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 but, 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 the corresponding crude and true effect measures. We also present results for coarsened and, under further assumptions, multiple misclassified confounders.