Semiparametric outcome regression-based estimator of Mann-Whitney-type causal effect

We introduce a novel semiparametric estimator for Mann-Whitney-type causal effects based on the cumulative probability model (CPM). CPMs are rank-based, invariant to monotone transformations of the outcome, and offer flexible outcome regression under confounding. We formalize the estimation under causal consistency, no interference, ignorability, and positivity assumptions, and develop accompanying inference procedures. Through simulations with varying sample sizes and effect magnitudes, the CPM estimator shows reduced variability and improved predictive accuracy relative to mis-specified parametric transformations. We demonstrate its applicability in a large cohort of people with HIV (PWH) in Northern Nigeria by assessing the causal effect of HIV status on albuminuria levels. Overall, our results highlight the value of robust semiparametric methods for causal inference in observational settings beyond average treatment effects. Findings should be interpreted in light of the observational design and the potential for unmeasured confounding.