Statistical analyses of clustered failure time data

This dissertation has three separate parts: the first part dealing with multiply matched cohort studies with two different comparison groups; the second part dealing with a nonparametric estimator of incidence rates for a nonparametric transformation model; and the third part dealing with estimating procedures and model diagnosis of a parametric transformation model.; The first part develops a new statistical method to analyze multiply matched cohort studies with two different comparison groups. I employ a linear logistic model to describe the underlying log odds ratios and use a conditional likelihood approach to conduct inference. Under the assumption of homogeneous log odds ratios, I provide methods to construct both asymptotic and exact confidence regions of the two log odds ratios in a simple case. I propose a score test to evaluate the assumption of homogeneous log odds ratios across strata. While the proposed methods are general, I develop them around a specific application, namely, the study of pregnancy rates in HIV-infected women. My analyses suggest that HIV infection is associated with a decrease in pregnancy rates and that this decrease in fertility becomes highly significant after accounting for illicit drug use.; Part II is concerned with a nonparametric estimator for clustered failure time data. In this part, the latent error distribution is unspecified, and the unknown transformation function can be heterogeneous across different clusters. In survival analysis, various parametric, semiparametric, and nonparametric models are employed to describe the failure time. The semiparametric transformation model includes the proportional hazards model and the proportional odds model as special cases. To estimate incidence rates based on a nonparametric transformation model, I propose a new M-estimator, which makes a nonparametric pair-wise comparison of all subjects within the same cluster. This new estimator takes censoring and clustering into account, and incorporates the maximum rank correlation (MRC) estimator as a special case.; In addition to the pair-wise comparison estimation of the nonparametric transformation model, Part III provides a parametric transformation model for the failure time. Various statistical methods have been proposed for semiparametric transformation models with a known latent error distribution, but no sophisticated methods are available to estimate a parameter that determines the latent error distribution. Part III specifies the transformation function and proposes a parametric form for the latent error distribution. For the parametric transformation model, I develop the estimating procedures and provide two diagnostic measures for evaluating goodness of fit.