Asymptotic variance estimation for the misclassification SIMEX

Abstract

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.

Bias Correction Methods for Misclassified Covariates in the Cox Model: Comparison of Five Correction Methods by Simulation and Data Analysis

“…Three variance estimation methods have been proposed: jackknife, asymptotic andbootstrap (Kuchenhoff et al, 2007; Kuchenhoff et al, 2006). The SIMEX methods rely on simulation andextrapolation functions, based on a premise that the effect of ME on an estimator can be determinedexperimentally via simulation.…”

An investigation of the MC‐SIMEX method with application to measurement error in periodontal outcomes

“…An asymptotic estimate of the variance ${\hat{\beta }}_{1,\mathrm{SIMEX}}$ has been derived by [18]. The simex R package [20, 21] additionally implements a jackknife variance estimate based on the work of Cook and Stefanski [17].…”

“…They further illustrated their methods using data from a longitudinal study of caries experience, in which the binary assessment of caries was subject to measurement error. Subsequent work derived an estimate of the asymptotic variance of the bias-corrected coefficient [18] and provided an R [19] package [20, 21] that implements SIMEX and MC-SIMEX for a number of common statistical models.…”

Some suggestions on dealing with measurement error in linkage analyses

“…Second, the estimates are extrapolated backwards to the point where no measurement error existed (extrapolation step). The method can deal with continuous variables measured with random normal error (the original SIMEX procedure; Carroll, Küchenhoff, Lombard, & Stefanski, 1996;Cook & Stefanski, 1994) and with discrete variables measured with misclassification (the MCSIMEX procedure; Küchenhoff, Lederer, & Lesaffre, 2007;Küchenhoff, Mwalili, & Lesaffre, 2006). Similar to matrix correction and errors-in-variables-models, information about the measurement error must be provided.…”