A Nonparametric Estimation Procedure for a Periodically Observed Three-State Markov Process, with Application to Aids

SUMMARY Estimation in a three-state Markov process with irreversible transitions in the presence of interval-censored data is considered. A nonparametric maximum likelihood procedure for the estimation of the cumulative transition intensities is presented. A self-consistent estimator of the parameters is defined and it is shown that the maximum likelihood estimator is a self-consistent estimator. This extends the idea of self-consistency introduced by Efron to the estimation of more than one parameter. An algorithm, based on self-consistency equations, is provided for the computation of the estimators. This algorithm is a generalization of an algorithm by Turnbull which yields an estimator of a distribution function for interval-censored univariate data. The methods are applied to Aids data.