Multiple Imputation Approach For Linear Transformation Cure Models

Survival analysis is a subject studying statistical methods for analyzing and modeling lifetime data or failure time data.One of the difficulties in analyzing survival data is that the data are very likely to be right or interval censored in practice.Such data analysis may be conducted under the setting where a fraction of patients can be considered as fully recovered and will not experience the event of interest in the future;while the other patients who did not recover totally will have the outcome of interest.When we analyze the censored data through the analysis method of the existing complete data,the reliability of the results will be reduced because of the censorship of some state variables.Therefore,it is urgent to study the censored data.There are various categories of censoring,such as right censoring,left censoring,and interval censoring.In this paper,we focus on the right censored data.Besides,the cure model is a very popular analysis method for survival data when a subgroup of patients are cured and there are two classes of cure rate models developed in the literature,one class is promotion time(non-mixture)cure models,the other is cure rate models.We consider flexible linear transformation models.By applying the underlying relationship between the transformation function and the baseline hazard function,we turn to estimate the latter alternatively.And by adopting the Bernstein polynomials,we can conveniently add shape constraints to the baseline hazard function according to different types of data.Bernstein polynomials have very appealing shape preserving properties and can convert the nonparametric estimation to the parameter estimation,which can help improve the performance of the estimation.At the same time,we propose a multiple imputation approach to solve the problem which part of the cure indicators is missing in right censored data based on the linear transformation cure model.And the results are compared with the maximum likelihood estimation method.By giving biases,standard deviation,coverage probability and other indexes,we show the advantages and the validity of our proposed method.We conduct extensive simulation studies and apply our estimation method to the bone marrow transplantation data from 1985 to 1991,verifying and evaluating this method.