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Nonparametric Estimation in a Markov “Illness–Death” Process from Interval Censored Observations with Missing Intermediate Transition Status


  • Halina Frydman,

    Corresponding author
    1. Stern School of Business, New York University, 44 West 4th Street, New York, New York 10012, U.S.A.
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  • Michael Szarek

    1. Division of Biostatistics, NYU School of Medicine, 650 First Avenue, New York, New York 10016, U.S.A.
    2. ImClone Systems Incorporated, 33 ImClone Drive, Branchburg, New Jersey 08876, U.S.A.
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Summary In many clinical trials patients are intermittently assessed for the transition to an intermediate state, such as occurrence of a disease-related nonfatal event, and death. Estimation of the distribution of nonfatal event free survival time, that is, the time to the first occurrence of the nonfatal event or death, is the primary focus of the data analysis. The difficulty with this estimation is that the intermittent assessment of patients results in two forms of incompleteness: the times of occurrence of nonfatal events are interval censored and, when a nonfatal event does not occur by the time of the last assessment, a patient's nonfatal event status is not known from the time of the last assessment until the end of follow-up for death. We consider both forms of incompleteness within the framework of an “illness–death” model. We develop nonparametric maximum likelihood (ML) estimation in an “illness–death” model from interval-censored observations with missing status of intermediate transition. We show that the ML estimators are self-consistent and propose an algorithm for obtaining them. This work thus provides new methodology for the analysis of incomplete data that arise from clinical trials. We apply this methodology to the data from a recently reported cancer clinical trial (Bonner et al., 2006, New England Journal of Medicine354, 567–578) and compare our estimation results with those obtained using a Food and Drug Administration recommended convention.