Generalized projection tests for function-valued parameters with applications to testing structural causal assumptions

TL;DR

This paper introduces generalized projection tests for function-valued parameters to evaluate structural causal assumptions, leveraging series estimators and machine learning, with straightforward null distribution computation and real-world COVID-19 application.

Contribution

It develops a new class of tests for function-valued parameters that are valid under flexible estimation methods and provides practical examples in causal inference.

Findings

Tests are valid under broad conditions.

Null distribution is straightforward to compute.

Applied successfully to COVID-19 vaccine trial data.

Abstract

Structural assumptions are central to the causal inference literature. In practice, it is often crucial to assess their validity or to test implications that follow from them. In many settings, such tests can be framed as evaluating whether a function-valued parameter equals zero. In this paper, we propose a class of generalized projection tests based on series estimators for function-valued parameters. We establish conditions under which the proposed tests are valid and illustrate their applicability through examples from the data fusion and instrumental variables literature. Our approach accommodates flexible machine learning methods for estimating nuisance parameters. In contrast to many existing approaches, the limiting distribution of the proposed test statistics is straightforward to compute under the null hypothesis. We apply our method to test the equality of conditional COVID-19 risk across vaccine arms in the COVID-19 Variant Immunologic Landscape (COVAIL) trial.