Bayesian sample size calculation for trials with multilevel data
The cluster randomized trial design is extensively used in social, behavioural and biomedical sciences (Moerbeek, 2019; Moerbeek & Teerenstra, 2016). Complete groups, such as schools or families, are randomized to treatment conditions in this design. For instance, the researchers can assign a school or class to a condition to evaluate the effectiveness of educational programs. Traditionally, the sample size for this type of design is based on null hypothesis statistical testing using p-values. This approach uses the effect size, Type I error, and statistical power (Cohen, 1988, as cited in Fu, 2022). However, focusing on p-values has led to questionable research practices and difficulties interpreting results (Hoijtink et al., 2019). Testing hypotheses using the Bayes can overcome the disadvantages of using p-values. The Bayes factor quantifies the relative support for each hypothesis considered in the study (Hoijtink et al., 2019). Previous research has proposed methods to determine the sample size, but these are limited to the t-test, Bayesian Welch’s test, and ANOVA (Fu, 2022).
Building on Fu (2022), the present project aims to determine the sample size necessary to test informative hypotheses using the Bayes factor in cluster randomized trials. At the beginning of the project, the focus will be on cluster randomized trials with a one-period parallel-group design; afterwards, the method will be extended to designs with multiple time periods, such as the cross-over trial and stepped-wedge design. As a result, an R package will be developed for sample size calculation.
Collaboration with an advisory group consisting of applied researchers and statisticians is expected during the project. Likewise, it is expected to organize workshops for applied researchers in order to teach the Bayesian approach for sample size calculation, and the R package developed. These actions are an effort to develop a tool that can benefit researchers in different fields.
Dr. ir. M.M. Moerbeek
Prof. dr. H.J.A.H. Hoijtink
January 2023 – Januari 2027