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

Abstract

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.

Keywords:

• Estimating equations
• length-biased sampling
• local linear fitting technique
• partially linear transformation model
• right-censoring

Acknowledgments

We thank the editor, the associate editor and two referees for helpful comments on a earlier draft of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Wei's work was supported by a research fund from the Shanghai University of Finance and Economics (No. 2017110070). Wan's work was supported by a General Research Fund (No. 9042086) from the Hong Kong Research Grants Council and a strategic grant from the City University of Hong Kong (No. 7004786). Zhou's work was supported by the State Key Program in the Major Research Plan of National Natural Science Foundation of China (No. 91546202), the State Key Program of National Natural Science Foundation of China (No. 71331006), and Innovative Research Team of Shanghai University of Finance and Economics (No. IRTSHUFE13122402).