The asymptotic relative efficiency of score tests in a generalized linear model with surrogate covariates

Abstract

SUMMARY In many epidemiological studies, the exposure variable of interest cannot be measured directly. The classical approaches to errors in variables in regression do not extend easily to the nonlinear models commonly used in epidemiologic al research. Furthermore, the traditional additive measurement error model cannot adequately represent many surrogate relationships. By considering the effect of using surrogate independent variables on the efficient score statistic, some of the difficulties inherent in the estimation problem may be avoided. For the null hypothesis of no association, a simple and flexible procedure can be used to calculate the optimal score test. The asymptotic relative efficiency of this test to the test based upon the true exposures is derived. The optimal test is also compared to the naive procedure of substituting the surrogate into the score test for the true exposure.