Orthogonal Locally Ancillary Estimating Functions for Matched-Pair Studies and Errors-in-Covariates

We propose an estimating function method for two related applications, matchedpair studies and studies with errors-in-covariates under a functional model, where a mismeasured unknown scalar covariate is treated as a xed nuisance parameter. Our method addresses the severe inferential problem posed by an abundance of nuisance parameters in these two applications. We propose orthogonal locally ancillary estimating functions for the above two applications that depend on merely the mean model and partial modeling of the variances of the observations (and observed mismeasured covariate, if applicable), and achieve rst-order bias correction of inferences under a \small dispersion and large sample size" asymptotic. Simulation results con rm that the proposed estimator is largely improved over that using a regular pro le estimating function. We apply the proposed approach to a coronary heart disease study with a mismeasured blood pressure covariate. keywords: Ancillarity; Estimating function; Matched pair study; Measurement error; Nuisance parameter; Orthogonality.