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Abstract:
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We propose a flexible regression approach for estimating interactions between a treatment variable and a set of baseline predictors in their effects on the outcome, without the need to model the main effects of the predictors. We introduce a parsimonious generalization of the single-index models that targets the possible nonlinear effect of the interaction between the treatment conditions and the predictors. A common approach to interrogate such treatment-by-predictor interaction is to fit a regression curve as a function of the predictors separately for each of the K treatment groups. For parsimony and insight, we propose a single-index model with multiple-links (SIMML) that estimates a single linear combination of the predictors (i.e., a single-index), with K treatment-specific nonparametric link functions. Further, we impose a condition on the model space that gives the orthogonality between the interaction effect component and the unspecified main effect component, and the approach obviates the need to model the main effects. An application to a study for the treatment of depression is presented to illustrate the proposed SIMML and the corresponding methods for deriving ITRs.
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