Optimal allocation schemes in mixed ANCOVA models for longitudinal data

Abstract

We discuss the construction of optimal allocation schemes for the linear mixed model with clustered outcomes or repeated measurements often encountered in longitudinal studies. We consider both treatment and covariate effects in the mixed model, where latent pro- cesses are used to describe random cluster or subject effects. A goal of optimal design schemes is to determine proportions of sample units allocated to each treatment for a given total sample size. We develop the optimal designs in a general setting using both D- and A- optimal design criteria. Specifically, we propose a two-stage design approach to deal with unknown parameters in the linear mixed model, where the variances of the random effects across the treatment groups are considered different. We study the empirical properties of the proposed designs using Monte Carlo simulations. An application is also provided using actual clinical data from a longitudinal study.

Journal of Statistical Research, Vol 56, No 2, p101-114