Surrogate-Assisted Targeted Learning for Nested Bridge Functionals under Administrative Censoring

Delayed primary outcomes and administratively censored follow-up create a general semiparametric estimation problem: the target causal functional depends on an endpoint observed only for a shrinking subset of units at analysis time, while earlier surrogate measurements remain widely available. In such settings, inverse-probabilityweighted estimators can become unstable as observation probabilities approach the positivity boundary, and complete-case model-based analyses can be highly sensitive to outcome-model specification. We develop a surrogate-assisted targeted minimum loss estimator for this nested causal functional. Identification proceeds through a surrogate-bridge representation that integrates an observed-outcome regression over the conditional surrogate distribution, thereby avoiding inverse observation weights in the target parameter itself. We show that the estimator is asymptotically linear and doubly robust (in the sense that first-order bias vanishes when either nuisance component is consistently estimated), and we characterize two structural features of the problem: under surrogate-mediated missing at random, the censoring mechanism contributes no separate tangent-space component to the efficient influence function; and for nested bridge functionals, a one-step debiased machine-learning construction leaves a second-order cross-product remainder involving the conditional surrogate law. The proposed two-stage targeting step removes this term without requiring direct estimation of that law. Simulation studies demonstrate stable finite-sample performance under substantial administrative censoring, and a design-calibrated analysis based on the Washington State EPT study illustrates the method in a realistic stepped-wedge cluster-randomized setting.