N-of-1 Surrogacy: Evaluating and Learning Surrogate Maps for Individual-level Treatment Decisions

The N-of-1 study design, i.e., experimentation on a single individual, is the gold standard for fully personalized treatment decisions. In practice, however, the primary outcome of interest can be too delayed or costly to measure, and is often observed only once, making an individual's counterfactual outcomes under different treatments unavailable. Treatment decisions must therefore rely on intermediate measurements, known as surrogate outcomes. Existing surrogate frameworks establish validity with respect to population-average treatment effects. However, population-level surrogacy need not imply correct _individual-level_ decisions. We formalize individual-level surrogacy through the regret of the treatment policy induced by a surrogate map, a function of intermediate measurements. Because individual-level regret depends on unobservable subject-level counterfactual outcomes, we propose an evaluation framework based on outcome imputation and establish identifiability of the individual-level regret under suitable assumptions. We propose an estimator that targets the individual-level regret of surrogate maps using observed data, and further discuss when how surrogate maps can be learned from data. In controlled experiments, we validate the finite-sample behavior of our evaluation procedure and its behavior under assumption violations. Finally, we apply the framework to longitudinal data from a large-scale wearable health study, and evaluate fixed biomarkers and learned surrogate maps as individual-level surrogates for the effect of changes in physical activity on the onset of cardiometabolic disease.