Nonparametric regression for correlated failure time data analysis.

Abstract

Correlated failure time data analysis has been an interesting topic for about 30 years. Nonparametric covariate effect models become interesting when the hazard function is unknown or too complicated to be able to use parametric models. In this dissertation, we focus on studying nonparametric regression methods using the local kernel and smoothing spline method for correlated failure time data. We start with an introduction in Chapter I. In Chapter II, We study nonparametric regression for correlated failure time data under a marginal proportional hazards model assumption. Kernel estimating equations are used. Independent and weighted kernel estimating equations (EE) are studied. The derivative of the covariate function is first estimated and the covariate function estimator is obtained by integrating the derivative estimator. The nonparametric estimator of the covariate function's derivative is consistent for any arbitrary working correlation matrix, and the asymptotic variance is minimized by assuming working independence. We evaluate the performance of the proposed kernel estimator using simulation studies and apply the proposed method to western Kenya parasitemia data. In Chapter III, we study the hazard model with time-dependent coefficients. We propose a kernel-based profile likelihood for semiparametric estimation. The parametric estimator is shown to be asymptotically normal and achieves the semiparametric efficiency bound. We also extend the profile likelihood method to correlated survival models. A working independence estimator is used. The estimator is consistent and asymptotically normal but not efficient. We also evaluate the estimators' small sample properties using numerical analysis. In Chapter IV we study nonparametric regression using smoothing splines for frailty models. We demonstrate the connection between the penalized partial likelihoods of a nonparametric Cox model and of a frailty model studied by Ripatti and Palgrem (2000). Hence, nonparametric covariate function can be fitted using software fitting Gaussian frailty models. For the Gaussian frailty models with nonparametric covariate function, we propose a double penalized partial likelihood (DPPL). Smoothing parameter selections, inference of nonparametric estimation and frailty can be done by using a parametric frailty model formulation. Simulation is used to evaluate the performance of proposed estimators. In Chapter V, we conclude the dissertation with a discussion of possible future work.