Methods for bounding the marginal survival distribution

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Abstract
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.