Extending calibrated transfer beyond the current inferential framework

Establish theoretical guarantees for calibrated transfer learning for survival prediction and treatment inference with estimated feature maps, inference after correction selection, time-varying treatment effects, covariate-dependent treatment allocation, joint efficiency using historical and target cohorts, and historical sampling uncertainty.

Background

The paper develops calibrated transfer learning for Cox survival prediction and conditional treatment inference using a historical prognostic function, target calibration, and a cross-fitted projected score. Its guarantees rely on prespecified feature maps and correction spaces, fixed treatment effects, randomized treatment independent of covariates, an independently fitted historical function treated as fixed in the target analysis, and results conditional on the historical fit.

The authors explicitly identify six aspects not covered by the presented theory: estimated feature maps, post-selection treatment inference, time-varying effects, covariate-dependent allocation, efficiency that jointly exploits both cohorts, and uncertainty arising from historical sampling. Resolving these issues would extend the method's applicability and establish inference under more realistic learning, design, and two-sample settings.