Internal pilot design for balanced repeated measures

Repeated measures are common in clinical trials and epidemiological studies. Designing studies with repeated measures requires reasonably accurate specifications of the variances and correlations to select an appropriate sample size. Underspecifying the variances leads to a sample size that is inadequate to detect a meaningful scientific difference, while overspecifying the variances results in an unnecessarily large sample size. Both lead to wasting resources and placing study participants in unwarranted risk. An internal pilot design allows sample size recalculation based on estimates of the nuisance parameters in the covariance matrix. We provide the theoretical results that account for the stochastic nature of the final sample size in a common class of linear mixed models. The results are useful for designing studies with repeated measures and balanced design. Simulations examine the impact of misspecification of the covariance matrix and demonstrate the accuracy of the approximations in controlling the type I error rate and achieving the target power. The proposed methods are applied to a longitudinal study assessing early antiretroviral therapy for youth living with HIV.