Interval censored data: A note on the nonparametric maximum likelihood estimator of the distribution function

Gentleman & Geyer (1994) discuss the analysis of interval censored data and present results based on standard convex optimisation theory. Here, this problem is viewed from the perspective of a mixing problem of indicator functions. Using an analogy with the problem of mixture distributions a variety of results are easily derived, including a characterisation theorem for the maximum likelihood estimator and various reliably convergent algorithms. Software for the analysis of mixture distributions can be used to find the nonparametric estimate of the distribution function of the interval-censored survival time. Examples are provided to demonstrate the theory