Comparing the efficiency of structural and functional methods in measurement error models

Abstract

The paper is a survey of recent investigations by the authors and others into the relative efficiencies of structural and functional estimators of the regression parameters in a measurement error model. While structural methods, in particular the quasi-score (QS) method, take advantage of the knowledge of the regressor distribution (if available), functional methods, in particular the corrected score (CS) method, discards such knowledge and works even if such knowledge is not available. Among other results, it has been shown that QS is more efficient than CS as long as the regressor distribution is completely known. However, if nuisance parameters in the regressor distribution have to be estimated, this is no more true in general. But by modifying the QS method, the adverse effect of the nuisance parameters can be overcome. For small measurement errors, the efficiencies of QS and CS become almost indistinguishable, whether nuisance parameters are present or not. QS is (asymptotically) biased if the regressor distribution has been misspecified, while CS is always consistent and thus more robust than QS.

Approximate maximum likelihood estimation for logistic regression with covariate measurement error

“…We conduct simulation studies to evaluate the finite sample performance of AMLE and compare it with several methods including naive estimation (naive), RC, quasi‐likelihood estimation (QLE) (Schneeweiss & Kukush, 2009), CS (Stefanski & Carroll, 1987), and Monte Carlo corrected score (MCCS) (Novick & Stefanski, 2002). For AMLE, we define estimators from the approximation of (6) by the second order and the fourth order of the Taylor expansion as AMLE2 and AMLE4, respectively.…”

“…Consequently, many correction methods have been proposed to handle covariates measured with error under logistic regression. For example, Rosner, Willett, and Spiegelman (1989); Cook and Stefanski (1994); Schneeweiss and Kukush (2009); Novick and Stefanski (2002); Freedman, Fainberg, Kipnis, Midthune, and Carroll (2004); Thomas, Stefanski, and Davidian (2011); Zucker, Gorfine, Li, Tadesse, and Spiegelman (2013); Yi, Ma, Spiegelman, and Carroll (2015); and so on. All these approaches can provide approximate consistent estimators and reduce bias on estimators as well.…”

Logistic regression with correlated measurement error and misclassification in covariates

“…Based on a similar idea of SIMEX, Novick and Stefanski 20 proposed a Monte Carlo corrected score method via complex variables. Schneeweiss and Kukush 21 studied quasi-likelihood estimation to deal with measurement error in GLM. Freedman et al 22 proposed the moment reconstruction correction method, and Thomas et al 23 explored an imputation approach called moment-adjusted imputation.…”

Estimation in a linear errors-in-variables model under a mixture of classical and Berkson errors

“…Regression models with measurement errors in covariates are quite popular nowadays [1,2,4], see also [5] for the comparison of various estimation methods in such models.…”