Bias attenuation results for nondifferentially mismeasured ordinal and coarsened confounders.

Suppose we are interested in the effect of a binary treatment on an outcome where that relationship is confounded by an ordinal confounder. We assume that the true confounder is not observed, rather we observe a nondifferentially mismeasured version of it. We show that under certain monotonicity assumptions about its effect on the treatment and on the outcome, an effect measure controlling for the mismeasured confounder will fall between its corresponding crude and the true effect measures. We present results for coarsened, and, under further assumptions, for multiple misclassified confounders.