03. Adjusting for covariate misclassification to quantify the relationship between diabetes and local access to healthy food

Without access to healthy food, it may be difficult to maintain a healthy lifestyle free from preventable illness. This access can be quantified for residents of a given area by measuring their distance to the nearest grocery store, but there is a trade off. We can either consider (i) the more accurate but cost-prohibitive distance measurement that only uses passable roads or (ii) the error-prone but easy-to-obtain straight-line distance calculation that ignores the location of infrastructure and potential natural barriers. Trying to fit a standard regression model to the relationship between disease prevalence and the error-prone, straight-line food access measures would introduce bias to the parameter estimates. Fully observing the more accurate, route-based food access measure is often impossible, and thus, if it can only be partially observed, a missing data problem arises. We address this bias and the missing data by deriving a new maximum likelihood estimator for Poisson regression with a binary, error-prone explanatory variable (representing access to healthy food based on distance to the nearest grocery store), where the errors may depend on additional error-free covariates. With simulation studies, 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 (i.e., deleting any neighborhoods with missing data). Finally, we apply our estimator to data from the Piedmont Triad region of North Carolina, where we model the relationship between diabetes prevalence and access to healthy food at various distance thresholds.

Mid-Level

Knowledge

Women in Statistics and Data Science 2024