Regression calibration for Cox regression under heteroscedastic measurement error: determining risk factors of cardiovascular diseases from error-prone nutritional replication data

For instance nutritional data are often subject to severe measurement error, and an adequate adjustment of the estimators is indispensable to avoid deceptive conclusions. This paper discusses and extends the method of regression calibration to correct for measurement error in Cox regression. Special attention is paid to the modelling of quadratic predictors, the role of heteroscedastic measurement error, and the efficient use of replicated measurements of the surrogates. The method is used to analyze data from the German part of the MONICA cohort study on cardiovascular diseases. The results corroborate the importance of taking into account measurement error carefully.