Optimal Experimental Designs for Multilevel Logistic Models with Two Binary Predictors

Abstract

ABSTRACT Many experiments aim at populations with persons nested within clusters. In the design stage of such experiments one has to decide whether to randomize complete clusters or persons within clusters to treatment conditions. Furthermore, the optimal sample sizes have to be calculated. In this article these two design issues will be dealt with for logistic models with a binary treatment condition and a binary covariate. The multilevel model is used to relate treatment condition and the covariate to the binary outcome. The optimal design is analytically derived for first order Marginal Quasi Likelihood (MQL) by linearizing the model using a Taylor series expansion. A simulation study shows results for second order Penalized Quasi Likelihood, (PQL), which is known to produce less biased estimates. The results show that person level randomization is preferred, especially when the cluster size and variance component at the cluster level are large. Two examples show how optimal sample sizes can be calculated in practice.