Nonparametric Estimation of Transition Intensities and Transition Probabilities: A Case Study of a Two‐State Markov Process

Aalen and Johansen have developed a powerful methodology of nonparametric inference on transition probabilities of discrete state Markov processes based on Aalen's framework for statistical inference based on counting processes. Because very few numerical case studies are on record, we present here some calculations for a two‐state process: psychiatric admissions and discharges of all Danish women who gave birth in 1975. We also present results on kernel function smoothing of the transition intensities following Ramlau‐Hansen. The methodology may be relevant for the study of reversible diseases. Although our main example concerns uncensored data, we briefly illustrate the application of the Aalen‐Johansen methods to censored data by presenting a simple calculation of confidence bounds for a ‘cumulative incidence’ recently studied by Matthews using a different approach.