"Smooth" Inference for Clustered Survival Data

Abstract

Regression analysis of censored clustered-correlated time-to-event data is of interest in family studies, litter-matched tumorigenesis studies, and other settings where the survival times may be thought of as arising in groups or ``clusters, " and the correlation among survival times in each cluster must be taken into account. A natural way to address such dependence is through incorporation of subject-specific random effects. In the first part of this disseration, we propose an accelerated failure time (AFT) model for such data that involves normally-distributed, mean zero random effects and a within-cluster ``error" term that is assumed to have distribution with a density satisfying mild ``smoothness" conditions. We approximate the smooth density by the ``seminonparametric" (SNP) representation of Gallant and Nychka (1987), which admits a ``parametric" form for the density depending on a known ``kernel" density and a tuning parameter that determines the degree of flexibility for capturing the true density. This representation facilitates likelihood-based inference on the regression parameter, random effects variance components, and the density, which we implement by a Monte Carlo expectation-maximization (MCEM) algorithm; and we choose the tuning parameter and ``kernel" using standard information criteria. Moreover, arbitrary censoring patterns may be accommodated straightforwardly. We illustrate the approach via simulations and by applications to data from Diabetic Retinopathy Study (DRS, Diabetic Retinopathy Study Research Group, 1981), from a litter-matched tumorigenesis study (Mantel, Bohidar, and Ciminera, 1977), and from western Kenya parasitaemia study (McElroy et al., 1997).

The second part of this dissertation focuses on estimation of a bivariate survival function. In many situations, such as twin studies, matched pair studies, and studies of organ such as the eyes and kidneys, correlated, bivariate failure times are recorded. Based on a sample of possibly censored such failure times, an objective of analysis is to estimate the joint survival distribution. We extend the use of SNP in the first part of the dissertation to the two dimensional case and represent the joint density of the failure time using SNP. We illustrate the approach via simulations and by application to data from the DRS.