Multivariate regression analysis in the probability of deaths in COVID-19 cases : a case study in the State of Pará , Amazon region , Brazil

Since the first detected cases of COVID-19 in Brazil, researchers have made a great effort to try to understand the disease. Understanding the impact of the disease on people can be instrumental in identifying which groups can be considered at risk. Therefore, this study researches a probabilistic model based on a statistical model of non-linear regression analyzing the following variables: age, if you are a health professional, if you are resident in the Metropolitan Region of Belém (RMB), State of Pará and gender with the objective of identifying those people who have a greater impact on the number of people infected and killed by COVID-19, that is, people who are more likely to die. To carry out the research, we used the data of all infected people by COVID-19 in the State of Pará until July 2020. It can be verified according to the proposal of the probabilistic model that elderly people, with a odds ratio of 1.69 (95% CI 1.52-1.88), residents of Metropolitan Region of Belém, with an odds ratio of 2.14 (95% CI 2.02 2.27) and men, with an odds ratio of 1.83 (95% CI 1.73 1.95) are groups of people with a higher risk of dying from diseases, while health professionals, with a 0.36 chance ratio (CI9 5% 0.29 0.45), are less likely to die.

. Average of 14 days of confirmed cases in metropolitan region of the city of Belém in the period between 03/18/2020 to 07/23/2020. Source: Authors. From the data in Table 1, it appears the majority of confirmed cases of the disease occurred in women (51.65%), however, the majority of deaths occurred in men. This can show men are more resistant when seeking medical help when necessary, causing the disease to worsen and consequently 198 delaying the start of treatment, (Martins, L. K. et al., 2020). According to the 2010 demographic census, 7.5% of the Pará population are aged between 30 and 39 years, (IBGE, 2010). A large part of the people in this age group are economically active, therefore, they need to travel a lot from their homes to work, increasing the chances of contagion. That may explain the fact almost 25% of confirmed cases in the state of Pará are exactly people in this age group, as can be seen in Fig. 4. Likewise, more than 20% of the population of Pará are under the age of 20. However, less than 10% of confirmed cases are from people in this age group. The main characteristic of people in this age group is made up of students, and because of the social isolation measures to contain COVID-19, presential teaching activities were suspended, which may suggest that these people are less vulnerable to being infected.
The gardity of the disease is more noticeable of advanced age people. This is even more evident when the percentage of death is observed in people over 60 years of age. The elderly developed the most severe form of the disease when they tested positive for COVID-19, especially when they had a history of associated comorbidities such as: cardio vascular diseases, uncontrolled blood pressure, diebetes and kidney diseases, among others. People over 60 years old had a rate of 75% of registered deaths in the state of Pará, which clearly shows they are part of the risk group.
Another characteristic observed in this research is related to the place where infected people reside. The results presented in Table 2 show the percentage of confirmed cases and deaths by COVID-19, by patient's place of residence. It is noted that just over 20% of confirmed cases in the state of Pará, occurred in the MRB. Due to the overcrowding of hospitals, the health system almost collapsed mainly in the capital (Belém, Brazil), where many patients did not receive adequate care, and some died.
Another fact that we can verify is that more than 40% of the deaths in the state of Pará. It is worth mentioning that if there was a greater availability of clinical beds, both in the public and private network, many lives could have been preserved.
To estimate the death probability of a person due to COVID-19 in the metropolitan region of the city of Belém, a probabilistic model was used by means of multiple logistic regression (MLR). The application of MRL is used to obtain the statistical model that best fits the response variable.  The statistical model obtained from the binary logistic regression for the probability of death by COVID-19 in the state of Pará (Yˆ), is given by Eq. 8: In Table 3, the positive coefficient (β1 = 0.072) for X1, suggests that deaths increase according to age. Thus, the odds ratio of 1.07 indicates that with each year older, a person diagnosed by COVID-19 has a greater than 7% probability of dying. This is only valid if the other variables are constant, which proves the severity of the disease for older people.
For variable X2, the negative estimate (β2 = −1.011) suggests that people who are health professionals are less likely to die. In addition, the odds ratio of 0.36 indicates that people diagnosed with COVID-19 who are not health professionals are almost 3 times more likely to die than health professionals, as long as the other variables are constant.
This probability for variable X2 can be explained due to the fact that every health professional, in order to exercise their activities, needs to undergo a rigorous immunization process, taking all vaccines recommended by the Ministry of Health, of Brazil, through the Reference Centers in Special Immunobiologicals (Cries). The unhealthy environment in which they work must also be taken into account, which supports the development of various antibodies.
For variable X3, the positive estimate (β3 = 0.525) suggests that people aged 60 or over are more likely to die from COVID-19. In addition, the odds ratio of 1.69 indicates that people in this age group who test positive for coronavirus have a 69% greater chance of dying than people diagnosed under 60 years of age.
The positive coefficient (β4 = 0.762) for variable X4 suggests that people residing in MRB are more likely to die from COVID-19 than people diagnosed and who do not live in MRB. The odds ratio is 2.14, which means that, as long as the other characteristics are constant, a person residing in the MRB is more than twice as likely to die by COVID-19 than a person who lives in other cities. The high occupancy rates and even the overcrowding of clinical beds in the metropolitan region's health system may explain this high probability.
Finally, for variable X5, the positive coefficient (β5 = 0.606), suggests that the probability of death is higher in men than in women. The odds ratio of 1.83 indicates that a man has an 83% greater chance of dying from COVID-19 than a woman, keeping the other variables constant.  Table 5 shows the estimated probabilities for the adjusted multiple logistic regression model. After validation, we used it to estimate the probability of deaths from COVID-19 in the MRB. Where it was possible to observe, for example, that a man aged 80, who is not a health professional, resident of MRB, has a 44.50% probability of dying from COVID-19. On the other hand, a young man (25 years old), a health professional and not a resident in the MRB region, is less likely to die from COVID-19, with approximately 0.10% of chances.