Longitudinal covariate-adjusted response-adaptive randomized designs

• Longitudinal CARA randomization procedures are proposed.
• Asymptotic properties of LCARA procedures are established.
• LCARA randomization balances the allocation across all covariates.
• LCARA randomization improves the estimation efficiency of regression parameters.
• Two treatments with continuous responses are studied in detail.

Clinical trials often involve longitudinal data set which has two important characteristics: repeated and correlated measurements and time-varying covariates. In this paper, we propose a general framework of longitudinal covariate-adjusted response-adaptive (LCARA) randomization procedures. We study their properties under widely satisfied conditions. This design skews the allocation probabilities which depend on both patients' first observed covariates and sequentially estimated parameters based on the accrued longitudinal responses and covariates. The asymptotic properties of estimators for the unknown parameters and allocation proportions are established. The special case of binary treatment and continuous responses is studied in detail. Simulation studies and an analysis of the National Cooperative Gallstone Study (NCGS) data are carried out to illustrate the advantages of the proposed LCARA randomization procedure.