An ecological study of socioeconomic predictors in detection of COVID-19 cases across neighborhoods in New York City

Table 1 Characteristics of four different base models (no predictors). Lower deviance information criterion (DIC) represents a better trade off between model fit and complexity. Models 1 and 3 have a random intercept; models 2 and 4 follow a BYM2 structure. \(D\left (\overline \theta \right)\), deviance of mean model parameters θ; p_D, effective number of parameters

Model	Distribution	Parameters	Hyperparameters	\(D\left (\overline \theta \right)\)	p_D	DIC
Model 1^*	Poisson	β₀, ν_i	τ_ν	1346.53	149.6	1645.73
Model 2^**	Poisson	β₀, \(\upsilon _{i}^{}\), \(\nu _{i}^{}\)	τ_γ, φ	1362.37	124.68	1611.73
Model 3^†	Negative binomial	β₀, ν_i	n, τ_ν	1855.47	3.30	1862.07
Model 4^‡	Negative binomial	β₀, \(\upsilon _{i}^{}\), \(\nu _{i}^{}\)	n, τ_γ, φ	1455.71	103.58	1662.87

^*Model 1: y_i|λ_i∼Pois(λ_i), log(λ_i)=η_i+log(E_i)=β₀+ν_i+log(E_i)
^**Model 2: y_i|λ_i∼Pois(λ_i), \(\log \left (\lambda _{i}\right)=\eta _{i}+\log \left (E_{i}\right)=\beta _{0}+\frac {1}{\sqrt {\tau _{\gamma }}}\left ({\sqrt {\varphi }\upsilon _{i}^{*}}+\sqrt {1-\varphi }\nu _{i}^{*}\right)+\log \left (E_{i}\right)\)
^†Model 3: y_i|λ_i∼NegBin(n,λ_i), log(λ_i)=η_i+log(E_i)=β₀+ν_i+log(E_i)
^‡Model 4: y_i|λ_i∼NegBin(n,λ_i), \(\log \left (\lambda _{i}\right)=\eta _{i}+\log \left (E_{i}\right)=\beta _{0}+\frac {1}{\sqrt {\tau _{\gamma }}}\left ({\sqrt {\varphi }\upsilon _{i}^{*}}+\sqrt {1-\varphi }\nu _{i}^{*}\right)+\log \left (E_{i}\right)\)
Symbols: y_i, count of cases in Zip Code Tabulation Area (ZCTA) i; λ_i, expected cases in ZCTA i; E_i, number of total COVID-19 tests in ZCTA i; η_i, linear predictor for ZCTA i; β₀, intercept; ν_i, nonspatial random-effect; \(\nu _{i}^{*}\), scaled nonspatial random-effect; \(\upsilon _{i}^{*}\), scaled spatial random-effect with intrinsic conditional autoregressive structure; τ_ν, precision for nonspatial random effect, log-gamma prior; τ_γ, overall precision, penalized complexity (PC) prior; φ, mixing parameter, PC prior; n, overdispersion parameter, PC gamma prior

ISSN: 1741-7015