Flexible Methods for Clustered Event History Data.

This dissertation investigates three interesting problems in clustered event history data. The first project considers a positive stable frailty proportional hazards model for clustered failure time data, with the frailty distribution allowed to depend on cluster-level covariates. We connect the cluster-level covariates with the dependence parameter through a link function. The mathematical property of the positive stable distribution enables proportionality for both the marginal and conditional hazard functions. As a result, the marginal regression parameter equals the product of the dependence parameter and the conditional regression parameter. We utilize this special feature and propose a two-step estimation approach, where the marginal regression parameters are obtained in the first step and the regression parameters for the link function are obtained in the second step based on the conditional intensity model.The second project proposes a computationally efficient marginal proportional rates model with piecewise-constant baseline rate function for clustered recurrent event data. The parametric specification of the baseline rate function enables the modeling of intermittent counts instead of recurrent event times, which results in data reduction and remedies computational issues resulting from the size of the databases. Large-sample distributions are derived for the proposed estimators. We show that the proposed method can be implemented using standard statistical software for Cox regression. An application based on national hospitalization data for end stage renal disease patients is provided.The third project investigates a fixed center effects model for recurrent event data with center effects multiplicatively acting on the rate functions. When the number of centers is large, traditional estimation methods that treat centers as categorical variables have many parameters and are sometimes not feasible to implement, especially with large number of distinct recurrent event times. We propose a new estimation method for center effects which avoids including indicator variables for centers. We then show that the center effect can be consistently estimated by the ratio of the observed cumulative number of events to the corresponding expected quantity in a center. Large sample results are developed for the proposed estimators. The method is then applied to national hospitalization data for end stage renal disease patients.