title: A semiparametric mixture cure survival model for left-truncated and right-censored data.
abstract: In follow-up studies, the disease event time can be subject to left truncation and right censoring. Furthermore, medical advancements have made it possible for patients to be cured of certain types of diseases. In this article, we consider a semiparametric mixture cure model for the regression analysis of left-truncated and right-censored data. The model combines a logistic regression for the probability of event occurrence with the class of transformation models for the time of occurrence. We investigate two techniques for estimating model parameters. The first approach is based on martingale estimating equations (EEs). The second approach is based on the conditional likelihood function given truncation variables. The asymptotic properties of both proposed estimators are established. Simulation studies indicate that the conditional maximum-likelihood estimator (cMLE) performs well while the estimator based on EEs is very unstable even though it is shown to be consistent. This is a special and intriguing phenomenon for the EE approach under cure model. We provide insights into this issue and find that the EE approach can be improved significantly by assigning appropriate weights to the censored observations in the EEs. This finding is useful in overcoming the instability of the EE approach in some more complicated situations, where the likelihood approach is not feasible. We illustrate the proposed estimation procedures by analyzing the age at onset of the occiput-wall distance event for patients with ankylosing spondylitis.
authors.affiliation: Institute of Public Health, School of Medicine, National Yang-Ming University, Taipei City, Taiwan.
authors.forename: Chyong-Mei
authors.initials: CM
authors.lastname: Chen
authors.affiliation: Department of Statistics, Tunghai University, Taichung City, Taiwan.
authors.forename: Pao-Sheng
authors.initials: PS
authors.lastname: Shen
authors.affiliation: Division of Allergy, Immunology and Rheumatology, Department of Medicine, Chung Shan Medical University Hospital, Taichung City, Taiwan.|Division of Allergy, Immunology and Rheumatology, Chung Shan Medical University Hospital, Taichung City, Taiwan.
authors.forename: James Cheng-Chung
authors.initials: JC
authors.lastname: Wei
authors.affiliation: Division of Allergy, Immunology and Rheumatology, Chung Shan Medical University Hospital, Taichung City, Taiwan.|Department of Statistics, Oklahoma State University, Stillwater, OK 74074, USA.
authors.forename: Lichi
authors.initials: L
authors.lastname: Lin
mesh_terms: D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D006801:Humans; D016013:Likelihood Functions; D015233:Models, Statistical; D012044:Regression Analysis; D013167:Spondylitis, Ankylosing / Q000401:mortality; D016019:Survival Analysis
keywords: Conditional likelihood; Cure; Estimating equation; Left truncation; Transformation