Random Effects Simulation for Sample Size Calculations Using SAS

Sample size calculations are a critical step in the planning of any experiment. In all but the simplest of experimental designs, closed-form equations are not readily available, and statisticians are required to use simulations to estimate an appropriate sample size for the experiment. Specifically, when multiple explanatory variables are thought to be predictive of the response or when missing data is likely to occur, simulation is a valuable approach for sample size calculation. In this paper we consider a simulation study for a continuous response measured at a set of fixed time points. We consider a randomized study comparing an experimental treatment plus standard of care (ET+SOC) to the standard of care (SOC). We assume that, based on data from a previous study, the response trajectory for the SOC subjects varies with respect to gender and that the response curves as reasonably well modeled by a quadratic polynomial in time. Using PROC IML, we simulate data from a linear mixed effects model including a gender main effect, linear and quadratic time, and treatment by time interactions. For this scenario, the primary (null) hypothesis is that there is no treatment effect. Model fitting is performed using PROC MIXED. Our technique for simulation is easily generalizable and efficient.