Targeted Deep Survival Contrasts: Valid Inference for Treatment-Specific Survival Benefit with Neural Networks

Abstract

Neural survival models are increasingly asked to support counterfactual claims---how much a treatment would change survival in a population---rather than only prognostic risk scores. Answering such questions from observational data requires valid inference for treatment-specific survival contrasts under confounding and covariate-dependent censoring, targets for which standard deep survival estimators are biased and provide no honest uncertainty. We propose Targeted Deep Survival Contrasts (TDSC), which extends Targeted Deep Architectures (TDA)---targeted maximum likelihood estimation embedded in a network's weight space---to the full vector of treatment-specific survival curves over a time grid, and hence to the benefit curve and the restricted mean survival time (RMST) difference. A single universal targeting path, one ridge projection of the stacked efficient influence functions onto closed-form last-layer gradients per iteration, simultaneously solves the projected estimating equations for all coordinates; a one-step residual top-up converts the plug-in into a doubly robust estimator of the unrestricted target; and a multiplier bootstrap yields simultaneous confidence bands for the benefit curve. We prove joint asymptotic linearity, band validity, and double robustness of the top-up for a cross-fitted variant requiring no Donsker conditions. Across seven Monte Carlo banks with confounded treatment, sign-varying effect heterogeneity, and dependent censoring, the TDSC plug-in attains nominal pointwise and simultaneous coverage with 35% lower MSE than a per-timepoint one-step (AIPCW) built from the same nuisance fits. Under a badly wrong outcome model the plug-in tracks its working parameter and its intervals fail (44% coverage), while the top-up restores nominal inference for the unrestricted causal target (94-95%)---and in-sample diagnostics separate the two regimes.

19 pages, 4 figures, 4 tables