Partial identification and efficient estimation for the stratum-specific probability of benefit with thresholds on a continuous outcome

Johan de Aguas, Sebastian Krumscheid, Johan Pensar, Guido Biele

Keywords: causal inference, semiparametric inference, bounds, partial identification

Abstract: We define the probability of benefit for a scenario involving a binary exposure, a continuous outcome, and a partition of the outcome support with $K$ fixed thresholds. As with other counterfactual queries, this parameter is often not $g$-identifiable, and we show that monotonicity assumption is not sufficient when $K>1$. We introduce a partial identification strategy by adapting existing bounds. Conducting asymptotic inference and uncertainty quantification for estimates of these bounds is challenging due to potential nonregularity and the lack of differentiability of the involved functionals. Moreover, results might be sensitive to model specification. To address this, we reformulate the problem in terms of individualized rules, adapting the available online one-step estimator with stabilizing weights. We show the connection with solutions based on conservative optimal transport and illustrate the advantages over surrogate bounds derived from smooth approximations. We present an application aimed at estimating the probability of benefit from pharmacological treatment for ADHD upon school performance using observational data.

Submission Number: 13