Orthogonal locally ancillary estimating functions for matched pair studies and errors in covariates

Summary. We propose an estimating function method for two related applications, matched pair studies and studies with errors in covariates under a functional model, where a mismeasured unknown scalar covariate is treated as a fixed nuisance parameter. Our method addresses the severe inferential problem that is posed by an abundance of nuisance parameters in these two applications. We propose orthogonal locally ancillary estimating functions for these two applications that depend on merely the mean model and partial modelling of the variances of the observations (and observed mismeasured covariate, if applicable), and we achieve first‐order bias correction of inferences under a ‘small dispersion and large sample size’ asymptotic. Simulation results confirm that the estimator proposed is largely improved over that using a regular profile estimating function. We apply the approach proposed to a length of hospital stay study with a mismeasured covariate.