A semiparametric correction for attenuation

A correction method is proposed for models including the generalized linear model when the covariate is measured with error. The method requires a separate validation data set that consists of the surrogate W and the true covariate X or an unbiased estimate X₊of X. We do not require the classical additive measurement error model in which the surrogate is unbiased for the true covariates. We first obtain an estimate of E(X W) by using nonparametric kernel regression of X or X₊on W based on the validation data. Then we perform a standard analysis with the unknown X replaced by the estimate of E(X W). The asymptotic distribution of the resulting regression parameter estimator is obtained. Generalizations to include components of X measured without error are also discussed.