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Abstract:
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When an exposure is measured with error, it is well known that the type I error rate of a hypothesis test for its causal effect on a given outcome will generally remain controlled at the nominal level. In contrast, classical measurement error of a confounder can hurt the type I error rate of a test of treatment effect. We have developed 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, which is known to be measured with error.
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