Using ml to estimate competing-risk models under interval censoring

Competing-risk models are survival models in which there is more than one type of event of interest. In the case where events can be treated as occurring at discrete, regularly-spaced times, it is relatively simple to estimate models for the hazard rates and to account for left-truncation and right-censoring. However, when one of the events may be left-censored, or, more generally, interval-censored, the likelihood function no longer takes a simple form, and estimation becomes more difficult -- or would, if not for Stata's ml command. We show how the ml command can be used to estimate discrete-time competing-risk models in the presence of interval censoring, with an application to modeling mortgage commitments.