Longitudinal studies allow us to investigate the natural history of chronic diseases. For some diseases the evolution of the process is characterized by transitions between a series of health states. For example, in cancer, subjects may transition from a cancer-free state to early stage disease, and subsequently to late stage disease. Semi-Markov processes provide a flexible framework for modeling multi-state disease processes. However, limited estimation methods are available for the application of Semi-Markov processes to the study of multi-state disease. Existing estimation methods require the imposition of numerous assumptions on the process, which may not be biologically plausible for many diseases. The lack of estimation methods is particularly acute for data collected under panel observation. In this proposal we develop flexible and biologically appropriate methods for estimating Semi-Markov processes in longitudinal multi-state disease studies. We propose a class of time transformation functions that allows us to bridge Semi-Markov and Markov processes in order to harness the straightforward estimation methods available for Markov processes. We then propose to use mixture models, coupled with a set of biologically reasonable assumptions, to extend these methods to allow for estimation under panel observation. These methods will be applied to the estimation of breast cancer recurrence rates and rates of second primary breast cancers subsequent to an incident breast cancer. Using 13 years of longitudinal data from the Breast Cancer Surveillance Consortium, we will demonstrate improved performance of our novel methods for estimating transition rates among breast event states relative to Markov process models and proportional hazards survival models.
Semi-Markov processes provide a flexible framework for modeling multi-state diseases characterized by transitions between a series of health states. However, limited estimation methods are available for the application of such processes. We will develop flexible methods for estimating Semi-Markov processes and will use our novel estimation methods to study rates of breast cancer recurrence and second primary breast cancers subsequent to an incident breast cancer using longitudinal data from the Breast Cancer Surveillance Consortium.
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