Aalen Additive Hazards Change-Point Model

We study a test comparing the full Aalen additive hazards modeland the change-point model, and suggest how to estimate theparameters of the change-point model. We also study a test forno change-point effect. Both tests are provided with large sampleproperties and a resampling method is applied to obtain p-values.The finite-sample properties of the proposed inference proceduresand estimators are assessed through a simulation study. Themethods are further applied to a dataset concerning myocardialinfarction.     

Goodness of Fit Tests for Proportional Hazards Regression Models

We present a test of goodness of fit for the proportional hazard regression model. The test is based on a score statistic for testing against local mixture alternatives. Contrary to the findings of several other authors, we detect a significant lack of fit in Freireich's leukemia data.     

A Bayesian Chi‐Squared Goodness‐of‐Fit Test for Censored Data Models

Summary We propose a Bayesian chi‐squared model diagnostic for analysis of data subject to censoring. The test statistic has the form of Pearson's chi‐squared test statistic and is easy to calculate from standard output of Markov chain Monte Carlo algorithms. The key innovation of this diagnostic is that it is based only on observed failure times. Because it does not rely on the imputation of failure times for observations that have been censored, we show that under heavy censoring it can have higher power for detecting model departures than a comparable test based on the complete data. In a simulation study, we show that tests based on this diagnostic exhibit comparable power and better nominal Type I error rates than a commonly used alternative test proposed by Akritas (1988, Journal of the American Statistical Association 83, 222–230). An important advantage of the proposed diagnostic is that it can be applied to a broad class of censored data models, including generalized linear models and other models with nonidentically distributed and nonadditive error structures. We illustrate the proposed model diagnostic for testing the adequacy of two parametric survival models for Space Shuttle main engine failures.     

Dynamic analysis of multivariate failure time data

We present an approach for analyzing internal dependencies in counting processes. This covers the case with repeated events on each of a number of individuals, and more generally, the situation where several processes are observed for each individual. We define dynamic covariates, i.e., covariates depending on the past of the processes. The statistical analysis is performed mainly by the nonparametric additive approach. This yields a method for analyzing multivariate survival data, which is an alternative to the frailty approach. We present cumulative regression plots, statistical tests, residual plots, and a hat matrix plot for studying outliers. A program in R and S-PLUS for analyzing survival data with the additive regression model is available on the web site http://www.med.uio.no/imb/stat/addreg. The program has been developed to fit the counting process framework.     

A goodness-of-fit test for the marginal Cox model for correlated interval-censored failure time data

The marginal Cox model approach is perhaps the most commonly used method in the analysis of correlated failure time data (Cai, 1999; Cai and Prentice, 1995; Lin, 1994; Wei, Lin and Weissfeld, 1989). It assumes that the marginal distributions for the correlated failure times can be described by the Cox model and leaves the dependence structure completely unspecified. This paper discusses the assessment of the marginal Cox model for correlated interval-censored data and a goodness-of-fit test is presented for the problem. The method is applied to a set of correlated interval-censored data arising from an AIDS clinical trial.     

Confidence Intervals for the Difference of Median Survival Times Using the Stratified Cox Proportional Hazards Model

The stratified Cox proportional hazards model is introduced to incorporate covariates and involve nonproportional treatment effect of two groups into the analysis and then the confidence interval estimators for the difference in median survival times of two treatments in stratified Cox model are proposed. The one is based on baseline survival functions of two groups, and the other on average survival functions of two groups. I illustrate the proposed methods with an example from a study conducted by the Radiation Therapy Oncology Group in cancer of the mouth and throat. Simulations are carried out to investigate the small‐sample properties of proposed methods in terms of coverage rates.     

On the KOLMOGOROV-SMIRNOV Test for the POISSON Distribution with Unknown Mean

The standard tables for the KOLMOGOROV -SMIRNOV test are valid only in the case of testing whether a set of observations is from a completely specified cumulative distribution, F₀(X), with all parameters known. If the parameters are unknown and must be estimated from the sample, then the tables are not valid. A table is given in this paper for use with the KOLMOGOROV -SMIRNOV statistic in the case of testing whether a set of observations is from the POISSON distribution with an unknown mean that must be estimated from the sample. The table is obtained from a Monte Carlo calculation.     

Modified GEE and Goodness of the Marginal Fit (GOMF) Test with Correlated Binary Responses for Contingency Tables

This paper addresses testing the goodness of fit of models for marginal probabilities estimated by generalized estimating equations. We develop a modified version of generalized estimating equation and a goodness‐of‐fit test based on the fitted marginal means. The test statistic is easy to compute and has a simple reference distribution. Its performance is evaluated asymptotically and in small samples. It is also compared to the deviance and Pearson X² statistics. Example applications are given. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Proportional Hazards Regression for the Analysis of Clustered Survival Data from Case–Cohort Studies

Summary Case–cohort sampling is a commonly used and efficient method for studying large cohorts. Most existing methods of analysis for case–cohort data have concerned the analysis of univariate failure time data. However, clustered failure time data are commonly encountered in public health studies. For example, patients treated at the same center are unlikely to be independent. In this article, we consider methods based on estimating equations for case–cohort designs for clustered failure time data. We assume a marginal hazards model, with a common baseline hazard and common regression coefficient across clusters. The proposed estimators of the regression parameter and cumulative baseline hazard are shown to be consistent and asymptotically normal, and consistent estimators of the asymptotic covariance matrices are derived. The regression parameter estimator is easily computed using any standard Cox regression software that allows for offset terms. The proposed estimators are investigated in simulation studies, and demonstrated empirically to have increased efficiency relative to some existing methods. The proposed methods are applied to a study of mortality among Canadian dialysis patients.     

A Measure of Dependence for the Stratified Cox Proportional Hazards Regression Model

Kent and O'Quigley (1988) apply the concept of information gain to measure both global and partial dependence between explanatory variables and a censored response within the framework of the proportional hazards regression model of Cox (1972). The definition of this measure is extended to cover also the stratified Cox model.     

Correlation Goodness‐of‐fit Test for the Logarithmically‐Decreasing Survival Distribution

In this paper, we use the correlation‐type goodness‐of‐fit test for the logarithmically‐decreasing survival distribution. This model was intoduced by Sultan , Balakrishnan and Childs (2001) as a special case of Type‐I truncated logistic distribution. The power of the test based on normal, Weibull and gamma distributions is also calculated. We also give application to real example.     

Finite Sample Properties of the Maximum Likelihood Estimator and of Likelihood Ratio Tests in Hidden Markov Models

Hidden Markov models were successfully applied in various fields of time series analysis, especially for analyzing ion channel recordings. The maximum likelihood estimator (MLE) has recently been proven to be asymptotically normally distributed. Here, we investigate finite sample properties of the MLE and of different types of likelihood ratio tests (LRTs) by means of simulation studies. The MLE is shown to reach the asymptotic behavior within sample sizes that are common for various applications. Thus, reliable estimates and confidence intervals can be obtained. We give an approximative scaling function for the estimation error for finite samples, and investigate the power of different LRTs suitable for applications to ion channels, including tests for superimposed hidden Markov processes. Our results are applied to physiological sodium channel data.