AbstractsMathematics

Many algorithms have been developed over the years to compute the nonparametric maximum likelihood estimate (NPMLE) for the cumulative distribution function of event times under interval censoring. The effective support of the NPMLE can be reduced to a set of disjoint so-called maximal intersection intervals. One feature of the NPMLE that is sometimes described as unsatisfactory is that, with most data sets, several of the estimated probabilities are equal to zero, implicitly inducing an ordering between overlapping intervals and leaving the user with a rather coarse estimate of the CDF. We attempt to overcome this problem by focusing on the natural interval order the censored data describe. A Precedence Probability Matrix (PPM) for the data can be constructed, an object that uses information about all the possible orderings within the interval order. By estimating the true PPM – in itself a non-trivial task – and penalising the nonparametric log-likelihood for deviations from the data’s true PPM, smoother estimates of the CDF that better represent the possible ordering of the data can be acquired.