Abstract: This study examines regression analyses of length-biased and right-censored failure time data arising from the short-term and long-term hazard ratio model. Compared with some commonly used models, such as the proportional hazards models, the short-term and long-term hazard ratio model has the advantage of allowing crossing hazard functions and, thus, is more flexible. We propose two methods for estimating the regression parameters, the conditional likelihood approach, and the composite conditional likelihood approach. We establish the asymptotic and finite-sample properties of the proposed estimators, and the numerical results suggest that the methods work well in practical situations. In addition, the approaches are applied to a set of real data arising from a dementia study.

Key words and phrases: Composite likelihood, length-biased, right-censored, short-term and long-term hazard ratio.