In a new arXiv preprint, Asaf Ben Arie and Malka Gorfine introduce FLEXI-Haz, a semiparametric deep neural network for right-censored survival data. The model pairs a linear component in the log-hazard, whose coefficients remain interpretable, with a flexible function of time and adjustment covariates. That split lets it absorb nonproportional nuisance effects without forcing analysts to choose between flexibility and clean inference.
The paper provides theoretical guarantees: under regularity conditions, the nuisance function converges at rates that are minimax optimal up to logarithmic factors over composite Hölder classes, while the regression parameter is root-n-consistent, asymptotically normal, and semiparametrically efficient. For adjustment covariates with finite support, the authors derive an explicit influence function for cumulative hazard and construct a cross-fitted one-step estimator that yields asymptotically valid pointwise confidence intervals for subject-specific survival.
Simulations show reduced bias and improved coverage relative to a proportional-hazards comparator when nuisance effects vary over time. An analysis of the Rotterdam breast cancer data demonstrates how flexible adjustment can change inference about treatment associations.