Sample size estimation for task-related functional MRI studies using Bayesian updating

Abstract

Task-related functional MRI (fMRI) studies need to be properly powered with an adequate sample size to reliably detect effects of interest. But for most fMRI studies, it is not straightforward to determine a proper sample size using power calculations based on published effect sizes. Here, we present an alternative approach of sample size estimation with empirical Bayesian updating. First, this method provides an estimate of the required sample size using existing data from a similar task and similar region of interest. Using this estimate researchers can plan their research project, and report empirically determined sample size estimations in their research proposal or pre-registration. Second, researchers can expand the sample size estimations with new data. We illustrate this approach using four existing fMRI data sets where Cohen's d is the effect size of interest for the hemodynamic response in the task condition of interest versus a control condition, and where a Pearson correlation between task effect and age is the covariate of interest. We show that sample sizes to reliably detect effects differ between various tasks and regions of interest. We provide an R package to allow researchers to use Bayesian updating with other task-related fMRI studies.

Keywords: Bayesian updating; Effect size; Power analysis; R package; Region of interest; Sample sizes.

Fig. 1

Estimates of task effects for five different sample sizes (starting with $N=20$, then 1/5th parts of the total dataset). For each sample size 10 randomly chosen HDCI’s out of the 1000 HDCI’s computed are displayed (in light blue). The average estimate with credible interval summarizing the 1000 HDCI’s for each sample size are plotted in reddish purple. DLPFC = dorsolateral prefrontal cortex; mPFC = medial prefrontal cortex; NAcc = nucleus accumbens.

Fig. 2

For each task, for five different sample sizes (starting with $n=20$, then 1/5th parts of the total dataset), the proportion of intervals not containing the value 0 is plotted in reddish purple.

Fig. 3

Estimates of Pearson’s correlation between age and the task effect for five different sample sizes (starting with $N=20$, then 1/5th parts of the total dataset). For each sample size 10 randomly chosen HDCI’s out of the 1000 HDCI’s computed are displayed (in green). The average estimate with credible interval summarizing the 1000 HDCI’s for each sample size are plotted in orange. DLPFC = dorsolateral prefrontal cortex; mPFC = medial prefrontal cortex; NAcc = nucleus accumbens. Age is modeled as linearly increasing or decreasing.

Fig. 4

For each task, for five different sample sizes (starting with $N=20$, then 1/5th parts of the total dataset), the proportion of intervals not containing the value 0 is plotted inorange. Age is modeled as linearly increasing or decreasing.