A Note on Confidence Interval Estimation in Measurement Error Adjustment

The goal of adjusting for covariate measurement error is generally to obtain valid point and confidence interval estimates for the parameters of a regression model that would be applied if all covariates were error-free. In this article, we point out a potentially undesirable feature of many standard adjusted confidence intervals. Specifically, the coverage can be unbalanced, in the sense that failure to encompass the true parameter of interest may occur much more often with the lower bound above the true value than with the upper bound below that value (or vice-versa). Since hypothesis tests about the true parameter typically have a direct connection with the adjusted confidence interval, this unbalancedness can have bearing upon the critical properties of such tests, and can be especially detrimental if one-sided alternatives are being considered. We illustrate this problem in the simple context of an additive-normal measurement error problem in linear regression, and we provide a partial solution by means of a variance stabilizing transformation. Our illustration suggests that investigators may sometimes wish to consider adjusted interval estimation methods that are less susceptible to variance instability, particularly when sample sizes are not large.