Components of Variance in a Multicentre Functional MRI Study and Implications for Calculation of Statistical Power

This article firstly presents a theoretical analysis of the statistical power of a parallel-group, repeated-measures (two-session) and two-centre design suitable for a placebo-controlled pharmacological MRI study. For arbitrary effect size, power is determined by the pooled between-session error, the pooled measurement error, the ratio of centre measurement errors, the total number of subjects and the proportion of subjects studied at the centre with greatest measurement error. Secondly, an experiment is described to obtain empirical estimates of variance components in task-related and resting state functional magnetic resonance imaging. Twelve healthy volunteers were scanned at two centres during performance of blocked and event-related versions of an affect processing task (each repeated twice per session) and rest. In activated regions, variance components were estimated: between-subject (23% of total), between-centre (2%), between-paradigm (4%), within-session occasion (paradigm repeat; 2%) and residual (measurement) error (69%). The between-centre ratio of measurement errors was 0.8. A similar analysis for the Hurst exponent estimated in resting data showed negligible contributions of between-subject and between-centre variability; measurement error accounted for 99% of total variance. Substituting these estimates in the theoretical expression for power, incorporation of two centres in the design necessitates a modest (10%) increase in the total number of subjects compared with a single-centre study. Furthermore, considerable improvements in power can be attained by repetition of the task within each scanning session. Thus, theoretical models of power and empirical data indicate that between-centre variability can be small enough to encourage multicentre designs without major compensatory increases in sample size.