Nonparametric maximum likelihood estimation for artificially truncated absence data

In manpower planning it is commonly the case that employees withdraw from active service for a period of time before returning to take up post at a later date. Such periods of absence are frequently of major concern to employers who are anxious to ensure that employees return as soon as possible. The distribution of duration of such periods of absence are therefore of considerable interest as is the probability that such employees will ever return to active service. In this paper we derive a nonparametric estimator for such a lifetime distribution based on renewal data which are subject to various forms of incompleteness, namely right censoring, left and right truncation, and forward recurrence. Artificial truncation is used to ensure that the data are time homogeneous. A nonparametric maximum likelihood estimator for the lifetime distribution is derived using the EM algorithm. The data analysed concern the Northern Ireland nursing profession.