Sample size planning for longitudinal data is crucial when designing mediation studies because sufficient statistical power is not only required in grant applications and peer-reviewed publications, but is essential to reliable research results. However, sample size determination is not straightforward for mediation analysis of longitudinal design. To facilitate planning the sample size for longitudinal mediation studies with a multilevel mediation model, this article provides the sample size required to achieve 80% power by simulations under various sizes of the mediation effect, within-subject correlations and numbers of repeated measures. The sample size calculation is based on three commonly used mediation tests: Sobel’s method, distribution of product method and the bootstrap method. Among the three methods of testing the mediation effects, Sobel’s method required the largest sample size to achieve 80% power. Bootstrapping and the distribution of the product method performed similarly and were more powerful than Sobel’s method, as reflected by the relatively smaller sample sizes. For all three methods, the sample size required to achieve 80% power depended on the value of the ICC (i.e., within-subject correlation). A larger value of ICC typically required a larger sample size to achieve 80% power. Simulation results also illustrated the advantage of the longitudinal study design. The sample size tables for most encountered scenarios in practice have also been published for convenient use. Extensive simulations study showed that the distribution of the product method and bootstrapping method have superior performance to the Sobel’s method, but the product method was recommended to use in practice in terms of less computation time load compared to the bootstrapping method. A R package has been developed for the product method of sample size determination in mediation longitudinal study design.

Background: Standard drug development conducts phase I dose finding and phase II dose expansion sequentially and separately. Information between the two phases is rarely shared. Administratively, such a sequential process is time-consuming and burdensome. Purpose: We propose seamless dose escalation/expansion with adaptive randomization scheme (SEARS), a seamless design that combines phase I dose escalation based on toxicity with phase II dose expansion and dose comparison based on efficacy. SEARS allows extension from phase I to phase II under one design with no gap in between and employs a dynamic and parallel procedure involving simultaneous dose escalation, dose graduation, and adaptive randomization. Methods: SEARS integrates three components into a seamless scheme. Specifically, in phase I, SEARS applies the modified toxicity probability interval (mTPI) method to monitor dose escalation based on toxicity outcome. Doses that show promising efficacy and safety are immediately graduated from phase I and placed to a phase II stage in which patients are adaptively randomized based on efficacy outcome. Phase I dose escalation, dose graduation, and phase II adaptive randomization proceed simultaneously throughout the entire trial. Results: Examples are given comparing SEARS with two other designs, in which superior performance of SEARS is demonstrated. An important and promising finding is that SEARS reduces sample sizes without losing power. R program and demo slides of SEARS can be obtained at http://health.bsd.uchicago.edu/yji/soft.html Limitation: We assume that the binary efficacy and toxicity response can be measured in the same time frame. This is often achievable with surrogate efficacy markers in practice.