Synthetic Power Analyses Empirical Evaluation and Application to Cognitive Neuroimaging Peiye Zhuang

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Synthetic Power Analyses: Empirical Evaluation

and Application to Cognitive Neuroimaging

Peiye Zhuang

Dept. of Comupter Science,

University of Illinois

at Urbana-Champaign

peiye@illinois.edu

Bliss Chapman

Apple

bliss.chapman@gmail.com

Ran Li

Google

ryannli1129@gmail.com

Sanmi Koyejo

Dept. of Comupter Science

& Beckman Institute,

University of Illinois

at Urbana-Champaign

sanmi@illinois.edu

Abstract—In the experimental sciences, statistical power anal-

yses are often used before data collection to determine the

required sample size. However, traditional power analyses can

be costly when data are difﬁcult or expensive to collect. We

propose synthetic power analyses; a framework for estimating

statistical power at various sample sizes, and empirically explore

the performance of synthetic power analysis for sample size

selection in cognitive neuroscience experiments. To this end,

brain imaging data is synthesized using an implicit generative

model conditioned on observed cognitive processes. Further, we

propose a simple procedure to modify the statistical tests which

result in conservative statistics. Our empirical results suggest that

synthetic power analysis could be a low-cost alternative to pilot

data collection when the proposed experiments share cognitive

processes with previously conducted experiments.

Index Terms—fMRI, GANs, power analyses

I. INTRODUCTION

Cognitive neuroscience studies how the brain produces

intelligent behavior. One of the most common measurement

tools for brain activity is functional magnetic resonance

imaging (fMRI), used to gain insight into how patterns in

brain activity correspond to cognitive functions. The use of

imaging tools to understand cognition is known as cognitive

neuroimaging. This paper proposes generative modeling tech-

niques that provide a promising methodological approach to

improve statistical analysis in cognitive neuroimaging.

Improvements to statistical analysis are particularly timely

due to an increasing focus on the quality of data-dependent

analysis in science and medicine, probably most publicly in the

psychological sciences [1], [2] One of the primary quantities

of interest in statistical analyses of scientiﬁc data is statistical

power; the probability that a test rejects the null hypothesis

given that the alternative hypothesis is correct. Lower power

reﬂects a low probability that the test correctly detects a

statistically signiﬁcant effect. Neuroscientists typically aim for

80% power [3]. However, in recent years, the statistical power

of published neuroscience studies has been demonstrated to

be much lower than initially claimed, especially in published

fMRI experiments [4].

Prospective power analyses promise an optimal experiment

design that maximizes statistical power and reduces the waste

of resources on futile experiments or additional subjects. In

traditional power analysis, real data is collected and used

to determine the sample size needed to achieve the desired

experimental power. Unfortunately, an MRI machine with

resolution at the level required for neuroscience research costs

between 0.5 and 3 million dollars [5], and the scanning can

cost about $500+ an hour [6]. Thus, resources are not always

available to run studies that could supply data for power

analysis. This barrier lowers the quality of proposed research

experiments and slows overall progress in neuroscience.

One approach to circumvent the data problem is to use

stand-in data from other research groups for power analysis.

However, even when the borrowed data is a good substitute

for the proposed experiment, this approach requires planning

well in advance and slows turnaround times. More importantly,

ﬁnding stand-in data can be challenging. An alternative ap-

proach is to determine effect sizes and variance estimates from

previously published studies. Again, even when one can ﬁnd

a sufﬁciently similar study, the experiment can suffer from

underpowered estimates because published articles are biased

towards reporting signiﬁcant effects [1], [2].

We propose the use of modern generative neural net-

work models to synthesize diverse, high-quality brain images.

Speciﬁcally, we use the three-dimensional Improved Con-

ditional Wasserstein Generative Adversarial Network (ICW-

GANs) model [7]. The observation motivates our use of

this generative approach to produce unlimited synthetic data,

which, in turn, promises informed power analyses with min-

imal cost overhead. In particular, our model can synthesize

cognitive processes corresponding to labels that are not present

in the original training set, thus enabling the direct application

of synthetic fMRI data to real-world power analyses for new

experiments.

The primary aim of this manuscript is to empirically eval-

uate the performance of synthetic power analyses through

simulated data and neuroimaging experiments. We compare

the power analysis results of synthetic to real data using

both the classic two-sample t-test and the non-parametric

maximum mean discrepancy (MMD) test [8]. Our experiments

demonstrate that the synthetic data has similar distributional

characteristics as real data, and that power analysis results cal-

culated with synthetic data are similar to those calculated with

real data. Taken together, our results suggest that synthetic data

arXiv:2210.05835v1 [cs.CV] 11 Oct 2022

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SyntheticPowerAnalyses:EmpiricalEvaluationandApplicationtoCognitiveNeuroimagingPeiyeZhuangDept.ofComupterScience,UniversityofIllinoisatUrbana-Champaignpeiye@illinois.eduBlissChapmanApplebliss.chapman@gmail.comRanLiGoogleryannli1129@gmail.comSanmiKoyejoDept.ofComupterScience&BeckmanInstitute,Universi...

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Synthetic Power Analyses Empirical Evaluation and Application to Cognitive Neuroimaging Peiye Zhuang

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