Semi-parametric and Parametric Methods for the Analysis of Multi-center Survival Data.

Abstract

Survival analysis plays an important role in the evaluation of center effects. In this dissertation, we develop semi-parametric and parametric methods to evaluate centers in the presence of censored data.

The standardized mortality ratio (SMR) based on Cox regression is often used to evaluate center-specific mortality. However, the asymptotic properties and finite-sample behavior of the Cox SMR are not well-studied. In the first chapter, we describe some strong limitations of the Cox SMR that relate to its underlying assumptions. To address these limitations, we develop modifications based on a stratified Cox model. In addition, since center effects computed through indirect standardization are not comparable, we propose a semiparametric generalization of direct standardization. Hypothesis testing procedures are developed to identify outlying centers and to evaluate whether a particular center has an effect that is constant over time.

In the context of survival data, the difference in mean lifetime is arguably a more meaningful measure than the ratio of death rates. In the second chapter, we propose a method which combines a log-normal frailty model and piece-wise exponential baseline rates to compare mean survival time across centers. Maximum likelihood based estimation is carried out using a Laplace approximation for integration. The proposed methods allow for estimation of mean survival time as opposed to the restricted mean lifetime and, within this context, robust profiling of long-term center-specific outcomes.

In the third chapter, we develop methods for evaluating center-specific survival using a center-stratified additive hazards model. We estimate the relative center effects by the ratio of baseline survival functions. The proposed measure is a semiparametric generalization of the relative risk, which is often used in clinical studies. An attractive property of our proposed method is that the ratio of survival function for a particular subject reduces to the ratio of baseline survival function, and such ratio of baseline survival functions is invariant to the choice of baseline covariate level.

For each of the proposed methods, we derive the asymptotic properties of the center effect estimators, with finite sample properties addressed through simulation. Each method is applied to kidney transplant data obtained from national registries.