title: Optimal estimation for regression models on τ-year survival probability.
abstract: A logistic regression method can be applied to regressing the [Formula: see text]-year survival probability to covariates, if there are no censored observations before time [Formula: see text]. But if some observations are incomplete due to censoring before time [Formula: see text], then the logistic regression cannot be applied. Jung (1996) proposed to modify the score function for logistic regression to accommodate the right-censored observations. His modified score function, motivated for a consistent estimation of regression parameters, becomes a regular logistic score function if no observations are censored before time [Formula: see text]. In this article, we propose a modification of Jung's estimating function for an optimal estimation for the regression parameters in addition to consistency. We prove that the optimal estimator is more efficient than Jung's estimator. This theoretical comparison is illustrated with a real example data analysis and simulations.
authors.affiliation: a Department of Statistics , Yeungnam University , Gyeongsan , Gyeongbuk , ROK.
authors.forename: Minjung
authors.initials: M
authors.lastname: Kwak
authors.forename: Jinseog
authors.initials: J
authors.lastname: Kim
authors.forename: Sin-Ho
authors.initials: SH
authors.lastname: Jung
mesh_terms: D001699:Biometry / Q000379:methods*; D003198:Computer Simulation; D006801:Humans; D053208:Kaplan-Meier Estimate; D016015:Logistic Models; D010634:Phenobarbital / Q000627:therapeutic use; D016032:Randomized Controlled Trials as Topic / Q000706:statistics & numerical data; D012044:Regression Analysis; D012640:Seizures / Q000453:epidemiology / Q000517:prevention & control; D016008:Statistical Distributions; D016019:Survival Analysis
chemical_list: D010634:Phenobarbital
keywords: Censoring distribution; Logistic regression; Non-negative definite; Survival probability