Synthetic Survival Control: Extending Synthetic Controls for "When-If" Decision

TL;DR

This paper introduces Synthetic Survival Control (SSC), a method for estimating counterfactual hazard trajectories in observational survival data, addressing challenges like censoring and treatment heterogeneity, with formal guarantees and real-world validation.

Contribution

The paper proposes SSC, a novel approach for causal survival analysis that leverages a low-rank panel data framework with formal identification and guarantees.

Findings

Access to new treatments improves survival outcomes.

SSC accurately estimates counterfactual hazard trajectories.

Method validated on multi-country cancer treatment data.

Abstract

Estimating causal effects on time-to-event outcomes from observational data is particularly challenging due to censoring, limited sample sizes, and non-random treatment assignment. The need for answering such "when-if" questions--how the timing of an event would change under a specified intervention--commonly arises in real-world settings with heterogeneous treatment adoption and confounding. To address these challenges, we propose Synthetic Survival Control (SSC) to estimate counterfactual hazard trajectories in a panel data setting where multiple units experience potentially different treatments over multiple periods. In such a setting, SSC estimates the counterfactual hazard trajectory for a unit of interest as a weighted combination of the observed trajectories from other units. To provide formal justification, we introduce a panel framework with a low-rank structure for causal survival analysis. Indeed, such a structure naturally arises under classical parametric survival models. Within this framework, for the causal estimand of interest, we establish identification and finite sample guarantees for SSC. We validate our approach using a multi-country clinical dataset of cancer treatment outcomes, where the staggered introduction of new therapies creates a quasi-experimental setting. Empirically, we find that access to novel treatments is associated with improved survival, as reflected by lower post-intervention hazard trajectories relative to their synthetic counterparts. Given the broad relevance of survival analysis across medicine, economics, and public policy, our framework offers a general and interpretable tool for counterfactual survival inference using observational data.