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A measurement error model with a Poisson distributed surrogate
Author(s) -
Li Liang,
Palta Mari,
Shao Jun
Publication year - 2004
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.1838
Subject(s) - covariate , estimator , statistics , poisson distribution , poisson regression , observational error , count data , econometrics , event (particle physics) , generalized linear model , mathematics , computer science , medicine , population , physics , environmental health , quantum mechanics
We study a linear model in which one of the covariates is measured with error. The surrogate for this covariate is the event count in unit time. We model the event count by a Poisson distribution, the rate of which is the unobserved true covariate. We show that ignoring the measurement error leads to inconsistent estimators of the regression coefficients and propose a set of unbiased estimating equations to correct the bias. The method is computationally simple and does not require using supplemental data as is often the case in other measurement error analyses. No distributional assumption is made for the unobserved covariate. The proposed method is illustrated with an example from the Wisconsin Sleep Cohort Study. Copyright © 2004 John Wiley & Sons, Ltd.