Weighted Semiparametric Likelihood Method for Fitting a Proportional Odds Regression Model to Data From the Case-Cohort Design

Abstract

The problem of fitting a proportional odds regression model to data from the case-cohort design proposed by Prentice is considered. A weighted semiparametric likelihood method is proposed. Under the proportional odds model, the maximum weighted-semiparametric likelihood estimators of both the regression parameter and the transformation function are shown to be consistent and normally distributed. The applicability of the weighted semiparametric likelihood method to the semiparametric transformation regression models is also discussed. In particular, when the proportional hazards regression model is fitted, estimators proposed by Chen and Lo can be generated by the weighted semiparametric likelihood method under different weighting schemes. A simulation study suggests that the case-cohort design is also useful under the proportional odds regression model and the proposed method performs well with practical finite sample sizes.