Adjusting for confounding by neighborhood using generalized linear mixed models and complex survey data.

When investigating health disparities, it can be of interest to explore whether adjustment for socioeconomic factors at the neighborhood level can account for, or even reverse, an unadjusted difference. Recently, we proposed new methods to adjust the effect of an individual-level covariate for confounding by unmeasured neighborhood-level covariates using complex survey data and a generalization of conditional likelihood methods. Generalized linear mixed models (GLMMs) are a popular alternative to conditional likelihood methods in many circumstances. Therefore, in the present article, we propose and investigate a new adaptation of GLMMs for complex survey data that achieves the same goal of adjusting for confounding by unmeasured neighborhood-level covariates. With the new GLMM approach, one must correctly model the expectation of the unmeasured neighborhood-level effect as a function of the individual-level covariates. We demonstrate using simulations that even if that model is correct, census data on the individual-level covariates are sometimes required for consistent estimation of the effect of the individual-level covariate. We apply the new methods to investigate disparities in recency of dental cleaning, treated as an ordinal outcome, using data from the 2008 Florida Behavioral Risk Factor Surveillance System (BRFSS) survey. We operationalize neighborhood as zip code and merge the BRFSS data with census data on ZIP Code Tabulated Areas to incorporate census data on the individual-level covariates. We compare the new results to our previous analysis, which used conditional likelihood methods. We find that the results are qualitatively similar.