Setting a Dose versus Observing One: Continuous Dose–Response Estimation under Right-Censoring

Optimizing radiotherapy dose for cancer patients is a continuous-treatment decision made on right-censored survival outcomes under strong confounding. That combination is not specific to radiotherapy, or to oncology: it recurs wherever a continuous exposure meets a censored time-to-event outcome, such as in drug dosing or occupational exposure. Existing causal estimators return a local dose effect or a partially linear form, or are not built with a survival likelihood, and none we know of returns whole dose–response curves for interpretable patient subgroups. We present PSPS-CS (continuous-treatment, censored-survival Predictive State Propensity Subclassification), a deep mixture-of-experts model trained end-to-end on one causal objective combining a Gaussian-mixture treatment-density model with a Weibull survival likelihood. It learns latent predictive states, groups of patients within which dose is approximately unconfounded. Setting a dose leaves a patient's state weights unchanged while observing one updates them, so PSPS-CS marginalizes over the states with the prior weights rather than dividing by a propensity score. Consequently it never forms the divergent weights of continuous-treatment inverse-propensity weighting. It returns population and state-specific dose–response curves, either of which may be non-monotone. We explored how PSPS-CS behaves in thirteen simulated scenarios and compared it with a parametric Weibull accelerated failure time model, a random survival forest and a causal forest with inverse-probability-of-censoring weighting. The scenarios vary outcome family, dose–response shape and confounding, and several favor another estimator by construction (a parametric model of the correct family, a tree-shaped dose effect, or no dose effect), so they do not favor PSPS-CS across the board. PSPS-CS trained with the prior weights had the first- or second-lowest mean error of the four estimators in ten of the thirteen (exploratory), including second place behind the favored model on the primary Weibull and tree scenarios (the pre-specified variant in six). However, both pre-specified comparisons against the parametric model failed, and in five of those ten scenarios almost every estimator did worse than predicting no dose effect. We then apply PSPS-CS to a real and messy clinical cohort, RADCURE (N=2,243 head and neck cancer patients), where dose is nearly a point mass, most patients are censored, and confounding is strong. PSPS-CS returns six states with distinct curve shapes and clinically plausible feature profiles, although the population curve is largely not identified on this dose axis. Overall, PSPS-CS is a new estimator for flexible dose–response curves under continuous treatment and censored survival. It has potentially broad applicability and can complement existing methods in oncology and beyond.