Partially linear transformation model for length-biased and right-censored data

• Published in: Journal of nonparametric statistics Vol. 30; no. 2; pp. 332 - 367
• Main Authors: Wei, Wenhua, Wan, Alan T. K., Zhou, Yong
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis Ltd 03.04.2018
• Subjects: Asymptotic methods; Biometrics; Censored data (mathematics); Computer simulation; Estimation; Iterative methods; Linear transformations; Resampling
• ISSN: 1048-5252; 1029-0311
• DOI: 10.1080/10485252.2018.1424335

In this paper, we consider a partially linear transformation model for data subject to length-biasedness and right-censoring which frequently arise simultaneously in biometrics and other fields. The partially linear transformation model can account for nonlinear covariate effects in addition to linear effects on survival time, and thus reconciles a major disadvantage of the popular semiparamnetric linear transformation model. We adopt local linear fitting technique and develop an unbiased global and local estimating equations approach for the estimation of unknown covariate effects. We provide an asymptotic justification for the proposed procedure, and develop an iterative computational algorithm for its practical implementation, and a bootstrap resampling procedure for estimating the standard errors of the estimator. A simulation study shows that the proposed method performs well in finite samples, and the proposed estimator is applied to analyse the Oscar data.