the estimated “significant” and “null” distributions. Indeed, 36.9% (CI [17%, 66%]) of the accuracies in the “significant” distribution fell below the 95th percentile of the uncentered null distribution of 57.3% whereas 24.8% fell below the centered null distribution of 55.3%. This overlap suggests that a number of previous studies were either not sufficiently powered to detect information coded in PFC BOLD patterns or had inflated false positive rates (over the usual 5%).

However, as has been recently pointed out, the results of such tests of group-level mean accuracies against chance levels do not, in fact, support the population-level inference that the effect is typically present in the population (Allefeld, Görgen, & Haynes, 2016). Instead, these tests assess the global null hypothesis (Nichols, Brett, Andersson, Wager, & Poline, 2005) that no participants show the effect. As an example, in our lab's fMRI data set, the group mean decoding accuracy of 55.4% was “significantly” above chance in a one-sample test against chance (t20 = 3.95, p = .00078). However, only 5 out of 21 participants showed a decoding accuracy that was significantly different from chance as determined by a nonparametric permutation test. Although this may be an underestimate of the true prevalence given that we may not have had sufficient power at the single-subject level, it emphasizes the point that it is critical to evaluate the prevalence of the effect. Indeed, it has been suggested that population inferences can be made based on the prevalence of an effect in a sample (Allefeld et al., 2016). As a consequence, the power to detect an effect at the level of an individual participant becomes particularly important.

It has not been common practice in the literature to report individual participant data, and therefore, it is difficult to get estimates of within-subject variance needed for power analysis. Indeed, standardized measures of multivariate effect size remain to be developed (Hebart & Baker, 2017). Nevertheless, it is possible to make some general points about power at the individual level. The empirical “null” distribution described above gives us an estimate of the variability in observed decoding accuracy for a participant who does not show an effect (given that in these analyses the global null hypothesis cannot be rejected), and the 95th percentile of the null distribution (55.3%) can serve as a rough estimate of a critical threshold, which must be crossed for significance. On the other hand, an estimate of the typical individual's decoding accuracy when they do show the effect may be derived from the “significant” distribution. Comparing these two values will allow to estimate the magnitude of the difference in decoding accuracies that a typical study is trying to detect.

We consider two boundary conditions to derive the typical subject-level decoding accuracy. Consider the boundary condition where we assume that every significant effect reported in our database was maximally prevalent in that study's sample (i.e., every participant shows the effect). In that condition, the median of the “significant” distribution is a good estimate of the typical participant-level decoding accuracy. Given a median of 58.4%, we are, therefore, looking to detect a difference of only 3.1% points to reject the null hypothesis of chance-level coding for a typical participant. For the studies that decoded rule information in our database, the median number of trials per condition2 were 87 (e.g., a total of 174 trials for two conditions or classes). Assuming that each trial contributed to the test set (in a leave-n-out scheme), in a typical study, this would imply a difference of less than six trials successfully classified compared with a classifier that was just guessing. Consider another boundary condition where every significant effect reported by studies in our database shows a prevalence of only 50% (this is the lower-bound prevalence, given that a population inference requires that at least a majority of the participants show the effect). Assuming this liberal boundary condition for the studies in our database, we can estimate, from the median of our significant distribution, the typical decoding accuracy of an individual who showed the effect to be approximately 66.8% (assuming that half of the participants in the study showed no effect and thus had a decoding accuracy of 50%). In that case, we would be looking to detect an 11.5% points difference—a difference of 20 trials (out of 174) successfully classified under the most liberal assumptions. These rough calculations suggest that typical PFC MVPA effects are small, and given low pattern reliability in PFC (Figure 4), more data would be required per participant to detect such effects reliably.

We emphasize again that we do not formally estimate effect sizes, which requires additional information of within-subject variance in decoding accuracies that was rarely reported in the studies we reviewed. Therefore, this analysis is not intended as a recommendation of trial numbers for future MVPA studies of PFC and should not be cited as such. Nor do we recommend that the “critical” value estimated above be generalized beyond this analysis to assess the significance of decoding accuracies in other studies. Rather, this analysis merely makes concrete the point that, given the low base rate decoding accuracy in PFC and given the importance of assessing prevalence, sufficiently powered studies at the individual participant level are essential. Given the regional differences, power calculations should be based on estimates of effect sizes from decoding of PFC BOLD patterns and not those observed in other regions of the brain.

Analysis of Outliers

Our estimate of a literature-derived decoding accuracy distribution provides a means of placing the results of any given PFC decoding analysis within the context of the wider literature. Studies with very high accuracies, for instance, merit attention as they may have identified classes of information that are particularly well represented in PFC or may have employed a particularly effective analysis approach. At the same time, given prior findings, these effects are surprising and, therefore, also merit closer scrutiny for the presence of other confounding factors that may drive the results. For these reasons, we examined the top 5% of reported decoding accuracies in our database (Table 3) to identify factors that might explain the high values.

Table 3. 

Analyses in the Top Fifth Percentile of the “Significant” Distribution

Study IDNo. of Analyses in Top 5% (Total 41)Decoding Accuracy RangeROI or SearchlightRegion(s)aDescription
48 13 76–93% ROI Right precentral gyrus; left precentral gyrus; left middle frontal gyrus; right supplementary motor area; left supplementary motor area Classified hand vs. saccade response 
66 79–90% ROI Right middle frontal gyrus; left middle frontal gyrus; bilateral anterior cingulate gyrus Classified anticipation/experience of electric shock on arm vs. leg 
39 76–82% Searchlight Right superior frontal gyrus; right anterior cingulate gyrus; bilateral medial frontal gyrus Classified to-be-purchases objects vs. neutral objects when attended/unattended. 
52 76–87% Searchlight Bilateral inferior frontal gyrus, pars orbitalis; bilateral inferior frontal gyrus, pars triangularis; bilateral inferior frontal gyrus, pars opercularis Classified speech/music vs. reordered speech/music 
70 78–88% ROI Left middle frontal gyrus; right middle frontal gyrus; left precentral gyrus; right precentral gyrus Classified tasks that involved different rules & stimuli 
71 84–86% ROI Bilateral superior frontal &b gyrus & bilateral middle frontal gyrus & bilateral medial frontal gyrus & bilateral supplementary motor area; bilateral superior frontal gyrus & bilateral middle frontal gyrus & bilateral medial frontal gyrus Classified reactive vs. predictive eye movement pursuit of stimuli 
69 78–84% ROI Bilateral anterior cingulate gyrus & bilateral midcingulate area Classified near vs. far semantic similarity of presented words 
54 81–83% ROI Bilateral precentral gyrus Classified execution vs. imagining/observing reaching movements 
50 75% Searchlight Left inferior frontal gyrus, pars triangularis Classified speech vs. spectrally rotated speech 
31 77% ROI Left middle frontal gyrus Classified prospective yes vs. no decisions across intentions (honest/dishonest) 
78 79% ROI Bilateral precentral gyrus Classified whole hand grasping vs. reaching movement 
Study IDNo. of Analyses in Top 5% (Total 41)Decoding Accuracy RangeROI or SearchlightRegion(s)aDescription
48 13 76–93% ROI Right precentral gyrus; left precentral gyrus; left middle frontal gyrus; right supplementary motor area; left supplementary motor area Classified hand vs. saccade response 
66 79–90% ROI Right middle frontal gyrus; left middle frontal gyrus; bilateral anterior cingulate gyrus Classified anticipation/experience of electric shock on arm vs. leg 
39 76–82% Searchlight Right superior frontal gyrus; right anterior cingulate gyrus; bilateral medial frontal gyrus Classified to-be-purchases objects vs. neutral objects when attended/unattended. 
52 76–87% Searchlight Bilateral inferior frontal gyrus, pars orbitalis; bilateral inferior frontal gyrus, pars triangularis; bilateral inferior frontal gyrus, pars opercularis Classified speech/music vs. reordered speech/music 
70 78–88% ROI Left middle frontal gyrus; right middle frontal gyrus; left precentral gyrus; right precentral gyrus Classified tasks that involved different rules & stimuli 
71 84–86% ROI Bilateral superior frontal &b gyrus & bilateral middle frontal gyrus & bilateral medial frontal gyrus & bilateral supplementary motor area; bilateral superior frontal gyrus & bilateral middle frontal gyrus & bilateral medial frontal gyrus Classified reactive vs. predictive eye movement pursuit of stimuli 
69 78–84% ROI Bilateral anterior cingulate gyrus & bilateral midcingulate area Classified near vs. far semantic similarity of presented words 
54 81–83% ROI Bilateral precentral gyrus Classified execution vs. imagining/observing reaching movements 
50 75% Searchlight Left inferior frontal gyrus, pars triangularis Classified speech vs. spectrally rotated speech 
31 77% ROI Left middle frontal gyrus Classified prospective yes vs. no decisions across intentions (honest/dishonest) 
78 79% ROI Bilateral precentral gyrus Classified whole hand grasping vs. reaching movement 
a

Regions were assigned to corresponding AAL region.

b

& refers to the union of AAL regions for constructing a larger ROI used in the corresponding study.

First, as many as 18 of the 41 analyses in the top 5% decoded some form of motor response (reaching, grasping, saccades, etc.). Five additional analyses involved classifying the anticipation or experience of electric shocks on very different parts of the body (arm vs. leg). Six other analyses classified ordered stimuli like speech or music versus unordered versions of the same stimuli. All of these studies manipulate conditions that likely produce univariate differences, either as a small mean response difference across a majority of the voxels or differential activation of adjacent subregions. For example, univariate analyses of ordered versus unordered stimuli contrasts are often used to localize language-specific regions in PFC (Fedorenko, Duncan, & Kanwisher, 2012; Fedorenko, Behr, & Kanwisher, 2011). Univariate contributions to decoding analyses do not invalidate the inference of information coding. But such cases do not represent typical decoding studies in PFC, where MVPA is usually employed because univariate analyses are uninformative.

Two studies employed unusual measurement or analysis methods. Study 39 (five analyses) deployed nonlinear classifiers, which produced significantly higher accuracies than linear classifiers on the same data. The decoding accuracies obtained from linear classifiers are much closer to the median of our distribution. Study 31 uniquely employed high-resolution scanning with a 7-T magnet.

Importantly, only four of these analyses, all from a single article (Study 70), involved decoding task or rule information as posited by models of cognitive control and observed in macaque studies. However, even in these analyses, task/rule was confounded with visual information as the contrasted task conditions involved different classes of stimuli. Indeed, when task/rule was decoded after controlling stimulus differences, classification accuracies were in the mid 50s, close to the median of our distribution. Therefore, the high classification accuracies may have been driven by the additive effects of multiple sources of information.

In summary, we did not find a particular factor or approach that consistently explained these outlying decoding accuracies beyond what basic univariate analysis could provide.

Factors Affecting Decoding Performance in PFC

We next sought to systematically examine whether particular subregions of frontal cortex, particular types of information, or particular methods were correlated with decoding accuracy levels. To do this, we assessed the partial influence of these factors in our full database using mixed-effects linear regression. We fit a single mixed-effects regression model with all the characteristics—region, information type, and analysis procedure. All these regressors were dummy-coded, with one category omitted from the model. To account for covariance between observations from the same study, we also included random study intercepts. Classification accuracies reported as nonsignificant were excluded as they are more likely to have small or no effects.

To assess the significance of each characteristic, regressors were dropped one at a time from the model and tested against the full model using the likelihood ratio test. Results are shown in Figure 6 and Table 4. The inclusion of classifier, temporal compression, and ROI versus searchlight as factors each significantly improved model fit (Table 4; L = 12.75, p = .026; L = 8.21, p = .042; L = 4.02, p = .045). Inspecting the effects (Figure 6) suggests that both nonlinear SVM and temporally averaging across training and TRs are associated with relatively higher accuracy values. The effect of classifier was driven by three of four studies using nonlinear SVM, each with accuracies above 70%, one of which was also identified by our outlier analysis. Searchlight analyses, which predominantly report peak accuracies, were expected to be associated with higher accuracy values. Given the small number of studies and the large number of regressors, we also tested each analysis characteristic in a separate univariate regression to check whether the main regression failed to detect effects for any set of correlated regressors (Table 5). This analysis confirmed the effects for classifier and temporal compression (L = 21.4, p = .001; L = 11.4, p = .01), but not ROI versus searchlight (L = 0.40, p = .53); it also did not reveal any further significant effects. We note that all these analyses were exploratory in nature, and we did not apply multiple-comparisons correction. In addition, it is possible that we may not have had sufficient power to detect small effects of these analysis characteristics of decoding accuracies.

Figure 6. 

Results of a mixed-effects regression model for all analysis characteristics (top) and regions (bottom). To visualize the contributions of each factor to decoding accuracy, “effects” were computed by taking each coefficient and adding the average value of all other regressors multiplied by their respective coefficients. Mean value of decoding accuracies reported significant was 62% and deviations from this mean reflect the contribution of the analysis characteristic or region. The only characteristic with a significant influence was the use of nonlinear SVM classifiers. Only analyses reported as significant and assigned to one AAL region were included in this analysis (425 analyses from 69 studies).

Figure 6. 

Results of a mixed-effects regression model for all analysis characteristics (top) and regions (bottom). To visualize the contributions of each factor to decoding accuracy, “effects” were computed by taking each coefficient and adding the average value of all other regressors multiplied by their respective coefficients. Mean value of decoding accuracies reported significant was 62% and deviations from this mean reflect the contribution of the analysis characteristic or region. The only characteristic with a significant influence was the use of nonlinear SVM classifiers. Only analyses reported as significant and assigned to one AAL region were included in this analysis (425 analyses from 69 studies).

Table 4. 

Likelihood Ratio Tests for Main Regression Analysis

Regressor TesteddfAICBICLog LikLik Ratiop
Full model (baseline) 60 −1100.3 −857.1 610.1 NA NA 
Classifier 55 −1097.5 −874.6 603.8 12.75 .026 
Info type 57 −1104.3 −873.3 609.2 1.95 .582 
Smoothing 59 −1101.9 −862.9 610 0.32 .572 
Coregistration 59 −1099.9 −860.8 608.9 2.4 .121 
Response normalization 58 −1099.4 −864.4 607.7 4.87 .088 
Number of participants 59 −1101.7 −862.7 609.9 0.52 .469 
Scanner strength 59 −1102.2 −863.2 610.1 0.01 .93 
Temporal averaging 57 −1098.1 −867.1 606 8.21 .042 
ROI vs. searchlight 59 −1098.2 −859.2 608.1 4.02 .045 
Region 21 −1139 −1053.9 590.5 39.29 .457 
Voxel size 59 −1102.2 −863.1 610.1 0.05 .824 
Voxel number 59 −1102 −863 610 0.22 .641 
Training set size 59 −1102.2 −863.1 610.1 0.06 .809 
Regressor TesteddfAICBICLog LikLik Ratiop
Full model (baseline) 60 −1100.3 −857.1 610.1 NA NA 
Classifier 55 −1097.5 −874.6 603.8 12.75 .026 
Info type 57 −1104.3 −873.3 609.2 1.95 .582 
Smoothing 59 −1101.9 −862.9 610 0.32 .572 
Coregistration 59 −1099.9 −860.8 608.9 2.4 .121 
Response normalization 58 −1099.4 −864.4 607.7 4.87 .088 
Number of participants 59 −1101.7 −862.7 609.9 0.52 .469 
Scanner strength 59 −1102.2 −863.2 610.1 0.01 .93 
Temporal averaging 57 −1098.1 −867.1 606 8.21 .042 
ROI vs. searchlight 59 −1098.2 −859.2 608.1 4.02 .045 
Region 21 −1139 −1053.9 590.5 39.29 .457 
Voxel size 59 −1102.2 −863.1 610.1 0.05 .824 
Voxel number 59 −1102 −863 610 0.22 .641 
Training set size 59 −1102.2 −863.1 610.1 0.06 .809 
Table 5. 

Results of Univariate Regression Analyses

Regressor TesteddfAICBICLog LikLik Ratiop
Classifier −1423.4 −1389.5 719.7 21.44 .001 
Info type −1406.6 −1381.2 709.3 0.65 .884 
Smoothing −1410.1 −1393.1 709 0.11 .739 
Coregistration −1409.9 −1393 709 .971 
Response normalization −1408.3 −1387.1 709.2 0.36 .835 
Number of participants −1411.3 −1394.3 709.6 1.33 .248 
Scanner strength −1410.1 −1393.1 709 0.12 .724 
ROI vs. searchlight −1410.3 −1393.4 709.2 0.4 .528 
Temporal averaging −1417.4 −1391.9 714.7 11.42 .01 
Voxel size −1410 −1393 709 0.03 .869 
Voxel number −1411 −1394.1 709.5 1.07 .3 
Training set size −1411 −1394 709.5 1.04 .309 
Regressor TesteddfAICBICLog LikLik Ratiop
Classifier −1423.4 −1389.5 719.7 21.44 .001 
Info type −1406.6 −1381.2 709.3 0.65 .884 
Smoothing −1410.1 −1393.1 709 0.11 .739 
Coregistration −1409.9 −1393 709 .971 
Response normalization −1408.3 −1387.1 709.2 0.36 .835 
Number of participants −1411.3 −1394.3 709.6 1.33 .248 
Scanner strength −1410.1 −1393.1 709 0.12 .724 
ROI vs. searchlight −1410.3 −1393.4 709.2 0.4 .528 
Temporal averaging −1417.4 −1391.9 714.7 11.42 .01 
Voxel size −1410 −1393 709 0.03 .869 
Voxel number −1411 −1394.1 709.5 1.07 .3 
Training set size −1411 −1394 709.5 1.04 .309 

The full regression model did not reveal differences in accuracy across regions. Our regression analyses may have been underpowered due to the large number of regions tested simultaneously and the few number of observations associated with each region. Given that we found no effect of ROI laterality in the main model, we combined the left, right, and bilateral portions of each ROI for a more powerful, exploratory follow-up analysis and observed that superior and middle frontal gyrus, orbital part (58.1%), and middle frontal gyrus (59.2%) were marginally lower than the grand mean (61.0%; Figure 7; t = −2.01, p = .046; t = −2.38, p = .018). Next, we tested whether accuracy differed across regions based on the type of information decoded. Not surprisingly, response decoding was associated with higher accuracy in superior frontal gyrus (66.7%, p = .03), and perceptual decoding was associated with higher accuracy in cingulate cortex (68.2%, p = .004). There were no other differences in accuracy across the rest of the regions.

Figure 7. 

Testing for differences in decoding accuracy across a reduced number of regions. All left, right, bilateral observations were combined into bilateral ROIs. Additionally, middle frontal gyrus, orbital part, was combined with superior frontal gyrus, orbital part, because each of these regions had only a few data points. This resulted in 85% of observations being assigned to a one region and 15% to more than one region. Regressors for these ROIs were entered into a mixed-effects regression. Superior and middle frontal gyrus, orbital part, and middle frontal gyrus (excluding orbital part) were less than the grand mean (t = −2.01, p = .045; t = −2.37, p = .018; two-tailed; df = 426). Error bars are standard errors obtained from mixed-effects regression. Only analyses reported as significant were included in this analysis (512 analyses from 75 studies).

Figure 7. 

Testing for differences in decoding accuracy across a reduced number of regions. All left, right, bilateral observations were combined into bilateral ROIs. Additionally, middle frontal gyrus, orbital part, was combined with superior frontal gyrus, orbital part, because each of these regions had only a few data points. This resulted in 85% of observations being assigned to a one region and 15% to more than one region. Regressors for these ROIs were entered into a mixed-effects regression. Superior and middle frontal gyrus, orbital part, and middle frontal gyrus (excluding orbital part) were less than the grand mean (t = −2.01, p = .045; t = −2.37, p = .018; two-tailed; df = 426). Error bars are standard errors obtained from mixed-effects regression. Only analyses reported as significant were included in this analysis (512 analyses from 75 studies).

Finally, we carried out a second regression that focused only on frontal regions within the MD network (Fedorenko, Duncan, & Kanwisher, 2013) that response robustly to manipulations of various cognitive demands. These ROIs are more representative of typical functional clusters observed in fMRI studies of frontal cortex (as opposed to the large AAL ROIs) and may better reflect frontal decoding properties. However, we again found no differences within MD regions or between MD and other regions. In summary, although these different analyses of our data suggest small differences across regions—OFC, motor, cingulate—exist, the distribution of classification accuracies is broadly similar and low across PFC.

DISCUSSION

Over the past decade, MVPA has emerged as an important method for studying information coding in the human brain with fMRI (Haynes, 2015; Tong & Pratte, 2012; Haynes & Rees, 2006; Kriegeskorte et al., 2006; Norman et al., 2006; Haxby et al., 2001). MVPA combines evidence across voxels to detect information encoded subtly in distributed patterns of activity. Given the many open and important questions regarding the content and format of PFC representations, MVPA has also been enthusiastically applied to this brain region. However, an impression has gained ground among practitioners (often heard at conferences) that decoding information from PFC BOLD patterns is uniquely challenging. Many previous studies have implicitly assumed that MVPA of fMRI BOLD is just as effective in decoding information encoded in PFC neural activity as it is in visual cortex. This assumption underlies choices about sample size and experiment design (e.g., trial numbers), as well as comparison of decoding accuracies from PFC with visual cortex and other regions of the brain. We estimated the base rate decoding accuracy for PFC and show that it is indeed lower than sensory (visual) cortex, thus placing the prevailing impression of the difficulty of decoding information from PFC BOLD patterns on firm empirical ground.

Our meta-analysis of prefrontal MVPA studies identified over 800 MVPA decoding analyses across 76 studies, each reporting a group-level mean classification accuracy. This data set includes attempts to decode a wide range of information from BOLD patterns in various subregions of PFC while employing a similarly wide range of MVPA methods. In this sense, our meta-analysis samples a space of possible approaches to decoding in PFC and so permits not only an estimate of a base rate but also asking if particular approaches are systematically more or less successful.

From this data set, we estimate the base rate for decoding information from prefrontal BOLD patterns at the low value of 55.4% for two-way classifications where chance performance is 50%. Furthermore, we observed that PFC base rate is markedly lower than base rates for decoding visual stimulus information from occipital and ventral temporal cortex BOLD patterns, which were at 66.6% and 71.0%, respectively. These differences are not due to the larger hypothesis space of PFC decoding studies. The differences remain stark even when we derive PFC base rate estimates solely from analyses that decode rule or task information, which we believe is very likely to be coded by PFC neurons given evidence from primate electrophysiology and human neuropsychology. In practical terms, this low base rate means that it is likely that the difference between studies reporting successful versus unsuccessful classification may hinge on only a few trials classified better than chance. This has significant implications for experimental design and inference that we discuss further below.

Indeed, PFC base rate we obtain is very likely to be an overestimate for a number of reasons. First, given that we only included studies that mentioned PFC in the abstract, other studies that ran whole-brain searchlights and found chance-level coding in PFC may have been excluded. Second, searchlight results are often expressed as peak classification accuracy values obtained in whole-brain maps, resulting in an inherent selection bias for higher values. Third, if some previous PFC studies were underpowered, as we suggest, the significant results that they do report would be exaggerated in magnitude (Type M errors, see Gelman & Carlin, 2014), thus upwardly biasing our estimate. In addition, the publication bias for positive results (the “file drawer” effect) and the prevalent practice of reporting a biased subset of the analyses carried out (“researchers degree of freedom” or, in some cases, “p-hacking”) would similarly result in an overrepresentation of large decoding accuracies, though we emphasize that we have no evidence of these practices in the studies we reviewed. Given these factors, we believe it is likely that decoding information from PFC may be even more difficult than our results suggest.

The base rate provides an empirically derived prior against which future decoding paradigms or methods can be compared. For example, studies that propose a new feature of the fMRI signal (e.g., Waskom & Wagner, 2017 recently decoded context information from local connectivity measures) or a new decoding method as capturing a special aspect of coding in PFC, can be viewed against this base rate prior. In other words, we can ask whether incremental gains in decoding accuracy, beyond those expected given the base rate, are achieved from applying the new feature or method. We emphasize, however, that decoding accuracies are not standardized effect size measures and large accuracy values do not imply a large or even reliable effect. Indeed, any comparisons of decoding accuracies must take into account the underlying variance. Therefore, the base rate decoding accuracy that we report should not be treated as a threshold for evaluating decoding accuracies in future studies. Instead, these values can enable the computation of the approximate likelihood of a result within the context of prior findings.

In the same vein, our base rate provides a principled basis on which to highlight past studies that were unusually successful at decoding information for further scrutiny. We probed several outlier analyses in our data set that showed large classification accuracies to look for a consistent feature that explained their success. Most of these cases could be attributed to the influence of large, previously known univariate effects. Beyond these effects, the few remaining outlier studies did not share a consistent approach or classification type that resulted in a marked shift in criterion. Nevertheless, our analysis places the likelihood of these outcomes in context given the broader literature. As such, these individual studies might merit further follow-up and replication.

Beyond consideration of the outliers, we leveraged the meta-analysis data set to ask whether particular information types or methodological choices were consistently associated with higher decoding performance using regression. We found some evidence that motor information in some regions of posterior PFC and perceptual information in cingulate cortex are associated with slightly higher decoding performance. Conversely, regions of midlateral PFC closely tied to cognitive control were associated with, if anything, even lower classification success than other areas of the frontal lobe. We also found a benefit of using nonlinear classifiers in the small number of studies that use them. However, this benefit may be offset by known complications associated with the use of nonlinear classifiers. Although they are indeed able to be able to read out a wider variety of representational formats, nonlinear classifiers are more susceptible to overfitting. Moreover, a “linear readout” (that a linear classifier implements) is often considered a hallmark of an explicit representation (Barak, Rigotti, & Fusi, 2013; Kriegeskorte & Kievit, 2013) under the assumption that downstream neurons usually implement such a readout. Therefore, the results of a linear classifier can support stronger claims about representations that those of a nonlinear classifier cannot. Nonetheless, the nonlinear SVM approach may merit further study and replication of its advantage for PFC classification. Beyond this, we found that decoding performance was robust to variations in methods, with the caveat that our power to detect these effects was not high. Collectively, these results suggest that the low base rate of decoding information from PFC BOLD patterns is a very general finding.

What makes decoding information from PFC BOLD patterns so difficult? It is important to clarify that the base rate is a joint property of a brain region, the kind of information one is trying to decode, and methodological factors. Indeed, neuronal populations in the same brain region may encode multiple different variables, and decoding some of them may be easier than others (Dubois, de Berker, & Tsao, 2015). The base rate we have estimated is based on a diverse set of studies that attempted to decode a wide variety of different kinds of information including stimulus information, motor responses, as well as higher-level “cognitive” aspects of tasks like rules or the contents of working memory. Given that we found no evidence that any particular kind of information was associated with higher decoding accuracies, we refer more generally to the base rate of decoding information from PFC. However, it is certainly possible that the difference we observe between base rates in PFC, on one hand, and occipital and ventral temporal cortex, on the other, are due to differences in the kinds of information that studies have generally tried to decode from these regions.

On the other hand, electrophysiology studies in the nonhuman primate have provided strong evidence for ubiquitous coding of task-relevant information in prefrontal firing rates (Mansouri et al., 2009; Wallis et al., 2001; White & Wise, 1999; Rainer et al., 1998; Sakagami & Niki, 1994). Table 6 lists decoding accuracies compiled from a small sample of macaque PFC electrophysiology studies that carried out ensemble decoding analyses. The median of these decoding accuracies (median = 82%) is higher than 98.7% of PFC BOLD accuracies in our database and markedly higher than the estimated base rate. Indeed, recent evidence suggests that macaque PFC representations of task variables are high dimensional and that this property enables these task variables and their conjunctions to be read out by a linear classifier (Rigotti et al., 2013). Thus, the finding of a low base rate of decoding such information from prefrontal BOLD patterns is surprising. Furthermore, the differences in base rates between prefrontal and occipital/ventral-temporal cortex suggest that the function relating the information content of spiking activity and that of BOLD patterns across voxels varies across regions. Of course, it is conceivable that human PFC representations have different properties than those of macaques and that we simply have not found the appropriate conditions for driving human PFC neurons as we have for visual cortex neurons. However, we deem this unlikely as a general account given the many parallels between human and nonhuman primate results and suggest that PFC BOLD patterns across voxels may only weakly reflect the information encoded in the firing rate of populations of prefrontal neurons.

Table 6. 

Prefrontal Decoding Accuracies from Macaque Electrophysiology

ReferenceInformation TypeRegionAccuracy Range
Astrand et al., 2014  Stimulus identity FEF 93% 
Rule/task FEF 77% 
Rigotti et al., 2013  Stimulus identity Lateral PFC ∼100% 
Rule/task Lateral PFC 85% 
Meyers et al., 2008  Stimulus category Lateral PFC 82% 
Stimulus category working memory Lateral PFC 66% 
Goodwin, Blackman, Sakellaridi, & Chafee, 2012  Rule Lateral PFC 70% 
Stimulus category Lateral PFC 82% 
Saez et al., 2015  Rule/context ACC 80% 
Stimulus identity ACC 100% 
Tremblay, Doucet, Pieper, Sachs, & Martinez-Trujillo, 2015  Attention to location Lateral PFC 74% 
Cue location Lateral PFC 82% 
Meyers, Qi, & Constantinidis, 2012  Rule Lateral PFC ∼100% 
  
Median     82% 
ReferenceInformation TypeRegionAccuracy Range
Astrand et al., 2014  Stimulus identity FEF 93% 
Rule/task FEF 77% 
Rigotti et al., 2013  Stimulus identity Lateral PFC ∼100% 
Rule/task Lateral PFC 85% 
Meyers et al., 2008  Stimulus category Lateral PFC 82% 
Stimulus category working memory Lateral PFC 66% 
Goodwin, Blackman, Sakellaridi, & Chafee, 2012  Rule Lateral PFC 70% 
Stimulus category Lateral PFC 82% 
Saez et al., 2015  Rule/context ACC 80% 
Stimulus identity ACC 100% 
Tremblay, Doucet, Pieper, Sachs, & Martinez-Trujillo, 2015  Attention to location Lateral PFC 74% 
Cue location Lateral PFC 82% 
Meyers, Qi, & Constantinidis, 2012  Rule Lateral PFC ∼100% 
  
Median     82% 

The base rate of decoding information is no doubt influenced by the properties of PFC representations. For example, an oft-cited feature of PFC neurons is that they display “mixed selectivity” (Rigotti et al., 2013) or “adaptive coding” (Duncan, 2001)—that is, their selectivity for particular task variables is highly context and task dependent. Such a feature of coding may render population activity patterns more susceptible to noise contributed by uncontrolled features of the environment like temporal context, thus making decoding more difficult. Similarly, the activity of PFC neurons is known to show a greater degree of temporal autocorrelation (Murray et al., 2014), which may heighten the similarity between condition-specific activity patterns. Finally, population representations of the contents of working memory in PFC are known to be highly dynamic (Stokes et al., 2013), with each to-be-remembered item producing a complex trajectory through neural state space, suggesting that information may be stored in the temporal profile of these trajectories, rather than only in overall activity. All of these properties likely affect the decoding of information, though note that they would affect decoding from electrophysiologically measured firing rate patterns as well, not just BOLD patterns. Therefore, they are not sufficient to explain the particular difficulty with decoding from BOLD patterns.

Low decoding base rates in PFC may be caused by MR-induced or physiological noise contributions to the BOLD signal that may influence the trial-by-trial variability of BOLD patterns in a region-specific manner. In our own fMRI data set, empirical estimates of raw SNRs were not lower in PFC compared with visual cortex. Therefore, the lower decoding accuracies we found in PFC could not have been driven by raw noise differences. However, both the univariate functional SNR and the reliability of BOLD patterns were lower in PFC than in visual cortex (Figure 4). A lower reliability of BOLD patterns in PFC would certainly make decoding more difficult. However, this lower reliability also demands explanation and would be affected by the other factors we discuss.

Another possibility we find more likely is that the particular local functional organization and distribution of neural populations in PFC may reduce differences between conditions at the voxel scale measured with fMRI (Guest & Love, 2017; Leavitt, Mendoza-Halliday, & Martinez-Trujillo, 2017). Tremblay et al. (2015) showed that it is more difficult to decode information from lateral PFC low-frequency potentials (which reflect local average activity) in macaques, compared with single-unit firing rates, consistent with reduced differences with local averaging. In a recent study, Dubois et al. (2015) examined the coding of face viewpoint and identity information using both MVPA of BOLD patterns and single-unit recordings in macaques. Although both viewpoint and identity were strongly coded in single-unit firing rates, MVPA of BOLD patterns only revealed viewpoint information. The authors concluded that identity decoding suffered because identity coding neurons were only weakly clustered spatially as compared with viewpoint-coding neurons. Clustering may enable nearby blood vessels to be strongly driven by neurons selective to one condition, thus enabling inhomogeneities in the sampling of the activity of selective neurons by voxels (Kamitani & Tong, 2005). Most single-unit studies in primate PFC, however, show very little evidence of clustering (Machens, Romo, & Brody, 2010), with neurons coding different task-relevant information being heterogeneously intermixed at a fine scale (e.g., Brody, Hernández, Zainos, & Romo, 2003; Chafee & Goldman-Rakic, 1998; Rainer et al., 1998; Rao, Rainer, & Miller, 1997; Quintana & Fuster, 1992; Kojima & Goldman-Rakic, 1982). By contrast, in the visual cortex MVPA effects may depend on clustering both at the fine scale in the form of columnar structure (Kamitani & Tong, 2005) and also at the coarse scale in the form of asymmetric spatial distribution of columns (Sengupta, Yakupov, Speck, Pollmann, & Hanke, 2017; Swisher et al., 2010; Sasaki et al., 2006). Future studies combining electrophysiology and fMRI in nonhuman primate PFC will be necessary to directly test this account. This account would predict that higher-resolution fMRI might ultimately help this base rate issue, though this might require still higher resolution than is currently feasible and is constrained by the vasculature. Alternately, PFC representations may perhaps be better studied by leveraging repetition suppression effects (Barron, Garvert, & Behrens, 2016; Grill-Spector & Malach, 2001), which are not affected by the local distribution of neural populations.

Regardless of the source of these differences, a base rate decoding difference between prefrontal and visual cortex has important implications for the interpretation of studies, which rely on comparisons of classification accuracies across these regions. Consider, for example, the debate surrounding the locus (prefrontal or sensory cortex) of detailed sensory information during working memory delays, which has been informed by the finding that, although classifiers readily decode sensory information from the BOLD signal recorded from visual cortex during such delays, they are much less successful in the frontal cortex (reviewed in Sreenivasan, Curtis, & D'Esposito, 2014). If the base rate for decoding is lower in PFC, such a finding, on its own, would provide limited support for an exclusive sensory cortex locus of working memory representations. In order for such comparisons to be interpreted, it would be critical to first consider the base rate for decoding information for the regions in question. Indeed, several researchers have recognized the fact that comparison of decoding accuracies across regions is problematic (Haynes, 2015; Etzel, Zacks, & Braver, 2013).

More generally, interpreting whole-brain maps of location information coding obtained from employing “roving searchlights” requires making the assumption that base rates across the brain are similar (Etzel et al., 2013). Statistical thresholding of such accuracy maps to correct for multiple comparisons through the control of family-wise error rate or false discovery rate implicitly privileges regions of the brain with higher base rates (assuming equivalent variance). Indeed, although we have focused on PFC in this study, our results also highlight the more general point that knowing base rates is critical to interpreting the findings of MVPA studies, including those employing other measurement modalities that span the brain like magnetoencephalography or EEG.

The empirical distribution of PFC classification accuracies that we have compiled allows any new result to be placed within the context of prior findings and for its likelihood to be computed. As also noted above, analyses that report unusually high classification accuracies should draw attention for the possibility that they may be false positives or be driven by confounding factors. Employing this logic, we compiled separate distributions of classification accuracies for significant and null effects from our data set and observed considerable overlap between these empirical distributions. This overlap suggests the presence of a number of analyses that either did not appropriately control false positive rates or were insufficiently powered to reject null hypothesis of chance-level coding. Indeed, we noted the widespread use of parametric statistics, which have been shown to inflate false positive rates for classification accuracies. We agree with recommendations that MVPA studies should rely primarily on appropriately conducted permutation testing at the individual level (Stelzer, Chen, & Turner, 2013) and the assessment of the prevalence of effects at the group level (Allefeld et al., 2016).

Indeed, given the importance of the prevalence of MVPA effects in making population-level inferences (Allefeld et al., 2016), it is important to consider the power of an experimental design to detect an effect at the individual-subject level. Based on our rough estimates of typical decoding accuracies from the “null” and “significant” distributions, we expect that significantly more data per participant will need to be collected to detect small differences in decoding accuracies more consistently. This is particularly important as future studies move beyond demonstrating information coding to examining the factors that may influence the properties of underlying representations. With classification accuracies typically hovering in the 50–60% range, there is little room to detect their modulation with experimental manipulation or by incorporating covariates without many more measurements. Similarly, improved statistical power will also be necessary to regress out the potentially confounding effects of small, idiosyncratic differences between task conditions on nuisance variables like difficulty or time-on-task (Todd, Nystrom, & Cohen, 2013). The prefrontal BOLD signal is known to be sensitive to such variables (Fedorenko et al., 2012; Duncan & Owen, 2000) and regressing out their effects post hoc is critical to unbiased inference.

In conclusion, we provide an estimate of the base rate of decoding information from PFC BOLD patterns and show that it is markedly lower than two brain regions in visual cortex. Our low estimate supports the prevailing impression that using MVPA to decode information in PFC is particularly challenging. The reasons for this difficulty remain open and—we suspect—may reflect an important property of neural coding in PFC, such as their spatial organization and distribution. Although we cannot pinpoint the specific factor driving this difference, our results have concrete implications for the design and interpretation of future studies—we recommend more data per participant, the use of permutation tests, reporting of prevalence at the group level, and a consideration of base rate when making direct comparisons across regions. Finally, this study provides an example of how meta-analyses of MVPA data can provide unique insights that are not available in single studies. To facilitate future investigations, we are sharing our database and code publicly via the Open Science Framework (https://osf.io/8dvzr/).

Acknowledgments

We are grateful to Marc Coutanche and colleagues for kindly sharing meta-analysis data of visual decoding studies. We thank Brittany Ciullo, Nada Hamzah, Juliana Trach, Sarah Master, and Celia Ford for their assistance with independently verifying the coding of the meta-analysis data. This work was support by grants from NINDS (NS065046) and NIMH (MH099078, MH111737) at the NIH and a MURI award from the Office of Naval Research (N00014-16-1-2832). A. B., C. G., and D. B. designed the study. C. G. and A. B. carried out the analyses. A. B., C. G., and D. B. wrote the paper. A. B. and C. G. contributed equally to this work.

Reprint requests should be sent to Apoorva Bhandari, Cognitive, Linguistic, & Psychological Sciences, Brown University, Providence, RI, or via e-mail: apoorva_bhandari@brown.edu.

Notes

1. 

Note that these confidence intervals are provided for descriptive purposes only (see Methods, Estimating Distributions).

2. 

Thirty-four of the 36 rule coding studies contributed trial count information. Number of trials per condition ranged from 27 to 520 across studies, with a mean of 125 and a median of 87.

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Author notes

*

These authors contributed equally to this study.