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A recharacterization of the semi-Markov model described by Lagakos, Sommer & Zelen (1978) permits the nonparametric maximum likelihood estimators to be expressed in terms of familiar and easily computable quantities, such as event-specific hazard estimators and Kaplan & Meier (1958) survival estimators. In addition to simplifying the calculation and clarifying the interpretation of the previously derived estimators, this reformulation also facilitates the estimation of covariance terms and suggests a simple test of equality among the outcome-specific distributions of sojourn times in a particular state.
Dinse et al. (Wed,) studied this question.