Nonparametric regression in the presence of measurement error

Carroll, Raymond J.; Maca, Jeffrey D.; Ruppert, David

doi:10.1093/biomet/86.3.541

Cited by 134 publications

(162 citation statements)

References 14 publications

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“…Regression calibration has been particularly widely used for linear associations but also extends to nonlinear associations (Carroll et al, 2006, Cheng andSchneeweiss, 1998). Other correction methods for nonlinear models include simulation extrapolation (SIMEX) (Cook and Stefanski, 1994, Carroll et al, 1999, Staudenmayer and Ruppert, 2004, Bayesian methods for P-splines (Berry et al, 2002, Cheng andCrainiceanu, 2009), and approaches using local polynomial estimators Truong, 1993, Delaigle et al, 2009).…”

Section: Discussionmentioning

confidence: 99%

Effects of Classical Exposure Measurement Error on the Shape of Exposure-Disease Associations

Keogh¹,

Strawbridge²,

White³

2012

Epidemiologic Methods

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In epidemiology many exposures of interest are measured with error. Random, or 'classical', error in exposure measurements attenuates linear exposure-disease associations. However, its precise effects on different nonlinear associations are not well known. We use simulation studies to assess how classical measurement error affects observed association shapes and power to detect nonlinearity. We focus on a proportional hazards model for the exposure-disease association and consider six true association shapes of relevance in epidemiology: linear, threshold, U-shaped, Jshaped, increasing quadratic, asymptotic. The association shapes are modeled using three popular methods: grouped exposure analyses, fractional polynomials, P-splines. Under each true association shape and each method we illustrate the effects of classical exposure measurement error, considering varying degrees of random error. We also assess what we refer to as MacMahon's method for correcting for classical exposure measurement error under grouped exposure analyses, which uses replicate measurements to estimate usual exposure within observed exposure groups. The validity of this method for nonlinear associations has not previously been investigated. Under nonlinear exposure-disease associations, classical measurement error results in increasingly linear shapes and not always an attenuated association at a given exposure level. Fractional polynomials and P-splines give similar results and offer advantages over grouped exposure analyses by providing realistic models. P-splines offer greatest power to detect nonlinearity, however random exposure measurement error results in a potential considerable loss of power to detect nonlinearity under all methods. MacMahon's method performs well for quadratic associations, but does not in general recover nonlinear shapes.

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Section: Discussionmentioning

confidence: 99%

Effects of Classical Exposure Measurement Error on the Shape of Exposure-Disease Associations

Keogh¹,

Strawbridge²,

White³

2012

Epidemiologic Methods

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“…There also exist a number of methods for correcting for the effects of error in a continuous exposure on the continuous exposure-outcome association. These include regression calibration (RC) (Rosner et al, 1989, 1992, Spiegelman et al, 1997, Carroll et al, 1999, which is widely used, multiple imputation (MI) (Cole et al, 2006, Freedman et al, 2008, moment reconstruction (MR) (Freedman et al, 2004(Freedman et al, , 2008, and simulation extrapolation (SIMEX) (Cook and Stefanski, 1994, Carroll et al, 2006, Staudenmayer and Ruppert, 2004. In this paper we investigate whether RC, MI, MR and SIMEX can be adapted for use in correcting for the effects of misclassification when the mismeasured observed continuous exposure is categorized.…”

Section: Introductionmentioning

confidence: 99%

Correcting for Bias due to Misclassification when Error-prone Continuous Exposures Are Misclassified

Keogh¹,

Strawbridge²,

White³

2012

Epidemiologic Methods

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To investigate the association between a continuous exposure and an outcome it is common to categorize the exposure and estimate the relative associations between categories. Error in measurement of the continuous exposure results in misclassification when the exposure is categorized. In this paper we investigate methods for correcting for this misclassification. We consider applications of methods for continuous exposures and for fundamentally categorical exposures. A particular challenge is that even nondifferential error in the underlying continuous exposure can result in differential misclassification in the categorized exposure, i.e. misclassification dependent on the outcome. For continuous exposures, there exist a range of methods for correcting for the effects of exposure measurement error on the exposure-outcome association, including regression calibration (RC), multiple imputation (MI), moment reconstruction (MR) and simulation extrapolation (SIMEX). There are also correction methods for use with genuinely categorical exposures, using estimated misclassification probabilities. Alongside simple methods using estimated misclassification probabilities, we also consider two RC based methods, MI and MR of the continuous exposure followed by categorization, and a new SIMEX method. Simulation studies are used to compare the methods when the true exposure is available in a validation study and the more common situation in which replicate or additional error-prone exposure measurements are available in a subsample. We restrict attention to the case where the underlying association between the continuous exposure and the outcome is linear on the appropriate scale. RC and SIMEX methods fail to correct adequately for bias. However, MI and MR perform well. Methods using estimated misclassification probabilities also perform well, provided differential misclassification is assumed, however these methods are restricted to estimation of odds ratios and have other practical drawbacks. MI and MR have the benefit of being flexible for use with different analysis models, with quantile-based cutpoints, and more easily accommodate covariate adjustment. In summary, we found that MI and MR can be applied to correct exposureoutcome associations for the effects of misclassification error when the association is linear. Extending MI and MR for use with categorized continuous exposures under nonlinear exposureoutcome associations is now an important area for further research.

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“…The SIMEX estimator was developed by Cook and Stefanski (1994) with related theory discussed in Carroll et al (1996), Stefanski and Cook (1995) and Carroll et al (2006) etc. This method has been well studied in both parametric (Wang et al 1998(Wang et al , 2000 and nonparametric problems (Carroll et al 1999). Among others, Apanasovich et al (2009) developed the general theory for SIMEX in semiparametric problems using kernel-based estimation methods.…”

Section: Introductionmentioning

confidence: 99%

Asymptotics of SIMEX-based variance estimation

Fang

Zhu

2010

Metrika

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In this paper, we study the asymptotic properties of simulation extrapolation (SIMEX) based variance estimation that was proposed by Wang et al. (J R Stat Soc Series B 71:425-445, 2009). We first investigate the asymptotic normality of the parameter estimator in general parametric variance function and the local linear estimator for nonparametric variance function when permutation SIMEX (PSIMEX) is used. The asymptotic optimal bandwidth selection with respect to approximate mean integrated squared error (AMISE) for nonparametric estimator is also studied. We finally discuss constructing confidence intervals/bands of the parameter/function of interest. Other than applying the asymptotic results so that normal approximation can be used, we recommend a nonparametric Monte Carlo algorithm to avoid estimating the asymptotic variance of estimator. Simulation studies are carried out for illustration.

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Nonparametric regression in the presence of measurement error

Cited by 134 publications

References 14 publications

Effects of Classical Exposure Measurement Error on the Shape of Exposure-Disease Associations

Effects of Classical Exposure Measurement Error on the Shape of Exposure-Disease Associations

Correcting for Bias due to Misclassification when Error-prone Continuous Exposures Are Misclassified

Asymptotics of SIMEX-based variance estimation

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