  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.
