A proportional hazards model for time-to-event data with epidemiological bias

In hepatitis C virus (HCV) epidemiological studies, the estimation of progression to cirrhosis and prognostic effects of associated risk factors is of particular importance when projecting national disease burden. However, the progression estimates obtained from conventional methods could be distorted due to a referral bias (Fu et al., 2007). In recent years, several approaches have been developed to handle this epidemiological bias in analyzing time-to-event data. This paper proposes a new estimation approach for this problem under a semiparametric proportional hazards framework. The new method uses a martingale approach based on the mean rate function, rather than the traditional hazard rate function, and develops an iterative algorithm to estimate the Cox regression parameter and baseline hazard rate simultaneously. The consistency and asymptotic properties of the proposed estimators are derived theoretically and evaluated via simulation studies. The new method is also applied to a real HCV cohort study.