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Biostatistics Advance Access originally published online on June 22, 2005
Biostatistics 2006 7(1):71-84; doi:10.1093/biostatistics/kxi041
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© The Author 2005. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oupjournals.org.

Extreme regression

Michael LeBlanc*, James Moon and Charles Kooperberg

Fred Hutchinson Cancer Research Center, 1100 Fairview Avenue North, M3-C102, Seattle, WA 98109, USA mleblanc{at}fhcrc.org

* To whom correspondence should be addressed.

We develop a new method for describing patient characteristics associated with extreme good or poor outcome. We address the problem with a regression model composed of extrema (maximum and minimum) functions of the predictor variables. This class of models allows for simple regression function inversion and results in level sets of the regression function which can be expressed as interpretable Boolean combinations of decisions based on individual predictors. We develop an estimation algorithm and present clinical applications to symptoms data for patients with Hodgkin's disease and survival data for patients with multiple myeloma.

Keywords: Decision rules; HARE; Non-linear MARS; Prognostic groups; Regression; Survival; Tree-based models


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