Goodness-of-Fit Tests for the Additive Risk Model with (p > 2)-Dimensional Time-Invariant Covariates

This paper presents methods for checking the goodness-of-fit of the additive risk model with p(> 2)-dimensional time-invariant covariates. The procedures are an extension of Kim and Lee (1996) who developed a test to assess the additive risk assumption for two-sample censored data. We apply the proposed tests to survival data from South Wales nikel refinery workers. Simulation studies are carried out to investigate the performance of the proposed tests for practical sample sizes.     

Estimation of the Average Survival Function Using a Censored Data Regression Model

In the presence of covariates information, assuming the linear relationship between a transformation of survival time and covariates, we propose a new estimator of survival function and show its consistency. In addition, a comparison of the proposed estimator with the product-limit estimator introduced by Kaplan and Meier (1958) is performed through Monte Carlo simulation studies. We illustrate the proposed estimator with the updated Stanford heart transplant data.     

The analysis of tumorigenicity data using a frailty effect

In animal tumorigenicity data, the time of occurrence of the tumor is not observed because the existence of the tumor is looked for only at either the time of death or the time of sacrifice of the animal. Such an incomplete data structure makes it difficult to investigate the impact of treatment on the occurrence of tumors. A three-state model (no tumor–tumor–death) is used to model events that occurred sequentially and to connect them. In this paper, we also employed a frailty effect to model the dependency of death on tumor occurrence. For the inference of parameters, an EM algorithm is considered. The method is applied to a real bladder tumor data set and a simulation study is performed to show the behavior of the proposed estimators.     

Nonparametric Quantile Estimation with Correlated Failure Time Data

In biomedical studies, correlated failure time data arise often. Although point and confidence interval estimation for quantiles with independent censored failure time data have been extensively studied, estimation for quantiles with correlated failure time data has not been developed. In this article, we propose a nonparametric estimation method for quantiles with correlated failure time data. We derive the asymptotic properties of the quantile estimator and propose confidence interval estimators based on the bootstrap and kernel smoothing methods. Simulation studies are carried out to investigate the finite sample properties of the proposed estimators. Finally, we illustrate the proposed method with a data set from a study of patients with otitis media.