Regression with covariates and outcome calculated from a common set of variables measured with error: estimation...

In medical research, a situation commonly arises where new variables are calculated from a common set of directly measured variables. When the directly measured variables each contain an error component, the relationship between the observed calculated variables can often be distorted. A source of this distortion is the presence of common measurement error in the observed calculated variables. Often known as coupled error, it is still possible to estimate the relationship between the calculated variables when measurement error is present. This paper presents two general methodologies that account for the presence of correlated measurement error when working with calculated variables. The equivalence of the methods will be established for one case, while the general advantage of the simulation extrapolation technique will be shown for more complicated situations. The performance of the estimators will be examined with examples arising from the medical literature.