Inference using surrogate outcome data and a validation sample

Abstract

SUMMARY In the context of estimating β from the regression model P β(Y|X), relating response Y to covariates X , suppose that only a surrogate response S is available for most study subjects. Suppose that for a random subsample of the study cohort, termed the validation sample, the true outcome Y is available in addition to S . We consider maximum likelihood estimation of β from such data and show that it is nonrobust to misspecification of the distribution relating the surrogate to the true outcome, P(S|Y, X) . An alternative semi-parametric method is also considered, which is nonparametric with respect to P(S|Y, X) , Large-sample distribution theory for maximum estimated likelihood estimates is developed. An illustrative example is presented.