Sample size estimation for longitudinal designs with attrition: Comparing time-related contrasts between two groups

Formulas for estimating sample sizes are presented to provide specified levels of power for tests of significance from a longitudinal design allowing for subject attrition. These formulas are derived for a comparison of two groups in terms of single degree-of-freedom contrasts of population means across the study timepoints. Contrasts of this type can often capture the main and interaction effects in a two-group repeated measures design. For example, a two-group comparison of either an average across time or a specific trend across time (e.g., linear or quadratic) can be considered. Since longitudinal data with attrition are often analyzed using an unbalanced repeated measures model (with a structured variance-covariance matrix for the repeated measures) or a random-effects model for incomplete longitudinal data, the variance-covariance matrix of the repeated measures is allowed to assume a variety of forms. Tables are presented listing sample size determinations assuming compound symmetry, a first-order autoregressive structure, and a non-stationary random-effects structure. Examples are provided to illustrate use of the formulas, and a computer program implementing the procedure is available from the first author.