Semiparametric Estimation of Delayed-Outcome Treatment Effects Using Short-Term Surrogates under Administrative Censoring
The multi-site registry studies, such as Stepped-wedge cluster-randomized trials (SW-CRT), staggered-enrollment RCTs, etc., share a structural feature: the primary long-term outcome is administratively censored for a non-negligible fraction of units, with censoring driven by calendar design rather than by the outcome itself. Standard inverse-probability-of-censoring weighting becomes unstable when observation probabilities $g_Δ$ concentrate near zero for late-crossing units, while parametric mixed-model analyses discard the information in any short-term intermediate measurement and rely on correct specification of the secular time trend. We study semiparametric estimation of the average treatment effect when a short-term surrogate, which is observed for all units and conditionally independent of the censoring mechanism given baseline covariates, is available. Identification takes a nested-integral form in which the outcome regression is marginalized over the conditional surrogate distribution, so the observation mechanism does not enter the target functional as an inverse weight. We show that a density-plug-in one-step debiased machine-learning construction for this functional leaves a second-order cross-product remainder $R_{SY}$ that has no doubly-robust complement in the efficient influence function and is not eliminated by cross-fitting . We propose a surrogate-assisted AIPW estimator (SA-AIPW) that integrates over the empirical surrogate distribution through treatment weighting rather than estimating the conditional surrogate density, and so structurally avoids $R_{SY}$. For clustered data, the estimator is shown to be $\sqrt{J}$-consistent and asymptotically linear under a product-rate double-robustness condition.