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Detecting multiple change points in piecewise constant hazard functions

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The National Cancer Institute (NCI) suggests a sudden reduction in prostate cancer mortality rates, likely due to highly successful treatments and screening methods for early diagnosis. We are interested in understanding the impact of medical breakthroughs, treatments, or interventions, on the survival experience for a population. For this purpose, estimating the underlying hazard function, with possible time change points, would be of substantial interest, as it will provide a general picture of the survival trend and when this trend is disrupted. Increasing attention has been given to testing the assumption of a constant failure rate against a failure rate that changes at a single point in time. We expand the set of alternatives to allow for the consideration of multiple change-points, and propose a model selection algorithm using sequential testing for the piecewise constant hazard model. These methods are data driven and allow us to estimate not only the number of change points in the hazard function but where those changes occur. Such an analysis allows for better understanding of how changing medical practice affects the survival experience for a patient population. We test for change points in prostate cancer mortality rates using the NCI Surveillance, Epidemiology, and End Results dataset.
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Keywords: cancer; change points; hazard function; piecewise constant; survival analysis

Document Type: Research Article

Affiliations: 1: Graduate Program in Public Health, Department of Preventive Medicine,Stony Brook University School of Medicine, Stony BrookNY, USA 2: Department of Biostatistics, Harvard University and Department of Biostatistics and Computational Biology,Dana Farber Cancer Institute, BostonMA, USA 3: Office of Biostatistics, Center for Drug Evaluation and Research, Food and Drug AdministrationSilver SpringMD, USA

Publication date: November 1, 2011

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