In causal mediation analysis, nonparametric identification of the natural indirect effect typically relies on, in addition to no unobserved pre-exposure confounding, fundamental assumptions of (i) so-called \"cross-world-countterfactuals\" independence and (ii) no exposure-induced confounding. When the mediator is binary, bounds for partial identification have been given when neither assumption is made, or alternatively when assuming only (ii). We extend existing bounds to the case of a polytomous mediator, and provide bounds for the case assuming only (i). We apply these bounds to data from the Harvard PEPFAR program in Nigeria, where we evaluate the extent to which the effects of antiretroviral therapy on virological failure are mediated by a patient\'s adherence, and show that inference on this effect is somewhat sensitive to model assumptions.

The main aim of mediation analysis is to study the direct and indirect effects of an exposure on an outcome. To date, the literature on mediation analysis with multiple mediators has mainly focused on continuous and dichotomous outcomes. However, the development of methods for multiple mediation analysis of survival outcomes is still limited. Here we extend to survival outcomes a method for multiple mediation analysis based on the computation of appropriate weights. The approach considered has the advantages of not requiring specific models for mediators, allowing nonindependent mediators of any nature, and not relying on the assumption of rare outcomes. Simulation studies show good performance of the proposed estimator in terms of bias and coverage probability. The method is further applied to an example from a published study on prostate cancer mortality aimed at understanding the extent to which the effect of DNA methyltransferase 3b (DNMT3b) genotype on mortality was explained by DNA methylation and tumor aggressiveness. This approach can be used to quantify the marginal time-dependent direct and indirect effects carried by multiple indirect pathways, and software code is provided to facilitate its application.