Model-based standardization to adjust for unmeasured cluster-level confounders with complex survey data

Model-based standardization uses a statistical model to estimate a standardized, or unconfounded, population-averaged effect. With it, one can compare groups had the distribution of confounders been identical in both groups to that of the standard population. We develop two methods for model-based standardization with complex survey data that accommodate a categorical confounder that clusters the individual observations into a very large number of subgroups. The first method combines a random-intercept generalized linear mixed model with a conditional pseudo-likelihood estimator of the fixed effects. The second method combines a between-within generalized linear mixed model with census data on the cluster-level means of the individual-level covariates. We conduct simulation studies to compare the two approaches. We apply the two methods to the 2008 Florida Behavioral Risk Factor Surveillance System survey data to estimate standardized proportions of people who drink alcohol, within age groups, adjusting for measured individual-level and unmeasured cluster-level confounders.