Transformation Models for Survival Data Analysis with Applications

Abstract

When the event of interest never occurs for a proportion of subjects during the study period, survival models with a cure fraction are more appropriate in analyzing this type of data. Considering the non-linear relationship between response variable and covariates, we propose a class of generalized transformation models motivated by Zeng et al. [1] transformed proportional time cure model, in which fractional polynomials are used instead of the simple linear combination of the covariates. Statistical properties of the proposed models are investigated, including identifiability of the parameters, asymptotic consistency, and asymptotic normality of the estimated regression coefficients. A simulation study is carried out to examine the performance of the power selection procedure. The generalized transformation cure rate models are applied to the First National Health and Nutrition Examination Survey Epidemiologic Follow-up Study (NHANES1) for the purpose of examining the relationship between survival time of patients and several risk factors.