A Comparison of Different Estimation Methods for Simulation-Based Sample Size Determination in Longitudinal Studies

Determining sample size necessary for correct results is a crucial step in the design of longitudinal studies. Simulation-based statistical power calculation is a flexible approach to determine number of subjects and repeated measures of longitudinal studies especially in complex design. Several papers have provided sample size/statistical power calculations for longitudinal studies incorporating data analysis by linear mixed effects models (LMMs). In this study, different estimation methods (methods based on maximum likelihood (ML) and restricted ML) with different iterative algorithms (quasi-Newton and ridge-stabilized Newton-Raphson) in fitting LMMs to generated longitudinal data for simulation-based power calculation are compared. This study examines statistical power of F-test statistics for parameter representing difference in responses over time from two treatment groups in the LMM with a longitudinal covariate. The most common procedures in SAS, such as PROC GLIMMIX using quasi-Newton algorithm and PROC MIXED using ridge-stabilized algorithm are used for analyzing generated longitudinal data in simulation. It is seen that both procedures present similar results. Moreover, it is found that the magnitude of the parameter of interest in the model for simulations affect statistical power calculations in both procedures substantially.