Methods for bounding the marginal survival distribution.

For time to event data with many potential failure types, one cannot uniquely determine the distribution of time to a specific event type, or marginal survival distribution, in the case where event types are mutually exclusive. In this paper we discuss several methods for estimating functions that bound the non-identifiable marginal survival distribution in the competing risks problem. We compute and compare bounds for data simulated from two bivariate survival distributions. Results show that the methods provide a suitable estimate of the marginal survival probability when one has specified dependence correctly. Data from a large clinical trial for breast cancer illustrate the methods.