Regression Inference With Censoring Indicators Missing At Random

Survival analysis encompasses a wide variety of methods for analyzing the tim-ing of events. Analysis of failure time in biostatistics has the richest tradition in thisarea. Linear regression model with censored failure time data is applied frequently inmany statistical areas. Various estimating approaches have been suggested. Censoreddata with missing indicators appear when the censoring indicator, which represents theinformation if the observed time is the survival time of interest or the censoring time,is missing. We consider the estimation of regression parameter, in which the responsevariable Y is censored by C. We can only observed (Y|~) = min(Y,C). The censor-ing indicator isδ= I(Y≤C), whileδis not completely observed.ξis the missingindicator.In chapter 2, we study linear regression analysis when some of the censoring in-dicators are missing at random. We propose regression calibration type estimation,imputation type estimation and augmented inverse probability weighting (AIPW) typeestimation by modifying the weighted least squared estimator to adapt missing indica-tor. We show that all our estimators'consistency and asymptotical normal property.Moreover, the AIPW type estimator can be proved consistent as long as the assumptionE(ξ|(Y|~) ) = E(ξ|(Y|~) ,X) is valid, or the censoring indicator parametric regression modelis specified correctly. The simulation part shows the finite properties of the proposedestimator, and two real data examples are provided to illustrate our methods.In Chapter 3, we consider the augmented inverse probability weighted type es-timator involves . We assume parametric model to estimate the propensity functionE[ξ|X, (Y|~) ] and the censoring indicator regression function E[δ|X, (Y|~) ], respectively. Ourprocedure adjust the method proposed by Cao et al (2009), Duan et al (2010) to themissing censoring indicator problem. When propensity function is correctly specified,the proposed estimator has the smallest trace of the asymptotic covariance matrix. Thesimulation study indicates that the proposed methodology performs well for practicalsituations. Two illustrative examples from clinical trial are provided.In Chapter 4, we assume that the propensity function can be specified correctly.Motivated by Qin et al (2008), in which they proposed an doubly robust imputationtype estimator for missing responses, we develop a procedure in the missing censoringindicator situation. The estimator based on imputation and empirical likelihood . It isworthnotingthattheproposedestimatorisconsistentevenwhenthecensoringindicator regression model is misspecified. A simulation study was conducted for the evaluationof the finite sample performance of the proposed methodology and indicates that theapproach performs well for practical situations. Two illustrative examples from clinicaltrial are provided.In Chapter 5, we extend the rank-based inference for the censored accelerated fail-ure time (AFT) model to the case when some of the censoring indicators are missingat random. We prove the estimators are asymptotically normal. Then we propose aniterative algorithm to solve the calculation problem. A simulation study was conductedto evaluate the finite properties of the proposed estimator, and two real data examplesare provided to illustrate our methods.