Single index methods for evaluation of marker‐guided treatment rules based on multivariate marker panels

Clinical practice may be enhanced by use of person-level information that could guide treatment choice and lead to better outcomes for both treated individuals and for the population. The scientific challenge is to identify and validate those factors that can reliably be used to target treatment, and to accurately quantify the expected treatment benefit as a function of candidate markers. Our proposal is to explicitly focus on smooth non-parametric evaluation of a canonical single index score that estimates the expected treatment benefit associated with patient characteristics. Our methods intentionally decouple the model used to generate the treatment benefit score from the methods that are adopted to evaluate the performance of the resulting single index score. We are motivated by the practical issue that model performance can not realistically be evaluated for every specific covariate value due to intrinsic sparseness. However, direct validation of a scalar treatment benefit score obtained through model-based dimension reduction is feasible, and we believe should be the focus of validation efforts. We also show that the canonical single index treatment benefit score can be used for selecting subsets of patients with enriched expected treatment response since patients can be easily ordered and grouped based on the scalar score. Our biomedical motivation comes from a recent randomized trial of steroid injections for low back pain where baseline clinical and imaging data are candidate measures for guiding therapeutic choice.