New estimating methods for surrogate outcome data

Surrogate outcome data arise frequently in medical research. The true outcomes of interest are expensive or hard to ascertain, but measurements of surrogate outcomes (or more generally speaking, the correlates of the true outcomes) are usually available. In this paper we assume that the conditional expectation of the true outcome given covariates is known up to a finite dimensional parameter. When the true outcome is missing at random, the e±cient score function for the parameter in the conditional mean model has a simple form, which is similar to the generalized estimating functions. There is no integral equation involved as in Robins, Rotnitzky and Zhao (1994) for general cases. We propose two estimating methods, parametric and nonparametric, to estimate the parameter by solving the e±cient score equations. Simulation studies show the proposed estimators work well for reasonable sample sizes.