Statistics and Its Interface

Volume 12 (2019)

Number 1

A semiparametric linear transformation model for general biased-sampling and right-censored data

Pages: 77 – 92



Wenhua Wei (School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai, China)

Yong Zhou (Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China)

Alan T. K. Wan (Department of Management Sciences, City University of Hong Kong, Kowloon, Hong Kong)


The semiparametric linear transformation (SLT) model is a useful alternative to the proportional hazards ([9]) and proportional odds ([4]) models for studying the dependency of survival time on covariates. In this paper, we consider the SLT model for biased-sampling and right-censored data, a feature commonly encountered in clinical trials. Specifically, we develop an unbiased estimating equations approach based on counting process for the simultaneous estimation of unknown coefficients and handling of sampling bias. We establish the consistency and the asymptotic normality of the proposed estimator, and provide a closed form expression for the estimator’s covariance matrix that can be consistently estimated by a plug-in method. In a simulation study, we compare the finite sample properties of the proposed estimator with those of existing methods that either assumes that the sampling bias is of the length-bias type, or ignores the sampling bias altogether. The proposed method is further illustrated by two real clinical datasets.


biased-sampling, estimating equation, right-censoring, semiparametric linear transformation model

2010 Mathematics Subject Classification

Primary 62N01. Secondary 62F12.

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Wei’s work was supported by a research fund from the Shanghai University of Finance and Economics (No. 2017110070). 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). Wan’s work was supported by a Theme-Based Research Scheme (No. T32-102/14N) and a General Research Fund (No. 9042086), both from the Hong Kong Research Grants Council, and a strategic grant from the City University of Hong Kong (No. 7004786). We thank the editor, the associate editor and two referees for helpful comments on an earlier draft of the paper. The usual disclaimer applies.

Received 15 April 2017

Published 26 October 2018