Abstract:
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Dimension reduction lies at the heart of many statistical methods. In regression, dimension reduction has been linked to the notion of sufficiency whereby the relation of the response to a set of predictors is explained by a lower dimensional subspace in the predictor space. In this work, we consider the notion of a dimension reduction in regression on subspaces that are sufficient to explain interaction effects between a set of predictors and another variable of interest, leading to a parsimonious parametrization of projection-pursuit regression models specifically defined for the interaction effects. The motivation for this work is from precision medicine where the performance of an individualized does rule, given a set of patient’s characteristics, is determined by interaction effects between dose and patient’s characteristics.
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