Regression analysis with nonignorably missing covariates using surrogate data

The paper considers parameter estimation in regression analysis with missing covariates when the missing data mechanism is nonignorable and unspecified, which is quite common in practice but has rarely been discussed in the literature. Assuming that surrogate data for the missed covariates is available for all the subjects, we propose a novel approach that constructs estimating equations based on the conditional expectation of the outcome given the always observed covariates and the surrogate data. Asymptotic properties and variance estimation of the parameter estimators from the new approach are established. Some simulation results are presented to compare the finite sample performance of various estimators. A real data set from the National Health and Nutrition Examination Survey is analyzed to illustrate the application of the method.