Statistical Design and Survival Analysis in Cluster Randomized Trials.

Cluster randomized trials, in which social units are selected as the units ofrandomization, have been increasingly used in the past three decades to evaluatethe effects of intervention. This thesis is devoted to design and analysis of clusterrandomized trials.Regarding design, we introduce a new randomization design in the first project,the balance match weighted (BMW) design, which applies the optimal full matchingwith constraints technique to a prospective randomized design and aims to minimizethe mean squared error (MSE) of the treatment effect estimator. In CRTs, there aretypically rather few participating units and several confounding variables to adjustfor. 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 inthe MSE of the treatment effect estimators as compared to various designs proposedin the literature.In the second project, we extend the BMW design to clinical trials with threearms or more and with staggered entry. The first extension involves finding optimaltripartite matching, which is shown as NP hard in graph theory. To circumvent this1problem, three ad hoc approaches which would lead to the near-optimal solutions areinvestigated and the design extended based on each of these approaches. Simulationstudies reveal the good properties of the generalized BMW designs.Dependencies among cluster members are typical of CRTs and must be consideredin the subsequent data analyses. The third project deals with the nonparametric regressionanalysis of correlated time-to-event data based on a Cox frailty model. Thereis much literature dealing with the identification and estimation of frailty models usingboth parametric and semiparametric approaches. We consider a frailty model withboth the frailty distribution and the cumulative baseline hazard left nonparametricand propose an approach based on nonparametric maximum likelihood estimation. Athree-step iterative algorithm is developed for implementation and a numerical studyshows that the proposed nonparametric approach performs well by providing importantgains in robustness while resulting in relatively small loss in efficiency comparedto the popular semiparametric approach by Therneau et al. (2003).