Optimal time-points in clinical trials with linearly divergent treatment effects

In repeated measures studies, equidistant time-points do not always yield efficient treatment effect estimators. In the present paper, the optimal allocation of time-points is calculated for a small number of repeated measures, different covariance structures and linearly divergent treatment effects. The gain in efficiency of the treatment effect estimator by using optimally allocated time-points instead of equidistant time-points or by adding optimally spaced measures (at the expense of patients) is then computed. The assumed covariance structure is crucial for the results. For a compound symmetric covariance structure, a large gain in efficiency is obtained by adding repeated measures at the end of the study. For a first-order auto-regressive covariance structure, highly efficient treatment effect estimators are obtained with only two repeated measures, i.e. at the start and at the end of the study. For a first-order auto-regressive covariance structure including measurement error, the gain in efficiency by adding optimally spaced measures depends on the covariance parameter values. The gain in efficiency is similar with or without a random intercept. For a fixed study budget, the commonly used design with more than two equally spaced measures was never optimal for the linear cost function and covariance structures that were used. If the covariance structure is unknown, the optimal design based on a first-order auto-regressive covariance structure with measurement error is preferable in terms of robustness against misspecification of the covariance structure. The numerical results are illustrated by two examples.