Statistics and Its Interface

Volume 9 (2016)

Number 2

Semiparametric transformation models with length-biased and right-censored data under the case-cohort design

Pages: 213 – 222



Huijuan Ma (Department of Biostatistics and Bioinformatics, Emory University, Atlanta, Georgia, U.S.A.)

Zhiping Qiu (School of Mathematical Sciences, Huaqiao University, Quanzhou, Fujian, China)

Yong Zhou (Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China; and School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai, China)


Case-cohort designs provide a cost effective way in large cohort studies. Semiparametric transformation models, which include the proportional hazards model and the proportional odds model as special cases, are considered here for length-biased right-censored data under case-cohort design. Weighted estimating equations, which can be used even when the censoring variables are dependent of the covariates, are proposed for simultaneous estimation of the regression parameters and the transformation function. The resulting regression estimators are shown to be asymptotically normal with a closed form of variance-covariance matrix and can be estimated by the plug-in method. Simulation studies show that the proposed approach performs well for practical use. An application to the Oscar data is also given to illustrate the methodology.


case-cohort design, length-biased and right-censored data, mean zero process, transformation model, weighted estimating equation

Published 4 November 2015