Bayesian sample size determination for longitudinal intervention studies with linear and log-linear growth

Abstract

A priori sample size determination (SSD) is essential for designing cost-efficient trials and in avoiding underpowered studies. In addition, reporting a solid justification for a certain sample size is required by most ethics committees and many funding agencies. Often, SSD is based on null hypothesis significance testing (NHST), an approach that has received severe criticism in the past decades. As an alternative, Bayesian hypothesis evaluation using Bayes factors has been developed. Bayes factors quantify the relative support in the data for a pair of competing hypotheses without suffering from some of the drawbacks of NHST. SSD for Bayesian hypothesis testing relies on simulations and has only been studied recently. Available software for this is limited to simple models such as ANOVA and the t test, in which observations are assumed to be independent from each other. However, this assumption is rendered untenable in longitudinal experiments where observations are nested within individuals. In that case, a multilevel model should be used. This paper provides researchers with a valuable tool for performing SSD for multilevel models with longitudinal data in a Bayesian framework, along with the necessary theoretical background and concrete empirical examples. The open-source R function that enables researchers to tailor the simulation to their trial at hand can be found on the GitHub page of the first author.