Power calculation for group fMRI studies accounting for arbitrary design and temporal autocorrelation

Abstract

When planning most scientific studies, one of the first steps is to carry out a power analysis to define a design and sample size that will result in a well-powered study. There are limited resources for calculating power for group fMRI studies due to the complexity of the model. Previous approaches for group fMRI power calculation simplify the study design and/or the variance structure in order to make the calculation possible. These approaches limit the designs that can be studied and may result in inaccurate power calculations. We introduce a flexible power calculation model that makes fewer simplifying assumptions, leading to a more accurate power analysis that can be used on a wide variety of study designs. Our power calculation model can be used to obtain region of interest (ROI) summaries of the mean parameters and variance parameters, which can be use to increase understanding of the data as well as calculate power for a future study. Our example illustrates that minimizing cost to achieve 80% power is not as simple as finding the smallest sample size capable of achieving 80% power, since smaller sample sizes require each subject to be scanned longer.

Figure 1

Comparing T-statistics derived using the FSL unstructured covariance from an analysis using a highpass filter (T_FSL) and the high pass filtered AR(1)+WN covariance derived from the ASL covariance (T_AR(1)+WN) across all voxels for a single subject. The red line shows the trend of the data using a loess fit.

Figure 2

An illustration of how power differs when the model is incorrectly specified either by not convolving a boxcar regressor with an HRF or assuming the noise is independent. This comparison is made over a range of ρ, ${\sigma }_{AR}^2$, and ${\sigma }_{\mathit{WN}}^2$ in the top, middle and bottom panels, respectively.

Figure 3

Power estimates for a block design study where the total cost is limited to $7600. Each curve is for a different sample size and the grey dotted line indicates 80% power.

Figure 4

Number of cycles and cost to achieve 80% power. The left panel shows how many cycles per subject are required and the right panel shows the total cost when there is a base cost of $300, for subject preparation, and additional scanner time is $10/minute.