Locally Ancillary Quasiscore Models for Errors-in-Covariates

We use the notion of locally ancillary estimating functions to develop a quasiscore method for tting regression models containing measurement error in the covariates. Suppose interest is on the model E(Y ju; w) for response Y , the observed data are (y; x; w), and X is a mismeasured surrogate for u. We take a functional modelling approach, treating the u as a xed nuisance parameter. Beginning with quasiscores for the regression parameter and the unknown u, a bias-corrected quasiscore for the regression parameter is derived that is second order locally ancillary for the nuisance u. The method used to accomplish this requires only the correct speci cation of the mean and variance functions for Y and X in terms of u, w and the regression parameter. When an estimator for u is plugged into the corrected quasiscore, local approximations show that the bias is small. Simulations verifying this result and an example from child psychiatry are presented, both using log-linear regression models.