Single-Index Models with a Surface-Link

An implementation of a single-index regression for optimizing individualized dose rules from an observational study. To model interaction effects between baseline covariates and a treatment variable defined on a continuum, we employ two-dimensional penalized spline regression on an index-treatment domain, where the index is defined as a linear combination of the covariates (a single-index). An unspecified main effect for the covariates is allowed, which can also be modeled through a parametric model. A unique contribution of this work is in the parsimonious single-index parametrization specifically defined for the interaction effect term. We refer to Park, Petkova, Tarpey, and Ogden (2020) (for the case of a discrete treatment) and Park, Petkova, Tarpey, and Ogden (2021) "A single-index model with a surface-link for optimizing individualized dose rules" for detail of the method. The model can take a member of the exponential family as a response variable and can also take an ordinal categorical response. The main function of this package is simsl().