A note on confidence interval estimation in measurement error adjustment

The goal of adjusting for covariate measurement error is generally to obtai n valid point and confidence interval estimates for the parameters of a reg ression model that would be applied if all covariates were error-free. In t his article, we point out a potentially undesirable feature of many standar d adjusted confidence intervals. Specifically, the coverage can be unbalanc ed, in the sense that failure to encompass the true parameter of interest m ay occur much more often with the lower bound above the true value than wit h the upper bound below that value (or vice-versa). Since hypothesis: tests about the true parameter typically have a direct connection with the adjus ted confidence interval, this unbalancedness can have bearing upon the crit ical properties of such tests, and can bi: especially detrimental if one-si ded alternatives are being considered. We illustrate this problem in the si mple content of an additive-normal measurement error problem in linear regr ession, and we provide a partial solution by means of a variance stabilizin g transformation. Our illustration suggests that investigators may sometime s wish to consider adjusted interval estimation methods that are less susce ptible to variance instability, particularly when sample sizes are not larg e.