Statistical Design and Survival Analysis in Cluster Randomized Trials.

Abstract

Cluster randomized trials, in which social units are selected as the units of randomization, have been increasingly used in the past three decades to evaluate the effects of intervention. This thesis is devoted to design and analysis of cluster randomized trials. Regarding design, we introduce a new randomization design in the first project, the balance match weighted (BMW) design, which applies the optimal full matching with constraints technique to a prospective randomized design and aims to minimize the mean squared error (MSE) of the treatment effect estimator. In CRTs, there are typically rather few participating units and several confounding variables to adjust for. It is important to balance across these factors given the constraint of sample size. A simulation study shows that the BMW design can yield substantial reductions in the MSE of the treatment effect estimators as compared to various designs proposed in the literature. In the second project, we extend the BMW design to clinical trials with three arms or more and with staggered entry. The first extension involves finding optimal tripartite matching, which is shown as NP hard in graph theory. To circumvent this 1 problem, three ad hoc approaches which would lead to the near-optimal solutions are investigated and the design extended based on each of these approaches. Simulation studies reveal the good properties of the generalized BMW designs. Dependencies among cluster members are typical of CRTs and must be considered in the subsequent data analyses. The third project deals with the nonparametric regression analysis of correlated time-to-event data based on a Cox frailty model. There is much literature dealing with the identification and estimation of frailty models using both parametric and semiparametric approaches. We consider a frailty model with both the frailty distribution and the cumulative baseline hazard left nonparametric and propose an approach based on nonparametric maximum likelihood estimation. A three-step iterative algorithm is developed for implementation and a numerical study shows that the proposed nonparametric approach performs well by providing important gains in robustness while resulting in relatively small loss in efficiency compared to the popular semiparametric approach by Therneau et al. (2003).