Joint Modeling of Spatial-Longitudinal Binary and Count Data Using Multilevel and Multiresolution Random Effects for Large Data Sets

Background: Medicaid adults have a high prevalence of diabetes and those with diabetes are recommended to receive low-density lipoprotein cholesterol (LDL-C) and hemoglobin A1c testing to reduce related short-term hospitalizations. It is important to identify those with low use of these preventive services as well as experiencing frequent hospitalizations for use in targeting future interventions. We developed a class of spatial-longitudinal generalized linear models with multilevel fixed and random effects for large data sets to examine individual and county-level predictors.

Methods: Michigan Medicaid (2011-13) data were analyzed to identify individual (race, gender, insurance plans) and county level factors (obesity rates, high school graduate percentage) associated with whether a person received recommended 1) LDC-C or 2) A1c testing as well as 3) count data on diabetes short-term complication-related admissions. Binary response variables were modeled using binomial distributions and zero-inflated negative binomial distribution was used for count data due to excess zeros and overdispersion. A multiresolution spatial covariance was developed to capture long range and small range spatial dependences. Temporal dependencies were imposed through first order autoregressive processes and within-subject dependencies were also incorporated. For model fitting and inferences, a data-augmentation Markov Chain Monte Carlo (MCMC) algorithm was developed.

Results: Females with diabetes were more likely to receive the recommended LDL-C (Bayesian p-value 0.0005) and those who get their LDL-C screening regularly were less likely to be hospitalized (Bayesian p-value 0.0121).

Conclusion: Some Medicaid plans had higher LDL-C screening rates. LDL-C was associated with decreased number of short-term hospitalizations.