title: Multiple imputation for cure rate quantile regression with censored data.
abstract: The main challenge in the context of cure rate analysis is that one never knows whether censored subjects are cured or uncured, or whether they are susceptible or insusceptible to the event of interest. Considering the susceptible indicator as missing data, we propose a multiple imputation approach to cure rate quantile regression for censored data with a survival fraction. We develop an iterative algorithm to estimate the conditionally uncured probability for each subject. By utilizing this estimated probability and Bernoulli sample imputation, we can classify each subject as cured or uncured, and then employ the locally weighted method to estimate the quantile regression coefficients with only the uncured subjects. Repeating the imputation procedure multiple times and taking an average over the resultant estimators, we obtain consistent estimators for the quantile regression coefficients. Our approach relaxes the usual global linearity assumption, so that we can apply quantile regression to any particular quantile of interest. We establish asymptotic properties for the proposed estimators, including both consistency and asymptotic normality. We conduct simulation studies to assess the finite-sample performance of the proposed multiple imputation method and apply it to a lung cancer study as an illustration.
authors.affiliation: School of Mathematics and Statistics, Wuhan University, Wuhan, Hubei 430072, China.
authors.forename: Yuanshan
authors.initials: Y
authors.lastname: Wu
authors.affiliation: Department of Statistics and Actuarial Science, University of Hong Kong, Pokfulam Road, Hong Kong.
authors.forename: Guosheng
authors.initials: G
authors.lastname: Yin
mesh_terms: D000328:Adult; D000368:Aged; D000369:Aged, 80 and over; D000465:Algorithms; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D006801:Humans; D008175:Lung Neoplasms / Q000401:mortality / Q000628:therapy; D008875:Middle Aged; D015233:Models, Statistical; D011336:Probability; D012044:Regression Analysis; D016019:Survival Analysis
keywords: Censored data; Censored quantile regression; Cure rate model; Missing data; Multiple imputation; Survival fraction