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

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.