Optimal number of repeated measures and group sizes in clinical trials with linearly divergent treatment effects

Abstract

The effect of number of repeated measures on the variance of the generalized least squares (GLS) treatment effect estimator is considered assuming a linearly divergent treatment effect, equidistant time-points and either a fixed number of subjects or a fixed study budget. The optimal combination of group sizes and number of repeated measures is calculated by minimizing this variance subject to a linear cost function. For a fixed number of subjects, the variance of the GLS treatment effect estimator can be decreased by adding intermediate measures per subject. This decrease is relatively large if a) the covariance structure is compound symmetric or b) the structure approaches compound symmetry and the correlation between two repeated measures does not exceed 0.80, or c) the correlation between two repeated measures does not exceed 0.60 if the time-lag goes to zero. In case the sample sizes and number of repeated measures are limited by budget constraints and the covariance structure includes a first-order auto-regression part, two repeated measures per subject yield highly efficient treatment effect estimators. Otherwise, it is more efficient to have more than two repeated measures. If the covariance structure is unknown, the optimal design based on a first-order auto-regressive structure with measurement error is preferable in terms of robustness against misspecification of the covariance structure. The numerical results are illustrated by three examples.