Sample Size Estimation for Random-effects Models

Panel study designs are common in environmental epidemiology, whereby repeated measurements are collected from a panel of subjects to evaluate short-term within-subject changes in response variables over time. In planning such studies, questions of how many subjects to include and how many different exposure conditions to measure are commonly asked at the design stage. In practice, these choices are constrained by budget, logistics, and participant burden and must be carefully balanced against statistical considerations of precision and power. In this article, we provide intuitive sample size formulae for the precision of regression coefficients derived from panel studies and show how they can be applied in planning such studies. We show that there are five determinants of the precision with which regression coefficients can be estimated: (1) the residual variance of the responses; (2) the variance of the slopes; (3) the number of subjects; (4) the number of measurements/subject; and (5) the within-subject range of the exposure values "X" at which the responses are measured. The planning of such studies would be greatly improved if investigators regularly reported all of the variance components in fitted random-effects models: currently, literature values for the relevant variance parameters are often not readily available and must be estimated through pilot studies or subjective estimates of "reasonable values."