A Class of Semiparametric Tests of Treatment Effect Robust to Confounder Classical Measurement Error

TL;DR

This paper introduces a class of semiparametric tests for treatment effects that are robust to classical measurement error in confounders, avoiding the need for validation data and ensuring correct type I error rates.

Contribution

The authors develop a novel class of semiparametric tests that are robust to measurement error in confounders without requiring external validation data.

Findings

Tests maintain correct type I error rate under measurement error.

Simulation studies demonstrate the tests' validity and power.

Application to real data shows practical utility in environmental health studies.

Abstract

When assessing the presence of an exposure causal effect on a given outcome, it is well known that classical measurement error of the exposure can reduce the power of a test of the null hypothesis in question, although its type I error rate will generally remain at the nominal level. In contrast, classical measurement error of a confounder can inflate the type I error rate of a test of treatment effect. In this paper, we develop a large class of semiparametric test statistics of an exposure causal effect, which are completely robust to classical measurement error of a subset of confounders. A unique and appealing feature of our proposed methods is that they require no external information such as validation data or replicates of error-prone confounders. We present a doubly-robust form of this test that requires only one of two models to be correctly specified for the resulting test statistic to have correct type I error rate. We demonstrate validity and power within our class of test statistics through simulation studies. We apply the methods to a multi-U.S.-city, time-series data set to test for an effect of temperature on mortality while adjusting for atmospheric particulate matter with diameter of 2.5 micrometres or less (PM2.5), which is known to be measured with error.