Power calculations for generalized linear models in observational longitudinal studies: a simulation approach in SAS.

Repeated measurements arising from longitudinal studies occur frequently in applied research. Methods to calculate power in the context of repeated measures are available for experimental settings where the covariate of interest is a discrete treatment indicator. However, no closed form expression exists to calculate power for generalized linear models with non-zero within-cluster correlation that are common in epidemiological and observational studies in which the covariate of interest varies over time and is often measured on a continuous scale, and where the researchers control for several potential confounders. We describe a Monte Carlo simulation approach conducted to calculate power, and illustrate its application in two models frequently encountered in practice, the normal linear mixed model, and the logistic regression model, both with repeated measurements and non-zero within-cluster correlation. This approach can be used to calculate the effect on power of changing various simulation conditions controlled by the researcher, such as sample size, within-cluster correlation structure, smallest meaningful difference to detect, and distributional assumptions.