B0330
Title: Optimal designs in mixed ANCOVA models for longitudinal data
Authors: Xiaojian Xu - Brock University (Canada) [presenting]
Sanjoy Sinha - Carleton University (Canada)
Abstract: The construction of optimal designs for linear mixed models with covariates is investigated when involving longitudinal data. Random effects are employed to accommodate the clusters. We consider both the treatment effects as well as continuous covariates in the model. The goal of the designs is to optimally select the levels of covariates as well as the proportions of the sample units allocated to each treatment within a given total sample size. Both D- and A-optimality are chosen to be the design criteria. Although the estimators can be given with analytic forms if normality is assumed, the optimal designs depend on the unknown parameters involved in the variance components. Therefore, we apply both two-stage and sequential approaches. The problem of interest can be formulated in an ANCOVA framework, and the following specific problems are addressed: (i) optimal allocations for treatment groups if heteroscedastic random effects appear when the covariate levels are specified; (ii) optimal designing the levels of covariates for balanced design if random effects appear to be homoscedastic; and (iii) optimizing both the allocations for treatment groups and design levels for the covariates in the ANCOVA models with possible heteroscedasticity.
