Testing Partially-Identifiable Causal Queries Using Ternary Tests

TL;DR

This paper introduces ternary statistical tests for partially-identifiable causal queries, providing a framework that extends binary tests to improve causal hypothesis testing from observational data.

Contribution

It proposes a novel approach using ternary tests for causal queries, establishes testability conditions, and shows how to construct these tests from binary ones for specific problems.

Findings

Ternary tests satisfy uniform consistency requirements.

Topological conditions guide the construction of ternary tests.

Complete methods for combining binary tests into ternary tests are developed.

Abstract

We consider hypothesis testing of binary causal queries using observational data. Since the mapping of causal models to the observational distribution that they induce is not one-to-one, in general, causal queries are often only partially identifiable. When binary statistical tests are used for testing partially-identifiable causal queries, their results do not translate in a straightforward manner to the causal hypothesis testing problem. We propose using ternary (three-outcome) statistical tests to test partially-identifiable causal queries. We establish testability requirements that ternary tests must satisfy in terms of uniform consistency and present equivalent topological conditions on the hypotheses. To leverage the existing toolbox of binary tests, we prove that obtaining ternary tests by combining binary tests is complete. Finally, we demonstrate how topological conditions serve as a guide to construct ternary tests for two concrete causal hypothesis testing problems, namely testing the instrumental variable (IV) inequalities and comparing treatment efficacy.