Generalized Linear Models with Covariate Measurement Error and Zero-Inflated Surrogates

Ching-Yun Wang (), Jean de Dieu Tapsoba, Catherine Duggan and Anne McTiernan
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Ching-Yun Wang: Division of Public Health Sciences, Fred Hutchinson Cancer Center, P.O. Box 19024, Seattle, WA 98109-1024, USA
Jean de Dieu Tapsoba: Vaccine and Infectious Disease Division, Fred Hutchinson Cancer Center, P.O. Box 19024, Seattle, WA 98109-1024, USA
Catherine Duggan: Division of Public Health Sciences, Fred Hutchinson Cancer Center, P.O. Box 19024, Seattle, WA 98109-1024, USA
Anne McTiernan: Division of Public Health Sciences, Fred Hutchinson Cancer Center, P.O. Box 19024, Seattle, WA 98109-1024, USA

Mathematics, 2024, vol. 12, issue 2, 1-14

Abstract: Epidemiological studies often encounter a challenge due to exposure measurement error when estimating an exposure–disease association. A surrogate variable may be available for the true unobserved exposure variable. However, zero-inflated data are encountered frequently in the surrogate variables. For example, many nutrient or physical activity measures may have a zero value (or a low detectable value) among a group of individuals. In this paper, we investigate regression analysis when the observed surrogates may have zero values among some individuals of the whole study cohort. A naive regression calibration without taking into account a probability mass of the surrogate variable at 0 (or a low detectable value) will be biased. We developed a regression calibration estimator which typically can have smaller biases than the naive regression calibration estimator. We propose an expected estimating equation estimator which is consistent under the zero-inflated surrogate regression model. Extensive simulations show that the proposed estimator performs well in terms of bias correction. These methods are applied to a physical activity intervention study.

Keywords: measurement error; surrogate; zero-inflated data (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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