Semiparametric Transformation Cure Models with Heteroscedasticity
Date Issued
2004
Date
2004
Author(s)
Chen, Chyong-Mei
DOI
en-US
Abstract
Survival analysis is a very useful statistical methodology to evaluate the efficiency of a treatment in the biomedical study with censored data. Typical survival models assume that the events will occur eventually for all subjects such that everyone has a finite failure time. In the recent two decades, the cure models have received more attentions to consider the problem that some people are cured permanently without failure times. The cure models can also be used to deal with nonsusceptible problems, such as age onset problems in which some people are susceptible to a disease but some are not. A cure model considers the distribution of event times of the susceptible with a typical survival model, for example, Cox's regression model and the accelerated failure time model. These models share the same representations of transformation models but do not consider the heteroscedasticity.
This dissertation proposes a more general class of failure models, semiparametric heteroscedastic transformation cure models, to fit the binary random variable for the occurrence of cure by a logistic regression and the event time of the non-cured by a heteroscedastic transformation model. The heteroscedastic transformation model can describe the phenomenon of crossing in survival curves.
Being motivated from Hsieh (2001) and Lu and Ying (2004), our proposed model adds the cure probability to Hsieh's heteroscedastic hazards regression model, or, equivalently, the heteroscedasticity to the semiparametric transformation cure model of Lu and Ying. The family of heteroscedastic transformation models allows different variances in a transformation model, and therefore includes Hsieh's heteroscedastic hazards regression model and the heteroscedastic proportional odds model by, respectively, specifying the extreme value distribution and the logistic distribution for error terms.
The principle of constructing estimating equations for the regression parameters is motivated from nonparametric maximum likelihood estimates and the martingale theory. Given a specific form of the transformation function, these estimating equations of regression parameters can be identically constructed based on Godambe's estimating function theory (1985) for martingale processes. In this situation, our approach is optimal in Godambe's criterion, while the optimality is not attainable in the reduced case of Lu and Ying. The relevant statistical properties of the estimators from the estimating equations include consistency, asymptotically normal distribution and a closed form of the asymptotical variance-covariance matrix. Simulation studies are performed to validate the large sample properties. We also compare the efficiency with estimators of Lu and Ying under the homoscedasticity through simulation studies. A real data analysis is conducted as an illustration.
Subjects
治癒模型
科克斯模型
不等變異性之風險迴歸模型
轉換模型
鞅論
估計方程式
transformation models
martingale processes
cure models
heteroscedastic hazards regression model
estimating equations
Type
thesis
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