Survival attributable to an exposure

In the survival analysis context, when an intervention either reduces a harmful exposure or introduces a beneficial treatment, it seems useful to quantify the gain in survival attributable to the intervention as an alternative to the reduction in risk. To accomplish this we introduce two new concepts, the attributable survival and attributable survival time, and study their properties. Our analysis includes comparison with the attributable risk function as well as hazard-based alternatives. We also extend the setting to the case where the intervention takes place at discrete points in time, and may either eliminate exposure or introduce a beneficial treatment in only a proportion of the available group. This generalization accommodates the more realistic situation where the treatment or exposure is dynamic. We apply these methods to assess the effect of introducing highly active antiretroviral therapy for the treatment of clinical AIDS at the population level.