Reducing the Effect of Correlated Additive Measurement Errors on Regression Model With no Ancillary Study

To adjust the effect of additive measurement error on estimation and hypothesis testing, one needs some information on the measurement error model, that is, an ancillary study (e.g., validation study, calibration study, or replicates study) for ascertaining the nature and the magnitude of measurement error. However, there is often a severe lack of information about measurement error in practice due to various reasons including time, money, and so on. In this article, we propose a method of estimation named derived estimation to reduce the effect of correlated additive measurement errors when no ancillary study is available. Derived estimate of regression coefficient for a target covariate is constructed based on the replacement of another covariate by a derived variable obtained from dividing this covariate by the target one. This easy to implement method can avoid misleading outcomes caused by highly correlated additive measurement errors in covariates. Furthermore, it is found that the derived estimation is approximately equal to the univariate estimation when covariates are standardized. This finding is supported by extensive simulation results. In addition, we derive rules under which both univariate and derived estimations produce less absolute biased estimates than the bivariate estimation. As shown by numerical studies, these rules are still held for a nonlinear regression, for example, Cox model. Finally, this method is illustrated by an example from the EPIC-InterAct Study.