Abstract
Abstract Biological and epidemiological phenomena are often measured with error or imperfectly captured in data. When the true state of this imperfect measure is a confounder of an outcome exposure relationship of interest, it was previously widely believed that adjustment for the mismeasured observed variables provides a less biased estimate of the true average causal effect than not adjusting. However, this is not always the case and depends on both the nature of the measurement and confounding. We describe two sets of conditions under which adjusting for a non-deferentially mismeasured proxy comes closer to the unidentifiable true average causal effect than the unadjusted or crude estimate. The first set of conditions apply when the exposure is discrete or continuous and the confounder is ordinal, and the expectation of the outcome is monotonic in the confounder for both treatment levels contrasted. The second set of conditions apply when the exposure and the confounder are categorical (nominal). In all settings, the mismeasurement must be non-differential, as differential mismeasurement, particularly an unknown pattern, can cause unpredictable results.
Highlights
In observational studies, it is often of interest to estimate the average causal effect of an exposure on an outcome when this relationship is confounded
For binary true confounder and proxy, Greenland [1] argued that adjusting for the proxy produces a partially adjusted measure of the average causal effect of the exposure on the outcome that is between the crude and the true measures
True confounder, and proxy, they showed that the result holds if the conditional expectation of the outcome is monotonic in the true confounder, i.e., it is either non-decreasing or non-increasing in the confounder for both exposure
Summary
It is often of interest to estimate the average causal effect of an exposure on an outcome when this relationship is confounded. True confounder, and proxy, they showed that the result holds if the conditional expectation of the outcome is monotonic in the true confounder, i.e., it is either non-decreasing or non-increasing in the confounder for both exposure. Ogburn and VanderWeele [3] extended these results to binary exposure and ordinal true confounder and proxy, still under the monotonicity assumption. Ogburn and VanderWeele [2] gave an example of the causal effect of type 2 diabetes on hypertension when confounded by the use of thiazide, a drug to treat hypertension. Peña [4] characterized nonmonotonic cases for binary exposure, true confounder, and proxy, where the partially adjusted average causal effect is still between the crude and the true ones. We show that the proof of the result in ref. [3] applies when the exposure is non-binary under additional assumptions
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