key: cord-0792697-vsw4azts authors: Diaz-Martinez, J. P.; Orozco-Becerril, K. J.; Gallegos-Herrada, M. A.; Fuentes-Garcia, R.; Gutierrez-Garcia, M. A.; Espin-Garcia, O. title: Multi-level multi-state modelling applied to hospital admission in mexican patients with COVID-19 date: 2021-05-26 journal: nan DOI: 10.1101/2021.05.24.21257752 sha: a9731c3ea2e056e3128714c64b9859868a66f6e6 doc_id: 792697 cord_uid: vsw4azts Since the beginning of the SARS-CoV 2 pandemic, healthcare authorities have made clear that it is crucial to track and identify COVID-19 symptoms and seek medical attention in the presence of the first warning signs, as immediate medical attention can improve the patient's prognosis. Therefore the present work aims to analyze the risks associated with the time between the patient's first symptoms and hospitalization followed by death. A cross-sectional study was performed among Mexican population diagnosed with COVID-19 and hospitalized from March to January 2021. Four different Bayesian models were developed to asses the risk associated with different patient trajectories: symptoms-hospitalization and hospitalization-death. Comorbidities that could worsen the patient outcome were included as linear predictions; these analyses were further broken down to the different states of the Mexican Republic and the healthcare providers within. Model III was chosen as the best performance through a validation of leaving one out (LOO). Increased risk for hospitalization was observed at the global population level for chronic renal disease, whereas for death such was the case for COPD and the interaction of diabetes:hypertension:obesity. Our results show that there are differences in mortality between the states without accounting for institution and it is related to the prompt time of death or viceversa. Regarding the 6 healthcare providers included in the analysis differences were also found. While state-managed hospitals and private sector showed lower risks, in contrast the IMSS seems to be the one with the highest risk. The proposed modelling can be helpful to improve healthcare assistance at a regional level, additionally it could inform statistical parameter inference in epidemiological models. The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) pandemic was 2 declared a Public Health Emergency of International Concern on January 30, 2020 by 3 the World Health Organization.The Mexican Health Authorities declared the first 4 lockdown on March 26 with 585 cases and 8 deaths reported for COVID-19 [1] ; by the 5 end of the first lockdown (June 5th, 2020) total number of cases and deaths were 110,026 6 and 13,170, respectively. By November 1, Mexico became the fourth country in number Over time it has become clear that comorbidity factors such as hypertension, type 2 10 diabetes mellitus, obesity and smoking increase the seriousness of the disease, leading to 11 a higher rate of hospitalizations with an additional 25% of the cases requiring intensive 12 care unit (ICU) admission and ultimately, intubation and death [4, 5] . 13 Mexico ranks second in obesity among OECD countries, with an obesity rate of 14 72.5% among the adult population, which is associated with the high prevalence of type 15 2 diabetes mellitus, estimated at 13% of the adult population in 2017, the highest rate 16 among OECD countries; the rate of hypertension is also one of the highest chronic 17 diseases among adult population with 30% [6] . The high prevalence of these 18 comorbidities besides the precarious healthcare system could be among the main reasons 19 of the elevated severity of the number of cases and deaths rates in the country [7, 8] . 20 In Mexico, healthcare providers are divided in public and private services. There are 21 different public institutions which provide care to different sets of the population: the 22 state employees (ISSSTE), the army (SEDENA) and naval members (SEMAR), the oil 23 state company (PEMEX) employees and private companies employees (IMSS). There 24 are also public hospitals for population with no health service coverage (SSA adn). In 25 general, the care withing different healthcare providers cannot be considered 26 homogeneous, therefore it should be relevant for the final outcome of a COVID-19 27 patient. There have been many efforts using local data to understand how patients with 29 comorbidities are affected by COVID-19; the work by Bello-Chavolla et al. [9] proposed 30 a clinical score to predict COVID-19 lethality, including different factors like type 2 31 diabetes mellitus and obesity among confirmed and negative This work lead to believe that obesity mediates 49.5% of the effect of diabetes on 33 COVID-19 lethality. Also, early-onset diabetes conferred an increased risk of 34 hospitalization while obesity increased the risk ICU for admission and intubation. Moreover, Olivas-Mart{'i}nez et al. [5] found that main risk factors associated with 36 in-hospital death were male sex, obesity and oxygen saturation < 80% on admission 37 using data from a SARS-CoV-2 referral center in Mexico City. After onset of infection there is a period of time between symptom detection and 39 hospitalization. The time elapsed before patients approach hospitals could be 40 excessively long. Once patients are admitted to hospital, there is also a period of time 41 between the admission and death. Estimation of these lengths of time through a 42 multilevel model could enable a better information system to estimate incidence and 43 transmission rates, particularly at regional level where differences can be apparent. In 44 addition, these times are useful for estimating hospitalisations and deaths in COVID-19 45 epidemiological models [10, 11] . This work considers a multi-state model under a Bayesian framework to estimate 47 times between symptom detection and hospitalization and between hospitalization and 48 death. We used data of confirmed and negative COVID-19 cases and their demographic 49 and health characteristics from the General Directorate of Epidemiology of the Mexican 50 Ministry of Health; the analysis provides of general overview of these times in each state 51 of the country and the different health institutions within. Variables affecting the 52 patient's final outcome such as the aforementioned comorbidites are included in the 53 model as fixed effects. Additionally, regional heterogeneity is accounted for as random 54 effects through nested models that consider the regional contribution and also the health 55 service provider. Other efforts in recent literature [12] have considered more states 56 (hospitalization-ICU, ICU-death, ICU-discharged), which allows researchers to asses 57 whether improvements in patient outcomes have been sustained, finding evidence that criteria were the observations with incomplete data about hospital admission, symptoms 77 or comorbidities. Additionally, patients whose time of initial symptoms was captured as 78 the day they were admitted to hospital were removed, since this time was likely to be 79 unknown. Finally, we only included patients who experienced either hospitalization or 80 death due to the lack of date of recovery in the dataset. The following variables were included as linear predictors for modeling time from 82 symptoms to hospitalization: presence of chronic obstructive pulmonary disease 83 (COPD), obesity, chronic kidney disease (CKD), asthma and immune-suppression. For 84 time from hospitalization to death, we included the next variables: presence of type 2 85 diabetes mellitus, COPD, obesity, hypertension, CKD and the interaction between 86 obesity, diabetes and hypertension. Both times also included age and sex as predictors. 87 About 87% of the population in Mexico is affiliated to some healthcare provider, but 88 during this pandemic the mexican government has established a list of hospitals 89 designated to treat COVID-19 patients without any affiliation distinction. In this study 90 we identified 6 different healthcare providers which were classified according to their We used a QR reparameterization for the predictor matrix X, i.e. X = QR , where 101 Q is an orthogonal matrix and R is an upper triangular matrix. This parameterization 102 is recommended when no prior information is available on the location of the predictors' 103 coefficients [15] . Moreover, we used a noncentered parameterization [16] by shifting the 104 data's correlation with the parameters to the hyperparameters. Each model captures different levels of information, as more levels were included it 106 was possible to differentiate the results according to the added information. Model I: One level 108 Let M and H correspond to survival times for deaths and hospitalizations, respectively. 109 We assumed that these times are observations from two independent Weibull 110 distributions, such that, where Q * and Q * * are the orthogonal matrices from the QR reparameterization, θ 112 and ϑ are the coefficient vectors for deaths and hospitalizations, µ m and µ h represent 113 the global intercepts for deaths and hospitalizations, alpha denotes the shape of the 114 Weibull distribution, and α r is an extra parameter for the noncentered parameterization 115 This part of the model is described in red in Figure 1 . The second model adds an additional level to account for each state of Mexico as a 118 random effect to explain deaths, such that, where µ l , l = 1, ..., 32 represents a local intercept per state (random effect), µ r l denotes 120 the extra paramateres for the noncentered parameterization, and σ is the dispersion All rights reserved. No reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted May 26, 2021. ; https://doi.org/10.1101/2021.05.24.21257752 doi: medRxiv preprint Model III: Three levels Based on Model II, we considered an extra random effect 124 µ k , l = 1, ..., 6 which take into account the healthcare provider previously described. Because of this, an extra dispersion parameter σ is added. This part of the model is 126 described in light pink in Figure 1 . The final model uses the same structure as Model III but nests healthcare provider 129 within each state. Inference is carried out using Markov chain Monte Carlo (MCMC), obtaining a 137 sample from the joint posterior distribution over the parameters given the observed data. 138 All Markov chains were generated with CmdStan [17] , using the No-U-Turn sampler [18] . 139 A check on the posterior predictive distributions is essential for validating results. Additionaly, to choose the model that best fits the data we considered the leave-one-out 141 cross-validation (LOO) proposed by Vehtari et al. [19] , which estimates pointwise 142 out-of-sample prediction accuracy, using the log-likelihood evaluated at the posterior 143 simulations of the parameter values. After applying exclusion criteria a total sample of 1200 registers of adult patients 146 belonging to any healthcare provider, either private or public in the 32 states of Mexico 147 was selected, preserving the population characteristics. We show results for model III which performed better in terms of the likelihood and 149 showed good convergence of all parameteres. The posterior 0.95 credibility intervals for 150 parameters of interest at different levels of the model are shown in Figures 2 and 3 . It is 151 worth pointing out that we are displaying the log hazard ratio, hence positive values for 152 parameters will point to increasing risks for the corresponding transition and level. Our results show that there are differences in mortality between the states without 160 accounting for institution and it is related to the prompt time of death or viceversa. Figure 4 displays evidence that 5 days after hospitalization there is a peak on 166 mortality rate, which could be related due the late hospitalization of patients with mild 167 symptoms who developed "happy hypoxemia," that is extremely low blood oxygenation, 168 but without sensation of dyspnea [20] . In Wuhan, within a cohort of patients infected 169 with (SARS-COV-2) who id not present dyspnea 62% showed severe disease and 46% 170 ended up intubated, ventilated or dead [21] . Regarding the 6 healthcare providers included in the analysis differences were also 172 found. While state-managed hospitals and private sector showed lower risks, in contrast 173 the IMSS seems to be the one with the highest risk ( Figure 3 ). Although it is worth 174 mentioning that following the national hospital transformation plan [13] found a higher risk of hospitalization, specifically in Veracruz which has been historically 208 unsteady regarding the public healthcare system in sectors like IMSS, ISSSTE, SEDENA/SEMAR/PEMEX. The fact that different final outcomes could be related to 210 patient's late hospitalization, hence suggesting that the average patient waits until the 211 symptoms are severe to seek professional healthcare, needs to be further investigated. One of the limitations of the study is the reduced number of states we were able to 213 include in the modls due to the lack of information regarding dates of disccharged of 214 recovered patient´s after hospitalization. May 24, 2021 10/11 All rights reserved. No reuse allowed without permission. (which was not certified by peer review) is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. The copyright holder for this preprint this version posted May 26, 2021. Early estimation of the risk factors for hospitalization and mortality 222 by COVID-19 in Mexico Sitio oficial COVID-19 México Dirección General de Epidemiología -228 Base del Sistema Nacional de Vigilancia Epidemiologica para el 230 In-hospital mortality from severe covid-19 in 234 a tertiary care center in mexico city; causes of death, risk factors and the impact of 235 hospital saturation COVID-19 in latin america. The Lancet Infectious Diseases mortality and health-care resource availability. The Lancet Global Health Predicting Mortality Due to SARS-CoV-2: 246 A Mechanistic Score Relating Obesity and Diabetes to COVID-19 Outcomes in Mexico Estimating the effects of non-pharmaceutical interventions on covid-19 in europe State-level tracking of covid-19 in the united states. Nature communications Trends in risks of severe events and lengths of stay for COVID-19 hospitalisations in 257 England over the pre-vaccination era : results from the Public Health England 258 Hospital reconversion in response to 261 the COVID-19 pandemic Sistema de Información de la Red IRAG 264 Stan user's guide A general framework for the 269 parametrization of hierarchical models CmdStan: The command-line interface to stan The no-u-turn sampler: Adaptively setting path 273 lengths in hamiltonian monte carlo Practical Bayesian model evaluation using 275 Is 'happy hypoxia' in COVID-19 a 278 disorder of autonomic interoception? A hypothesis Characteristics of Coronavirus Disease 2019 in China