Linking Potentially Misclassified Healthy Food Access to Diabetes Prevalence

Music City Center 

Without access to healthy food, preventing illnesses like diabetes is difficult. This access can be quantified for an area by measuring its distance to the nearest grocery store, but there is a trade off. We can either measure a more accurate but expensive distance only using passable roads or an error-prone but easy-to-obtain straight-line metric ignoring infrastructure and natural barriers. Fitting a standard regression model to the relationship between disease prevalence and error-prone food access would introduce bias, but fully observing the more accurate measure is often impossible, creating a missing data problem. We address these challenges by deriving a new maximum likelihood estimator for Poisson regression with a binary, error-prone exposure where the errors may depend on additional error-free covariates. Via simulation, we show the consequences of ignoring the error and how the proposed estimator corrects for that bias while preserving more statistical efficiency than the complete case analysis. Finally, we apply our estimator to data from the Piedmont Triad in North Carolina, where we model the relationship between diabetes prevalence and access to healthy food.

Grocery Stores

Maximum Likelihood Estimation

Measurement Error

Missing Data

One-Sided Misclassification

Poisson Regression 

ENAR