A missing data approach to semi-competing risks problems

For event time data involving multiple mutually exclusive competing causes of failure, classic competing risks results show that marginal survival distributions are not identifiable. In a related instance, one or more failure modes may be observed provided that the failure events occur in a specific order. In such situations, sometimes referred to as semi-competing risks problems, the observations may under realistic assumptions lend information about parameters of interest that would be nonidentifiable in the strict competing risks case. Here, we present an approach that makes use of partially observable multiple modes of failures to obtain an estimate of the marginal distribution of one event type that may occur prior to the occurrence of another event type or be precluded by it. We apply the proposed method to the problem of estimating the distribution of time to tumour recurrence at specific sites among breast cancer patients participating in randomized clinical trials.