Extreme regression.

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.