Adding subjects or adding measurements in repeated measurement studies under financial constraints

Budget constraint is a challenge faced by investigators in planning almost every clinical trial. For a repeated measurement study, investigators need to decide whether to increase the number of participating subjects or to increase the number of repeated measurements per subject, with the ultimate goal of maximizing power for a given financial constraint. This financially constrained design problem is further complicated when taking into account things such as missing data and various correlation structures among the repeated measurements. We propose an approach that combines a GEE estimator of slope coefficients with the cost constraint. In the case where we have no missing data and the compound symmetric correlation structure, the optimal design is derived analytically. In the case where we have missing data or other correlation structures, the optimal design is identified through numerical search. We present an extensive simulation study to explore the impacts of cost ratio, missing pattern, dropout rate, and correlation structure. We also present an application example.