# Spatial–temporal distribution of incidence, mortality, and case-fatality ratios of coronavirus disease 2019 and its social determinants in Brazilian municipalities

### Design

Ecological studies use a population group as a unit of analysis, commonly delimited by a geographic area, to assess the possible relationship between socio-environmental and health characteristics^{34}.

This analytical ecological study evaluated, at municipal level, the spatial and temporal association between demographic, socioeconomic, and healthcare variables and the three outcomes: incidence, mortality, and case-fatality ratios due to severe acute respiratory syndrome (SARS) caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2).

### Data collection

Information on cases and deaths associated with SARS due to COVID-19 in Brazil were obtained from the Influenza Epidemiological Surveillance Information System database and used to the calculate the incidence, mortality, and case-fatality ratios for severe cases.

The geographic units of analysis were the 5570 Brazilian municipalities. The temporal cut-off points were the EWs 13–53 of 2020 and 1–38 in 2021, corresponding to 22 March 2020 to 25 September 2021^{35}. For analysis, the sequence of EWs started in 2020 and continued into 2021.

Figure 10 shows the administrative division of Brazil into 26 federative units (FUs) and the Federal District (DF). These FUs are administratively grouped into five regions.

To identify all cases of SARS due to COVID-19 in the database, we re-evaluated SARS cases with unknown aetiology. Among these cases, COVID-19 was considered in patients who tested positive for SARS-CoV-2 by reverse-transcriptase polymerase chain reaction (RT-PCR), who showed IgG, IgM, or IgA antibodies against this virus, and those with imaging test (chest computed tomography scan) findings typical of COVID-19, including the ground-glass opacity or reverse halo sign criteria adopted by the Brazilian Ministry of Health^{36}.

### Data analysis

The heterogeneity of the distributions of outcomes in the Brazilian territory may produce biased risk estimates. In some municipalities, the number of cases was extremely low during the study period. Furthermore, the age structure of the population can also influence the results. Thus, the indirect standardization method was used to calculate the incidence, mortality, and fatality ratios of COVID-19^{37}. Thus, we assessed whether the observed and expected values between the three outcomes for each municipality \((i)\) and EW \((t)\) differed from those of the reference population. The reference population in this study had the same age distribution as that of Brazilian individuals in 2020. The age groups were 0–4, 5–9, 10–14, 15–19, 20–29, 30–39, 40–49, 50–59, 60–69, 70–79, and 80 years or older. The expected number of cases and deaths, as well as the case-fatality rate per age group in each municipality for each EW, was calculated by multiplying the population values of each municipality by the specific incidence, mortality, or case-fatality rates. For \(i \left( {i = 1, \ldots , 5570} \right)\) municipalities, \(t \left( {t = 13, \ldots , 64} \right)\) weeks, where y_{c}, y_{d} are the number of cases and deaths in municipality i and week t; E_{c} (1), E_{d} (2), and E_{l} (3) are the expected number of cases, deaths, and SARS case fatalities in municipality i and week j; and P_{itn} is the reference population, as follows^{38}.

$$E_{{c_{{it}} }} = P_{{it_{n} }} \left( {\frac{{\mathop \sum \nolimits_{{i = 1}}^{n} \mathop \sum \nolimits_{{t = 1}}^{T} y_{{cit_{{1, \ldots ,n}} }} }}{{\mathop \sum \nolimits_{{i = 1}}^{n} \mathop \sum \nolimits_{{t = 1}}^{T} p_{{it_{{1, \ldots ,n}} }} }}} \right)$$

(1)

$$E_{{d_{{it}} }} = P_{{it_{n} }} \left( {\frac{{\mathop \sum \nolimits_{{i = 1}}^{n} \mathop \sum \nolimits_{{t = 1}}^{T} y_{{dit_{{1, \ldots ,n}} }} }}{{\mathop \sum \nolimits_{{i = 1}}^{n} \mathop \sum \nolimits_{{t = 1}}^{T} p_{{it_{{1, \ldots ,n}} }} }}} \right)$$

(2)

$$E_{{l_{{it}} }} = P_{{it_{n} }} \left( {\frac{{\mathop \sum \nolimits_{{i = 1}}^{n} \mathop \sum \nolimits_{{t = 1}}^{T} y_{{dit_{{1, \ldots ,n}} }} }}{{\mathop \sum \nolimits_{{i = 1}}^{n} \mathop \sum \nolimits_{{t = 1}}^{T} y_{{cit_{{1, \ldots ,n}} }} }}} \right)$$

(3)

After calculating the expected case, death, and case-fatality values, the relative risk estimators, standardised incidence rate (SIR), standardised mortality rate (SMR), and standardised case-fatality ratio (SCFR) were determined.

A Bayesian space–time model was adjusted using integrated nested Laplace approximation (INLA) to evaluate the risk of SARS by municipality and EW^{39}. The outcomes of each municipality *i* to EW *t* followed a Poisson distribution. If the model showed overdispersion, a negative binomial distribution was used. Since the pandemic spread at different moments in time among the municipalities, zero-inflated (zero-inflated Poisson [ZIP] and zero-inflated negative binomial [ZINB]) models were used. The selection of the probability distribution that best fitted the data was based on the smallest Watanabe-Akaike information criterion (WAIC) by comparing the models to the intercept^{40} (the statistical results are showed in Table S1). The Besag-York-Mollié model (BYM2), a variation of the conditional autoregressive (CAR) model, was included to characterise the spatial dependence, in which events occurring in neighbouring areas had greater correlations than those occurring in distant areas^{41,42}. A second-order random walk model (RW2) was used to calculate the time dependence, which was characterised by consecutive time units presenting similar risk estimates (the results of the comparison between models are included in Table S2). The space–time interaction was included with an unstructured random effect term^{43}. Thus, the INLA model with the space–time structure was constructed using the number of cases and deaths as independent variables and the expected value as an offset in a logarithmic scale.

For assessing the degree of uncertainty of RR, we calculate the probability of excess risk > 1. The probabilities of excess risk greater than or equal to 75% indicate an RR high certainty to detect true raised-risk municipality^{40}.

Demographic, socioeconomic, and healthcare covariates were included to investigate their possible associations with the outcomes. These covariates originated from different databases, which are detailed in Table 2.

Due to the Covid-19 pandemic, from April to December 2020, beneficiary families eligible for the Bolsa Família Programme received emergency assistance, a supplement to the benefit provided by the federal government.

Due to the large number of covariates, they were initially selected following the epidemiological criteria and statistical correlations. Spearman’s correlation coefficients with a significance level of 5% were used to evaluate the correlations between the outcomes and covariates (the Spearman’s correlation matrix is included in Table S3).

Furthermore, the collinearity among the selected covariates was tested using the variation inflation factor of the linear model. Collinearity was considered present for tolerance values < 10^{44}. All analyses were performed using R statistical software version 4.0.5.