Attributable risk function in the proportional hazards model for censored time-to-event

Time-to-event endpoints are often used in clinical and epidemiological studies to evaluate disease association with hazardous exposures. In the statistical literature of time-to-event analysis, such association is usually measured by the hazard ratio in the proportional hazards model. In public health, it is also of important interest to assess the excess risk attributable to an exposure in a given population. In this article, we extend the notion of 'population attributable fraction' for the binary outcomes to the attributable risk function for the event times in prospective studies. A simple estimator of the time-varying attributable risk function is proposed under the proportional hazards model. Its inference procedures are established. Monte-Carlo simulation studies are conducted to evaluate its validity and performance. The proposed methodology is motivated and demonstrated by the data collected in a multicenter acquired immunodeficiency syndrome (AIDS) cohort study to estimate the attributable risk of human immunodeficiency virus type 1 (HIV-1) infections due to several potential risk factors.