Causal EpiNets: Calibrated Causal-Response Bounds from Experimental and Observational Evidence

Drug development decisions require more than estimates of average treatment effects: they also require evidence about which patient subgroups may benefit or be harmed. These causal response probabilities are generally only partially identified, even when treatment effects are identifiable. We present Causal EpiNets, a framework for estimating covariate-conditional bounds on the probability of benefit from finite experimental and observational datasets. An anchored neural parameterization enforces compatibility among the probabilities entering the analytical bounds, while a precision correction accounts for the selection bias introduced by their maximum and minimum operations. EpiNet perturbations provide a computationally tractable representation of joint estimation uncertainty. Experiments on synthetic and semi-synthetic data show that the resulting intervals achieve near-nominal coverage in low-dimensional settings and reveal the effect of first-stage estimation error in high dimensions. The framework also applies directly to existing bounds on the probability of harm. Causal EpiNets therefore provide uncertainty-aware estimates of heterogeneous causal response when evidence must be combined across study designs.