Analysis of functional status transitions by using a semi-Markov process model in the presence of left-censored spells

To analyse functional status transitions in the older population better, we fit a semi-Markov process model to data from the 1992-2002 Medicare Current Beneficiary Survey We used an analogue of the stochastic EM algorithm to address the problem of left censoring of spells in longitudinal data. The iterative algorithm converged robustly under various initial values for the unobserved elapsed durations of spells in progress at base-line. Results on life expectancy and recovery from functional limitations based on the semi-Markov process model differ from those based on the traditional multistate life-table method. The proposed treatment of left-censored spells has the potential to expand the modelling capability that is available to researchers in fields where left censoring is a concern.