Regression calibration with more surrogates than mismeasured variables

Handle URI:
http://hdl.handle.net/10754/599485
Title:
Regression calibration with more surrogates than mismeasured variables
Authors:
Kipnis, Victor; Midthune, Douglas; Freedman, Laurence S.; Carroll, Raymond J.
Abstract:
In a recent paper (Weller EA, Milton DK, Eisen EA, Spiegelman D. Regression calibration for logistic regression with multiple surrogates for one exposure. Journal of Statistical Planning and Inference 2007; 137: 449-461), the authors discussed fitting logistic regression models when a scalar main explanatory variable is measured with error by several surrogates, that is, a situation with more surrogates than variables measured with error. They compared two methods of adjusting for measurement error using a regression calibration approximate model as if it were exact. One is the standard regression calibration approach consisting of substituting an estimated conditional expectation of the true covariate given observed data in the logistic regression. The other is a novel two-stage approach when the logistic regression is fitted to multiple surrogates, and then a linear combination of estimated slopes is formed as the estimate of interest. Applying estimated asymptotic variances for both methods in a single data set with some sensitivity analysis, the authors asserted superiority of their two-stage approach. We investigate this claim in some detail. A troubling aspect of the proposed two-stage method is that, unlike standard regression calibration and a natural form of maximum likelihood, the resulting estimates are not invariant to reparameterization of nuisance parameters in the model. We show, however, that, under the regression calibration approximation, the two-stage method is asymptotically equivalent to a maximum likelihood formulation, and is therefore in theory superior to standard regression calibration. However, our extensive finite-sample simulations in the practically important parameter space where the regression calibration model provides a good approximation failed to uncover such superiority of the two-stage method. We also discuss extensions to different data structures.
Citation:
Kipnis V, Midthune D, Freedman LS, Carroll RJ (2012) Regression calibration with more surrogates than mismeasured variables. Statistics in Medicine 31: 2713–2732. Available: http://dx.doi.org/10.1002/sim.5435.
Publisher:
Wiley-Blackwell
Journal:
Statistics in Medicine
KAUST Grant Number:
KUS-CI-016-04
Issue Date:
29-Jun-2012
DOI:
10.1002/sim.5435
PubMed ID:
22744878
PubMed Central ID:
PMC3640838
Type:
Article
ISSN:
0277-6715
Sponsors:
We thank Dr. Weller for providing us with the data used in their original analysis. Carroll's research was supported by a grant from the National Cancer Institute (CA57030) and by Award Number KUS-CI-016-04, made by King Abdullah University of Science and Technology (KAUST).
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Full metadata record

DC FieldValue Language
dc.contributor.authorKipnis, Victoren
dc.contributor.authorMidthune, Douglasen
dc.contributor.authorFreedman, Laurence S.en
dc.contributor.authorCarroll, Raymond J.en
dc.date.accessioned2016-02-28T05:52:00Zen
dc.date.available2016-02-28T05:52:00Zen
dc.date.issued2012-06-29en
dc.identifier.citationKipnis V, Midthune D, Freedman LS, Carroll RJ (2012) Regression calibration with more surrogates than mismeasured variables. Statistics in Medicine 31: 2713–2732. Available: http://dx.doi.org/10.1002/sim.5435.en
dc.identifier.issn0277-6715en
dc.identifier.pmid22744878en
dc.identifier.doi10.1002/sim.5435en
dc.identifier.urihttp://hdl.handle.net/10754/599485en
dc.description.abstractIn a recent paper (Weller EA, Milton DK, Eisen EA, Spiegelman D. Regression calibration for logistic regression with multiple surrogates for one exposure. Journal of Statistical Planning and Inference 2007; 137: 449-461), the authors discussed fitting logistic regression models when a scalar main explanatory variable is measured with error by several surrogates, that is, a situation with more surrogates than variables measured with error. They compared two methods of adjusting for measurement error using a regression calibration approximate model as if it were exact. One is the standard regression calibration approach consisting of substituting an estimated conditional expectation of the true covariate given observed data in the logistic regression. The other is a novel two-stage approach when the logistic regression is fitted to multiple surrogates, and then a linear combination of estimated slopes is formed as the estimate of interest. Applying estimated asymptotic variances for both methods in a single data set with some sensitivity analysis, the authors asserted superiority of their two-stage approach. We investigate this claim in some detail. A troubling aspect of the proposed two-stage method is that, unlike standard regression calibration and a natural form of maximum likelihood, the resulting estimates are not invariant to reparameterization of nuisance parameters in the model. We show, however, that, under the regression calibration approximation, the two-stage method is asymptotically equivalent to a maximum likelihood formulation, and is therefore in theory superior to standard regression calibration. However, our extensive finite-sample simulations in the practically important parameter space where the regression calibration model provides a good approximation failed to uncover such superiority of the two-stage method. We also discuss extensions to different data structures.en
dc.description.sponsorshipWe thank Dr. Weller for providing us with the data used in their original analysis. Carroll's research was supported by a grant from the National Cancer Institute (CA57030) and by Award Number KUS-CI-016-04, made by King Abdullah University of Science and Technology (KAUST).en
dc.publisherWiley-Blackwellen
dc.subjectAttenuationen
dc.subjectLogistic regressionen
dc.subjectMeasurement erroren
dc.subjectReparameterizationen
dc.subject.meshModels, Statisticalen
dc.titleRegression calibration with more surrogates than mismeasured variablesen
dc.typeArticleen
dc.identifier.journalStatistics in Medicineen
dc.identifier.pmcidPMC3640838en
dc.contributor.institutionBiometry Research Group, Division of Cancer Prevention; National Cancer Institute; Bethesda; MD; U.S.A.en
dc.contributor.institutionGertner Institute for Epidemiology and Health Policy Research; Sheba Medical Center; Tel Hashomer; Israelen
dc.contributor.institutionDepartment of Statistics; Texas A&M University; College Station; TX; U.S.A.en
kaust.grant.numberKUS-CI-016-04en
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