Nonparametric inference and uniqueness for periodically observed progressive disease models |
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Authors: | Beth Ann Griffin Stephen W Lagakos |
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Institution: | (1) RAND Corporation, 1200 South Hayes Street, Arlington, VA 22202, USA;(2) Department of Biostatistics, Harvard University, Boston, MA 02115, USA |
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Abstract: | In many studies examining the progression of HIV and other chronic diseases, subjects are periodically monitored to assess
their progression through disease states. This gives rise to a specific type of panel data which have been termed “chain-of-events
data”; e.g. data that result from periodic observation of a progressive disease process whose states occur in a prescribed
order and where state transitions are not observable. Using a discrete time semi-Markov model, we develop an algorithm for
nonparametric estimation of the distribution functions of sojourn times in a J state progressive disease model. Issues of uniqueness for chain-of-events data are not well-understood. Thus, a main goal
of this paper is to determine the uniqueness of the nonparametric estimators of the distribution functions of sojourn times
within states. We develop sufficient conditions for uniqueness of the nonparametric maximum likelihood estimator, including
situations where some but not all of its components are unique. We illustrate the methods with three examples. |
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