We consider logistic regression with covariate measurement error. Most existing approaches require certain replicates of the error‐contaminated covariates, which may not be available in the data. We propose generalized method of moments (GMM) nonparametric correction approaches that use instrumental variables observed in a calibration subsample. The instrumental variable is related to the underlying true covariates through a general nonparametric model, and the probability of being in the calibration subsample may depend on the observed variables. We first take a simple approach adopting the inverse selection probability weighting technique using the calibration subsample. We then improve the approach based on the GMM using the whole sample. The asymptotic properties are derived, and the finite sample performance is evaluated through simulation studies and an application to a real data set.
Biomedical researchers are often interested in estimating the effect of an environmental exposure in relation to a chronic disease endpoint. However, the exposure variable of interest may be measured with errors. In a subset of the whole cohort, a surrogate variable is available for the true unobserved exposure variable. The surrogate variable satisfies an additive measurement error model, but it may not have repeated measurements. The subset in which the surrogate variables are available is called a
- PAR ID:
- 10234047
- Publisher / Repository:
- Wiley Blackwell (John Wiley & Sons)
- Date Published:
- Journal Name:
- Biometrical Journal
- Volume:
- 58
- Issue:
- 6
- ISSN:
- 0323-3847
- Format(s):
- Medium: X Size: p. 1465-1484
- Size(s):
- p. 1465-1484
- Sponsoring Org:
- National Science Foundation
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