Integrative ecological regression analysis of U.S. county and state level COVID-19 death data for studying health disparity associations

It is of substantial interest to study health disparity associations with COVID-19 death rates. Although high-quality individual-level COVID-19 epidemiological data have been difficult to collect on a national scale, all United States (U.S.) counties have reported total COVID-19 death counts. A standard ecological analysis would then regress county total death counts by county-level covariates such as age, sex, and race percentages. However, such an analysis is limited by ecological bias and fallacy in which estimated county-level associations are different from individual-level associations. Fortunately, state-level age, sex, and race specific COVID-19 death counts are also available for all U.S. states, so this information can be integrated with county-level data for more informative ecological analyses. We propose an approximate log-linear random effects model to jointly model county-level total death counts and state-level age, sex, and race specific death counts. We then develop a penalized composite log-likelihood method for parameter estimation and perform simulation studies to evaluate our proposed approach. Lastly, we analyze COVID-19 death data from the entire U.S., show how incorporating state-level counts can prevent ecological bias and fallacy, and illustrate the heterogeneity in health disparity associations across different U.S. states.