Exact, Nonparametric Inference When Doses Are Measured With Random Errors

Studies that estimate the effects of exposure to a possibly harmful agent often compare exposed subjects who received varied doses with matched controls who received zero dose. If the doses are measured with error, then one may wish to use the fallible doses to estimate a linear relationship between the unobserved true dose and the observed response. If one is willing to assume that the dose errors for exposed subjects are symmetrically distributed about 0—that is, the dose errors are pure errors and not, say, systematic underreporting of exposure—then the presence of zero-dose controls is all that is needed to obtain exact, distribution-free confidence intervals and tests, and consistent point estimates. The method is simpler for matched pairs than for matched sets with two or more matched subjects, and it is illustrated using two studies, one of each kind. With matched pairs, as in this first example, the method uses Wilcoxon’s signed rank test as the basis for inference. When there are several zero-dose controls matched to each exposed subject, the familiar null distribution of the signed rank statistic is no longer applicable because of dependence within matched sets, so the appropriate exact distribution and large-sample approximation are developed.