Tree-Structured and Direct Parametric Regression Models for the Subdistribution of Competing Risks

Traditionally, the regression analysis for competing risks survival time is based on the cause-specific hazard that treat failures from causes other than the cause of interest as censored observations. That includes technique such as the Cox proportional hazard model. The modelling of hazard rate may or may not match the objective of investigator. It is often more desirable to investigate the subdistribution function, because cause-specific hazard doesn’t obviously give the information about proportion of individuals experiencing a cause of interest. Furthermore, the subdistribution and cause-specific hazard function are not interchangeable. Thus, if we intended to draw inference from subdistribution function, then we must model on subdistribution function directly or indirectly. Sometimes, we do not only intend to investigate the relationship between response and covariates through regression analysis, but also we want to identify the presence of subgroup of individuals in our data. We could then utilize tree-structured regression for this purpose. In this thesis, we developed statistical methods for competing risks data analysis through direct, indirect and parametric subdistribution modelling. Indirect model is employed via hazard of subdistribution. Evaluation of the performance of proposed methods is conducted through series of simulation studies as well as real data application. We developed four methods: 1) a method to categorize continuous covariate by considering the competing risks survival time outcome variables, called outcome-oriented categorization method, 2) a tree-structured competing risks regression to extract meaningful sub-groups of subjects determined by the value of covariates, 3) a hybrid model which boost the available subdistribution hazards regression by ugmenting it with tree-structured regression resulted from the previous step, 4) two kinds of parametric direct subdistribution model. These models are constructed based on non-mixture cure model. The first model is developed by taking into account the fraction of individuals who did not experience the event of interest in the long term. The second model is developed by reparameterizing the first model in order to mimic Gompertz distribution which allows no immune fraction. Research finding is as follows: 1) Method of outcome-oriented categorization based on deviance statistic is the best. The application of the method to contraceptive discontinuation data showed good result. 2) Regression tree for competing risks data can uncover the structure of data and yield the sub-group of individuals with a clear description based on their covariates. The application of the method to contraceptive discontinuation data showed good result. Extensive Monte Carlo simulation suggests the method has good performance in identifying the structure of data. 3) Application of the hybrid model to the contraceptive discontinuation data showed that the hybrid model is better than the available subdistribution regression in terms of AIC. 4) By using some well known kernel distribution, the parametric direct subdistribution models are developed. The maximum likelihood estimations are carried out simultaneously for all causes of event. In Bone Marrow Transplantation (BMT) data analysis, the first proposed model gave noticeably good fit to the nonparametric counterpart. The second proposed model is fitted to contraceptive discontinuation data and showed that Gompertz-like subdistribution with Gompertz kernel is the best fit.

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