Long-term Causal Inference via Modeling Sequential Latent Confounding

TL;DR

This paper introduces a new assumption and method for long-term causal inference that models sequential confounding biases across temporal outcomes, extending previous approaches and providing theoretical guarantees.

Contribution

We propose a novel assumption linking sequential confounding biases, enabling identification of long-term causal effects in complex temporal settings, with an estimator and theoretical analysis.

Findings

The proposed method accurately estimates long-term causal effects.

Theoretical analysis confirms estimator consistency and asymptotic properties.

Experiments demonstrate improved performance over existing methods.

Abstract

Long-term causal inference is an important but challenging problem across various scientific domains. To solve the latent confounding problem in long-term observational studies, existing methods leverage short-term experimental data. Ghassami et al. propose an approach based on the Conditional Additive Equi-Confounding Bias (CAECB) assumption, which asserts that the confounding bias in the short-term outcome is equal to that in the long-term outcome, so that the long-term confounding bias and the causal effects can be identified. While effective in certain cases, this assumption is limited to scenarios where there is only one short-term outcome with the same scale as the long-term outcome. In this paper, we introduce a novel assumption that extends the CAECB assumption to accommodate temporal short-term outcomes. Our proposed assumption states a functional relationship between sequential confounding biases across temporal short-term outcomes, under which we theoretically establish the identification of long-term causal effects. Based on the identification result, we develop an estimator and conduct a theoretical analysis of its asymptotic properties. Extensive experiments validate our theoretical results and demonstrate the effectiveness of the proposed method.