A class of semiparametric tests of treatment effect robust to confounder measurement error

When assessing the presence of an exposure causal effect on a given outcome, measurement error of a confounder can inflate the type I error rate of a treatment effect in even the simplest of settings. In this paper, we develop a large class of semiparametric test statistics of an exposure causal effect, which are completely robust to additive unbiased measurement error of a subset of confounders. A unique and appealing feature of our proposed methodology is that it requires no external information such as validation data or replicates of error-prone confounders. We present a doubly robust form of this test that requires the exposure mean model to be linear in the mismeasured confounders, and only one of two models involving error-free confounders to be correctly specified for the resulting test statistic to have correct type I error rate. We demonstrate validity within our class of test statistics through simulation studies. We apply the methods to a multi-US-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, which is known to be measured with error.