Maximum likelihood, multiple imputation and regression calibration for measurement error adjustment

Abstract

In epidemiologic studies of exposure-disease association, often only a surrogate measure of exposure is available for the majority of the sample. A validation sub-study may be conducted to estimate the relation between the surrogate measure and true exposure levels. In this article, we discuss three methods of estimation for such a main study/validation study design: (i) maximum likelihood (ML), (ii) multiple imputation (MI) and (iii) regression calibration (RC). For logistic regression, we show how each method depends on a different numerical approximation to the likelihood, and we adapt standard software to compute both MI and ML estimates. We use simulation to compare the performance of the estimators for both realistic and extreme settings, and for both internal and external validation designs. Our results indicate that with large measurement error or large enough sample sizes, ML performs as well as or better than MI and RC. However, for smaller measurement error and small sample sizes, either ML or RC may have the advantage. Interestingly, in most cases the relative advantage of RC versus ML was determined by the relative variance rather than the bias of the estimators. Software code for all three methods in SAS is provided.