On Testing for the Cox Model Using Resampling Methods

This dissertation, "On Testing for the Cox Model Using Resampling Methods" by Jing, Fang, 方婧, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: Abstract of thesis entitled ON TESTING FOR THE COX MODEL USING RESAMPLING METHODS Submitted by FANG JING for the degree of Master of Philosophy at The University of Hong Kong in September 2007 The study of survival data, which is termed survival analysis, is a key topic in statistics. In the past few decades, many potential models have been raised to t the survival data. The Cox proportional hazards model, which suggests a multi- plicative relationship between the lifetime and its covariates, has been one of the most frequently used statistical tools in the analysis of survival data. When analyzing survival data using the Cox model, it is necessary to exam- ine whether the model assumptions are fullled. Many graphical methods were developed to perform model checking in the literature. However, model checks based on graphical plots are rather subjective and quite often lead to incorrect conclusions. Abettermethodforcheckingmodeladequacyistoconstructformal signicance tests. Thisthesisaimsat developingaglobalgoodness-of-t testfortheCoxmodel.Our test statistic is derived from a model-based process which is asymptotically Gaussian. The asymptotic covariance structure of the Gaussian process is rather complicated and depends on the underlying distribution of the data. Thus, the sampling distribution and the asymptotic null distribution of the test statistic are analytically intractable. Todealwiththedistributionalproblemsoftheteststatistic, resamplingtech- niques can be applied to approximate critical values of the test. Burke and Yuen (1995) employed the naive bootstrap method to implement the test for the Cox model. It is well known that another resampling method, namely the random symmetrization (RS) method, is computationally more ecient. This motivates us to make use of the RS method to construct another resampling test for the Cox model. It can be shown that the proposed test is consistent against general alternatives. To assess the performance of the RS test, simulation studies were carried out, and comparisons among the RS test and some other tests in the literature including the afore-mentioned bootstrap test were made. Finally, the RS test was applied to two real data sets. DOI: 10.5353/th_b3955835 Subjects: Random data (Statistics) Survival analysis (Biometry) Gaussian processes