Approximate nonparametric corrected-score method for joint modeling of survival and longitudinal data measured with error

• Published in: Biometrical journal Vol. 53; no. 4; pp. 557 - 577
• Main Authors: de Dieu Tapsoba, Jean, Lee, Shen-Ming, Wang, C. Y.
• Format: Journal Article
• Language: English
• Published: Weinheim WILEY-VCH Verlag 01.07.2011; WILEY‐VCH Verlag; Wiley-VCH
• Subjects: Analysis of Variance; Applications; Biology, psychology, social sciences; Corrected score; Cumulant generating function; Exact sciences and technology; General topics; Likelihood Functions; Longitudinal Studies; Mathematics; Measurement error; Multivariate analysis; Nonparametric inference; Probability and statistics; Proportional hazards; Proportional Hazards Models; Random effects; Research Design; Sciences and techniques of general use; Statistics; Statistics, Nonparametric; Survival Analysis; Time Factors; Biometrics; Error estimation; Sample size; Cumulant generating function; Non parametric method; Corrected score; Non parametric estimation; Multivariate analysis; Covariate; Statistical simulation; Medical science; Random effect; Clinical trial; Survival model; Sample survey; Measurement error; Survival data; Approximate method; Generating function; Life science; Asymptotic behavior; Finite sample; AIDS; Random effects; Statistical association; Statistical estimation; Proportional hazards; Random distribution; Infection; Statistical method; Sampling theory; Survival time; Viral disease
• ISSN: 0323-3847; 1521-4036; 1521-4036
• DOI: 10.1002/bimj.201000180

We consider the problem of jointly modeling survival time and longitudinal data subject to measurement error. The survival times are modeled through the proportional hazards model and a random effects model is assumed for the longitudinal covariate process. Under this framework, we propose an approximate nonparametric corrected‐score estimator for the parameter, which describes the association between the time‐to‐event and the longitudinal covariate. The term nonparametric refers to the fact that assumptions regarding the distribution of the random effects and that of the measurement error are unnecessary. The finite sample size performance of the approximate nonparametric corrected‐score estimator is examined through simulation studies and its asymptotic properties are also developed. Furthermore, the proposed estimator and some existing estimators are applied to real data from an AIDS clinical trial.