A robust imputation method for surrogate outcome data

We consider estimation for regression analysis with surrogate or auxiliary outcome data. Assume that the regression model for the conditional mean of the outcome is a known function of a linear combination of the covariates with unknown coefficients, which are the regression parameters of interest. Such a class of models includes the generalised linear models as special cases. Suppose further that the outcome variable of interest is only observed in a validation subset, which is a simple random subsample from the whole sample, and that data on covariates as well as on one or more easily measured but less accurate surrogate outcome variables is collected from the whole sample. We propose a robust imputation approach which replaces the unobserved value of the outcome by its 'predicted' value generated from a specified 'working' parametric model. Estimation of the regression parameters is conducted as if the outcome data were completely observed. The resulting estimator of the regression parameter is consistent even if the 'working model' is misspecified. Large and finite sample properties for the proposed estimator are investigated.