# Evaluating A Key Instrumental Variable Assumption Using Randomization Tests

## TL;DR

This paper introduces a new falsification test for instrumental variable validity that compares observed covariate balance to what would be expected under randomization, providing a global and assumption-free assessment.

## Contribution

It proposes an innovative, non-parametric falsification test that evaluates IV validity by comparing covariate balance to a randomized benchmark, applicable across all covariates.

## Key findings

- The test can assess if the IV is closer to randomization than the exposure.
- It allows for graphical and global balance assessments.
- Demonstrated on ICU bed availability as an IV in healthcare data.

## Abstract

Instrumental variable (IV) analyses are becoming common in health services research and epidemiology. Most IV analyses use naturally occurring instruments, such as distance to a hospital. In these analyses, investigators must assume the instrument is as-if randomly assigned. This assumption cannot be tested directly, but it can be falsified. Most falsification tests in the literature compare relative prevalence or bias in observed covariates between the instrument and the exposure. These tests require investigators to make a covariate-by-covariate judgment about the validity of the IV design. Often, only some of the covariates are well-balanced, making it unclear if as-if randomization can be assumed for the instrument across all covariates. We propose an alternative falsification test that compares IV balance or bias to the balance or bias that would have been produced under randomization. A key advantage of our test is that it allows for global balance measures as well as easily interpretable graphical comparisons. Furthermore, our test does not rely on any parametric assumptions and can be used to validly assess if the instrument is significantly closer to being as-if randomized than the exposure. We demonstrate our approach on a recent IV application that uses bed availability in the intensive care unit (ICU) as an instrument for admission to the ICU.