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

## TL;DR

This paper introduces a new method to correct for measurement errors in regression analysis when surrogate data have many zero values, improving accuracy in epidemiological studies.

## Contribution

A novel regression calibration estimator is proposed to handle zero-inflated surrogate variables in exposure–disease association studies.

## Key findings

- The proposed estimator reduces bias compared to naive regression calibration methods.
- Simulations confirm the estimator's effectiveness in correcting bias in zero-inflated data.
- The method was successfully applied to a physical activity intervention study.

## 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.