Statistical results

To simultaneously test county- and state-level effects of contextual factors on the outbreak rate with cross-level interactions, we estimate a two-level linear model using full maximum likelihood in HLM 7.03 (Figure 3). This accounts for potential similarities in counties within the same state.24 We center all predictors around the group mean at level 1 and grand mean at level 2.
We first estimate a one-way random effects ANOVA (unconditional model), which has an intraclass correlation coefficient (ICC) of 0.243. That is, more than 24% of the variation in the outbreak rate is between states, and about 76% is within the states and between their counties. The variation between states is statistically significant (u 0 = 4.50E-04, p < 0.001). We thus deem it prudent to proceed with a multilevel model as follows:
Level 1 (counties):\(\text{Outbreak\ rate}_{\text{ij}}=\beta_{0j}+\beta_{1j}\left[Black\ \&\ African\ American\right]+\ \beta_{2j}\left[\text{Native\ American}\right]+\beta_{3j}\left[\text{Asian\ American}\right]+\beta_{4j}\left[\text{Native\ Hawaiian}\right]+\beta_{5j}\left[\text{Hispanic\ American}\right]+\beta_{6j}\left[\text{Household\ income}\right]+\beta_{7j}\left[\text{Nonproficiency\ in\ English}\right]+\beta_{8j}\left[\text{Math\ grade}\right]+\beta_{9j}\left[Persons\ under\ 18\ years\right]+\beta_{10j}\left[\text{Median\ age}\right]+\beta_{11j}\left[\text{Female\ persons}\right]+\beta_{12j}\left[\text{Social\ associations}\right]+\beta_{13j}\left[\text{Sleep\ deprivation}\right]+\beta_{14j}\left[\text{Preventable\ hospitalization}\right]+\beta_{15j}\left[\text{Obesity}\right]+\beta_{16j}\left[\text{Smoking}\right]+\beta_{17j}\left[\text{Air\ pollution}\right]+\beta_{18j}\left[\text{Rural\ area}\right]+\beta_{19j}\left[\text{Food\ environment}\right]+\beta_{20j}\left[\text{Outbreak\ date}\right]+\beta_{21j}\left[\text{Density}\right]+\beta_{22j}\left[\text{Temperature}\right]+r_{\text{ij}}\)
Level 2 (states):\(\beta_{0j}=\gamma_{00}+\gamma_{01}\left[\text{Party\ control}\right]+\gamma_{02}\left[\text{Gender\ of\ governor}\right]+\gamma_{03}\left[\text{Government\ spending}\right]+\gamma_{04}\left[\text{Collectivism}\right]+u_{0j}\);\(\beta_{1j}=\gamma_{10}+u_{1j}\); \(\beta_{2j}=\gamma_{20}\);\(\beta_{3j}=\gamma_{30}\); \(\beta_{4j}=\gamma_{40}\);\(\beta_{5j}=\gamma_{50}\); \(\beta_{6j}=\gamma_{60}\);\(\beta_{7j}=\gamma_{70}\); \(\beta_{8j}=\gamma_{80}\);\(\beta_{9j}=\gamma_{90}\); \(\beta_{10j}=\gamma_{100}\);\(\beta_{11j}=\gamma_{110}\); \(\beta_{12j}=\gamma_{120}\);\(\beta_{13j}=\gamma_{130}\); \(\beta_{14j}=\gamma_{140}\);\(\beta_{15j}=\gamma_{150}\); \(\beta_{16j}=\gamma_{160}\);\(\beta_{17j}=\gamma_{170}\); \(\beta_{18j}=\gamma_{180}\);\(\beta_{19j}=\gamma_{190}+u_{19j}\);\(\beta_{20j}=\gamma_{200}+u_{20j}\); \(\beta_{21j}=\gamma_{21}\);\(\beta_{22j}=\gamma_{22}\)
We provide the inter-item correlation matrix in Table 2, and the results of the multilevel model in Table 3. Additionally, we perform several robustness tests to inform our results.
First, because outbreak rates change over time and their estimation is somewhat sensitive to the starting figure, we alternatively calculate them after 10 and 25 cases in the respective unit, finding a high correlation among the rates. When using the rate after 10 cases, the outbreak date as a control variable changes its sign and loses significance (p = 0.065). Notably, the following coefficients gain significance: government spending (p  = 0.064); temperature (p  = 0.011). Conversely, the following coefficients lose significance: household income (p  = 0.989); food environment (p  = 0.144); density (p  = 0.709). More importantly, the signs of the coefficients remain the same. The variable outbreak date controls for temporality of the outbreak in the original model (1.912, [1.322; 2.502], p  < 0.001).
Second, we iteratively include several other contextual variables and logged versions to assess the robustness of the results. But because it is nearly impossible to establish a complete list of confounding variables, we quantify the potential impact of unobserved confounds (Table 3; impact threshold).28 For instance, the necessary impact of such a confound for air pollution would be 0.043, that is, to invalidate the variable’s inference on the outbreak rate, a confounding variable would have to be correlated with both the outbreak rate and air pollution at \(\sqrt{0.043}=0.207\). Next, to alleviate concerns that some counties are omitted from the analysis because they are not yet affected by the virus,24 we ask how many counties would have to be replaced with unobserved cases for which the null hypothesis is true (i.e., a contextual variables has no influence on the outbreak rate) in order to invalidate the inference.28 As Table 3 (confound threshold) shows, 43.962% of the counties would have to be replaced with counties for which the effect is zero in order to invalidate the influence of air pollution. In summary, it can be claimed that the influence of the identified contextual variables on the pandemic is reasonably robust.
Third, a potential omission of relevant variables can lead to multicollinearity issues, which are generally a serious problem in epidemiological studies.29 Even though HLM 7.03 checks for multicollinearity, we conduct several additional diagnostics to eliminate any potential issues. In the inter-item correlation matrix (Table 2), the average (absolute) correlation is 0.172, and the highest correlation is 0.754, which is below the typical cutoff of 0.8. Most high correlations exist between racial composition and income and education. Additionally, we conduct a linear regression analysis at level 1 in IBM SPSS 26 (R 2 = 0.495; without variable math grade; pairwise exclusion of missing values), and find that the variable inflation factor (VIF) never exceeds the threshold of 5 (highest being nonproficiency in English, 4.024). The variance-decomposition matrix also does not show any groups of predictors with high values.
Fourth, we rerun our model excluding the 23 counties of the New York metropolitan area. As a COVID-19 hotspot, they could unduly influence our analysis. All signs remain the same, and the following coefficients gain significance: household income (p  = 0.009); persons under 18 years (p  = 0.038).
Fifth, because there is no statistically correct choice for centering decisions in multi-level models30, we retest our model with raw values. With the exception of the variable collectivism losing statistical significance (p  = 0.711), the results are fully consistent with the group- and grand-mean centered predictors in Table 3.
Lastly, we are aware that an accurate estimation and comparison of the outbreak rate across units depends on similar testing strategies, test sensitivities, specificities, and reporting of tests performed vs. individuals tested.10,31 Even within the U.S., some states report tests performed and others individuals tested.31 The number of tests administered and the number of confirmed cases therefore correlates to varying extents across states.32 By using a multi-level model, we aim to accommodate such differences between states.