key: cord-0794535-qmpgqxbu
authors: Polo, Gina; Soler-Tovar, Diego; Villamil Jimenez, Luis Carlos; Benavides-Ortiz, Efraín; Acosta, Carlos Mera
title: Bayesian spatial modeling of COVID-19 case-fatality rate inequalities
date: 2022-03-25
journal: Spat Spatiotemporal Epidemiol
DOI: 10.1016/j.sste.2022.100494
sha: cae5ccd9940268a813b9e55db7f4b55509dbcd50
doc_id: 794535
cord_uid: qmpgqxbu

The ongoing outbreak of COVID-19 challenges the health systems and epidemiological responses of all countries worldwide. Although preventive measures have been globally considered, the spatial heterogeneity of its effectiveness is evident, underscoring global health inequalities. Using Bayesian-based Markov chain Monte Carlo simulations, we identify the spatial association of socioeconomic factors and the risk for dying from COVID-19 in Colombia. We confirm that from March 16 to October 04, 2020, the COVID-19 case-fatality rate and the multidimensional poverty index have a heterogeneous spatial distribution. Spatial analysis reveals that the risk of dying from COVID-19 increases in regions with a higher proportion of poor people with dwelling (RR 1.74 95%CI [Formula: see text] 1.54-9.75), educational (RR 1.69 95%CI [Formula: see text] 1.36-5.94), childhood/youth (RR 1.35 95%CI [Formula: see text] 1.08-4.03), and health (RR 1.16 95%CI [Formula: see text] 1.06-2.04) deprivations. These findings evidence the vulnerability of most disadvantaged members of society to dying in a pandemic and assist the spatial planning of preventive strategies focused on vulnerable communities.

The MPI in Colombia comprises five dimensions: health, 6 educational, childhood/youth, employment, and dwelling, in 7 turn, composed of fifteen indicators (lack of health insur-8 ance, barriers to health services, illiteracy, low educational 9 attainment, school non-attendance, school lag, barriers to 10 childhood care services, child labor, informal employment, 11 economic dependency, lack of access to safe water, inade-12 quate disposal of human feces, poor floor/walls construction, 13 and critical overcrowding). Concerning the health dimen-14 sion, the MPI considers the definition of barriers to health 15 services, as the proportion of individuals who do not attend 16 a health service due to an illness that does not require hospi-17 talization (DANE, 2020).

The educational and childhood/youth dimensions in Colom-19 bia are mainly associated with access to education, the level 20 of schooling, school backwardness, and child labor (DANE, 21 2020). Regarding these indicators, previous research shows 22 that people with less educational resources are more vul-23 nerable to poor health and mortality from different causes 24 (Drefhal et al., 2020; Selvan, 2020; Hummer and Lariscy, 25 2011; Cutler et al., 2011 ). In addition, regarding human-to-26 human transmission diseases, poor people could be at greater 27 risk due to the impossibility of working remotely and the ex- 28 igency to go out to work daily in informal activities (Henao- 29 Céspedes et al., 2021). 30 Furthermore, conditions associated with the dwelling such 31 as the provision of safe water, sanitation, and waste man-32 agement are essential for preventing and protecting human 33 health during the COVID-19 outbreak (WHO and UNICEF, 34 2020). Basic prevention measures for the human-to-human 35 transmission of COVID-19, such as handwashing (Desai et To better understand the association between CFR and socioeconomic factors across the Colombian administrative units, we consider the standardized CFR (SCFR). In our analysis, this metric corresponds to the CFR for each department , CFR( ), divided by the NCFR. The SCFR can be rewritten in a more suitable way for the Bayesian modeling discussed in the next sections, i.e.,

where is the number of expected resolved cases ( = 

These parameters are described in Table 1 . An SCFR equal 22 to 1 means that the CFR in the specific department is equal 23 to the national CFR. 

As proxy socioeconomic covariates, we consider the Colombian Multidimensional Poverty Index (MPI) database cal-culated by the National Administrative Department of National Statistics considering a departmental level. (DANE, 2020). The MPI comprises five dimensions: educational (EMPI), childhood / youth (YMPI), employment (WMPI), health (HMPI), and dwelling (DMPI) poverty conditions containing information on 15 variables (EMPI: illiteracy, low educational attainment; YMPI: school non-attendance, school lag, barriers to childhood care services, child labor; WMPI: informal employment, economic dependency; HMPI: lack of health insurance, barriers to health services; DMPI: lack of access to safe water, inadequate disposal of human feces, poor housing construction, and critical overcrowding). Variables definition of the MPI can be found in Table 2 In order to focus on the spatial variation and spatial het-5 erogeneity, rather than time-dependent factors (e.g., unem-6 ployment), we consider the CFR in the complete study pe-7 riod. This intrinsically addresses problems associated with 8 the strong CFR daily and weekly variation. Indeed, the above-9 mentioned components of the Multidimensional Poverty In-10 dex are constant during the pandemic, since no variation is 11 reported by the Colombian Territorial Health Directorates. Initially, a Poisson log-linear model was formulated as:

∼ Poisson( ) for = 1, ..., 33. ln( ) = 0 + 1 (HMPI) + 2 (EMPI)

where is the SCFR relative to , in the department . 22 The number of deaths is denoted by = ( 1 , ..., ) × , 23 where = ( 1 , ..., ) denotes the × 1 column vector of 24 observed deaths for all departments. The vector of covari-25 ate regression parameters is denoted by , and a multivari-26 ate Gaussian prior was assumed with mean and diagonal 27 variance matrix Σ . To check for the null hypothesis of spatial independence we used the Moran's I statistic based on 10000 random permutations of the data given by:

wherēis the mean of each MPI, denotes MPI's for the 1 th department and denote MPI's at another department

share a common border, and

Finally, we considered a spatial structure through a latent component for the department by , encompassing spatially autocorrelated random effects (Amsalu et al., 2019). Thus, adjusting equation 1, ln( ) = 0 + 1 (HMPI) + 2 (EMPI)

where a vector of known offsets is denoted by = ( 1 , ...,

) . Then, the model was concluded by considering (Leroux et al., 2000):

where is a spatial dependence parameter taking values in 5 the unit interval, specifically = 1 corresponds to the in-6 trinsic CAR model and = 0 corresponds to independence 7 ( ∼ N(0, 2 ) ). The spatial autocorrelation is induced by 8 the neighbourhood matrix . The prior specification for 2 9 is conformed by (a = 1,b = 0.01). 10 We generated MCMC samples from three independent 11 Markov chains. Each chain was run for 2200000 samples, of 12 which 200000 were removed as the burn-in period and the 13 remaining 2000000 samples were thinned by 1000 to remove 14 correlation amongst the samples. This leaves 1000 samples 15 for inference from each chain. All analyzes were conducted 16 in R version Version 1.3.959 (R Core Team, 2020), using the 17 'CARBayes' package version 5.1 (Lee, 2013) .

The effects of each MPI on the COVID-19 SCFR were quantified as relative risks, for a fixed increase in each co- Vaupés exhibited the lowest SCFR (SCFR= 0.41), which 27 corresponds to a decrease of 59% in the observed COVID- 28 19 deaths compared to the national CFR value over the 29 29 weeks study period. Before incorporating spatial autocorrelated random ef-14 fects into the model, we modeled the data with a Bayesian 15 multivariate Poisson log-linear model (Table 3 Supplemen-16 tary Material). To quantify the presence of spatial autocor-17 relation in the residuals from this model, we compute the 18 Moran's I statistic and conduct a permutation test to assess 19 its significance. Based on 10000 random permutations of the 20 data, Moran's I statistic suggests that the residuals contain 21 substantial positive spatial autocorrelation (p<0.05). Table 22 3 describes the results of the spatial Bayesian model with 23 the lowest criteria deviance information criterion (DIC) after 24 considering all possible permutations of the MPI covariates. 25 In addition to the median and 95% confidence intervals, 26 Table 3 contains the effective number of independent sam-27 ples (n.effective), and the result of Geweke diagnostic (Geweke, 28 1992), an MCMC convergence diagnostic that should lie be-29 tween -2.0 and 2.0 to indicate convergence. The output shows 30 that the health, dwelling, educational, and childhood/youth 31 dimensions, exhibits positive relationships with the SCFR. 32 Furthermore, the spatial dependence parameter exhibit that 33 autocorrelation is present in these data after adjusting for 34 the effects of the covariates. Additionally, the prior related 35 to the work dimension (WMPI) is near zero, indicating that 36 this dimension does not contribute (i.e., it is not relevant) to 37 the spatial heterogeneity of the SCFR. On the other hand, 38 the most relevant dimension is the dwelling (DMPI) with a 39 weight of about 0.9, which potentially means that for an in-40 crease of 0.1 in the DMPI, the SCFR would then increase 41 by 9%. In other words, if the contribution of the DMPI to 42 the total MPI increases by 10%, then the SCFR would then 43 almost half of the weight of the DMPI (Table 3) . Estimated relative risks for the regression parameters show 2 that the posterior relative risk for the DMPI dimension was 3 1.74 (Table 4) . Thus, departments with a higher proportion 4 of poor people with deprivation of the dwelling dimension 5 (lack of access to safe water, inadequate disposal of human 6 feces, poor housing construction, and critical overcrowding) 7 have 74% higher risk of dying from COVID-19. The pos-8 terior relative risk for the EMPI dimension was 1.69, thus, 9 in administrative units with a higher proportion of poor peo-10 ple with deprivation of the educational dimension (illiteracy, 11 low educational attainment), the risk of dying from COVID-12 19 is higher by 69%. Furthermore, in administrative units 13 with a higher proportion of poor people with deprivation 14 of the childhood/youth dimension (school non-attendance, 15 school lag, barriers to childhood care services, child labor), 16 the risk of dying from COVID-19 is higher by 35%. More-17 over, the posterior relative risk for the HMPI dimension was 18 1.16, suggesting that departments with a higher proportion 19 of poor people with deprivation of the health dimension (lack 20 of health insurance, barriers to health services) have 16% 21 higher risk of dying from COVID-19. Finally, the poste-22 Figure 3A shows the spatial pattern of the relative risk of Figure 3B shows the results of testing the performance of 

We provide a comprehensive study of socioeconomic risk 17 factors for dying from COVID-19 in Colombia, using the 18 multidimensional poverty index and the official COVID-19 19 death reports of the Colombian National Institute of Health. 20 Our results corroborate that people living in more socioe-21 3 We consider the official COVID-19 dataset even con-4 taining biases inherent to underreporting and the number 5 of diagnostic tests performed. However, we contemplated 6 the spatial isotropic underreporting rate (INS, 2020), which 7 implies that although the values found for the case-fatality 8 rate are not definite, the described spatial trend is expected 9 to continue. We verify that a spatially homogeneous incre-10 ment in the observed cases generates an adjustment of the 11 intercept, however, maintaining the importance of each MPI 12 dimension, as shown in the results of this work. 13 We evidence that health, dwelling, educational, and child- The employment dimension associated with informal work 5 and economic dependency was not significantly related to 6 COVID-19 dying risk, despite the large proportion of so-7 cioeconomically disadvantaged people who are dependent 8 on informal activities in all Colombian departments. At the 9 beginning of the COVID-19 outbreak in Colombia, the Colom-10 bian government declared a national measure of Mandatory 11 Preventive Isolation, canceling, among others, informal work 12 activities, despite the absence of social and labor security 13 protection for these workers and the impossibility of work-14 ing remotely (Romero-Michel et al., 2021) . This measure of 15 confinement of informal workers along with the staying-at-16 home pattern of economically dependent people could gen-17 erate the prevention of these populations getting infected and 18 dying from COVID-19. Persons working in production and 19 transportation have been reported as predictors of deaths from 20 COVID-19, possibly because many of these occupations of-21 fer below-average salaries and lack paid sick leave (Harring-22 ton, 2020).

In a given population, age and race/ethnicity can drasti-24 cally affect the COVID-19 fatality, indicating that these can 25 be natural factors to explain the spatial heterogeneity of the 26 SCFR. However, this relation is not necessarily direct. For 27 instance, the heterogeneity of the case fatality risk cannot 28 be related to a homogeneous variable, indicating that a spa-29 tially homogeneous density of elderly or race/ethnicity can-30 not be statistically related to the SCFR. Additionally, it is 31 also possible that in a department with a high MPI, an in-32 dividual of a specific population group (Afro-descendant or 33 elderly) has drastically more risk for dying from COVID-19 34 than an individual from an area with better socioeconomic 35 conditions, i.e., there is a spatial variation of the density of 36 elderly or race/ethnicity, but it is not relevant (or statistically 37 significant) to the spatial distribution of the case fatality risk. 38 We find that in the specific case of Colombia, the contribu-39 tions of the dimensions describing the MPI are more relevant 40 than the age or the ethnic group populations. The compari-41 son of the spatial distribution of both populations older than 42 60 years and the Afro-descendant population with the SCFR 43 can be found in the Supplementary Material. 

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Bogotá DC., 04 December, 2021The authors declare: -This manuscript has not been submitted to, nor is under review at, another journal or other publishing venue.-The authors have no affiliation with any organization with a direct or indirect financial interest in the subject matter discussed in the manuscript Sincerely, The authors.