The optimal pre-post allocation for randomized clinical trials

In pre-post designs, analysis of covariance (ANCOVA) is a standard technique to detect the treatment effect with a continuous variable measured at baseline and follow-up. For measurements subject to a high degree of variability, it may be advisable to repeat the pre-treatment and/or follow-up assessments. In general, repeating the follow-up measurements is more advantageous than repeating the pre-treatment measurements, while the latter can still be valuable and improve efficiency in clinical trials.

In this article, we report investigations of using multiple pre-treatment and post-treatment measurements in randomized clinical trials. We consider the sample size formula for ANCOVA under general correlation structures with the pre-treatment mean included as the covariate and the mean follow-up value included as the response. We propose an optimal experimental design of multiple pre-post allocations under a specified constraint, that is, given the total number of pre-post treatment visits. The optimal number of the pre-treatment measurements is derived. For non-linear models, closed-form formulas for sample size/power calculations are generally unavailable, but we conduct Monte Carlo simulation studies instead.

Theoretical formulas and simulation studies show the benefits of repeating the pre-treatment measurements in pre-post randomized studies. The optimal pre-post allocation derived from the ANCOVA extends well to binary measurements in simulation studies, using logistic regression and generalized estimating equations (GEE).

Repeating baselines and follow-up assessments is a valuable and efficient technique in pre-post design. The proposed optimal pre-post allocation designs can minimize the sample size, i.e., achieve maximum power.