Asymptotic Variance Estimation for the Misclassification SIMEX

Most epidemiological studies suffer from misclassification in the
response and/or the covariates. Since ignoring misclassification
induces bias on the parameter estimates, correction for such errors
is important. For measurement error, the continuous analog to
misclassification, a general approach for bias correction is the
SIMEX (simulation extrapolation) originally suggested by Cook and
Stefanski (1994). This approach has been recently extended to
regression models with a possibly misclassified categorical
response and/or the covariates by Küchenhoff et al. (2005), and is
called the MC-SIMEX approach. To assess the importance of a
regressor not only its (corrected) estimate is needed, but also its
standard error. For the original SIMEX approach. Carroll et al.
(1996) developed a method for estimating the asymptotic variance.
Here we derive the asymptotic variance estimators for the MC-SIMEX
approach, extending the methodology of Carroll et al. (1996). We
also include the case where the misclassification probabilities are
estimated by a validation study. An extensive simulation study
shows the good performance of our approach. The approach is
illustrated using an example in caries research including a
logistic regression model, where the response and a binary
covariate are possibly misclassified.