Bias results for nondifferential mismeasurement of a binary confounder

Suppose we want to estimate the causal effect of an exposure on an outcome, while adjusting for a binary confounder. Suppose that the confounder is measured with error, but that the measurement error is nondifferential. We show that, under certain assumptions, adjusting for the mismeasured confounder produces a biased parameter that lies between the corresponding true and crude parameters. We further show how these assumptions can be tested empirically. We finally show that the bias when adjusting for the mismeasured confounder decreases with the sensitivity and specificity of the mismeasured confounder, provided that the sum of the sensitivity and specificity is at least one. These results have been shown previously for binary exposures and for specific effect measures. We generalize the results for exposures of any class (e.g. continuous and multilevel categorical) and for a wide range of effect measures that includes, but is not limited to, those considered previously.Funding Agencies|Swedish Research Council [202001188]