Estimation for the Cox Model with Biased Sampling Data via Risk Set Sampling

Prevalent cohort sampling is commonly used to study the natural history of a disease when the disease is rare or it usually takes a long time to observe the failure event. It is known, however, that the collected sample in this situation is not representative of the target population which in turn leads to biased sample risk sets. In addition, when survival times are subject to censoring, the censoring mechanism is informative. In this paper, I propose a pseudo-partial likelihood estimation method for estimating parameters in the Cox proportional hazards model with right-censored and biased sampling data by adjusting sample risk sets. I study the asymptotic properties of the resulting estimator and conduct a simulation study to illustrate its finite sample performance of the proposed method. I also use the proposed method to analyze a set of HIV/AIDS data.