key: cord-0496844-cvbpgvso
authors: Dinamarca, Jos'e Luis; Aguilar, Sara; Runzer-Colmenares, Fernando; Morales, Alexander
title: Clinical concepts might be included in health-related mathematic models
date: 2020-04-23
journal: nan
DOI: nan
sha: 529076e3b1ecf8b2e7ef44c9ccaf34812277ff6d
doc_id: 496844
cord_uid: cvbpgvso

The construction of mathematical models that allow comprehensive approach of decision-making in situations of absence of robust evidence is important. While it is interesting to use models that are easy to understand, using values of direct interpretation, we analized a published index (COVID-19 Burden Index) and found it seems to be oversimplified. It is possible that the proposed index, with current data, could be useful in geographically and administratively narrowed places. But it is inaccurate to be applied throughout the process and in places as broad as American countries. It would be ideal to correct and refine the referred model, bearing in mind clinical concepts described, to take advantage of the proposal and generate a more accurate response, which can serve as an input both in the implementation of measures and in the prediction of the behavior of a pandemic like the current one. However, what we propose is to improve the accuracy of the model in terms of quantities and applicability, agreeing with the concept of"stay at home". The approach between complementary areas of knowledge should be the door that we must open to generate the new evidence we need. Mathematics should not dispense clinical sciences.

We have carefully read the ar cle "Is a COVID19 Quaran ne jus fied in Chile or USA right now?", published by RI González, F Muñoz, PS Moya and M 1 Kiwi . The construc on of mathema cal models that allow comprehensive approach of decision-making in situa ons of absence of robust evidence is important. As such, the approach from the exact sciences is ma er of interest to the current pandemic.

Indeed, we have some examples of current models. In Mexico, an a empt has been made to predict the behavior of COVID-19 and es mate possible scenarios through Gauss model. With the Universidad de Guadalajara´s data, "contagion cri cal days" between March 20th-24th, were determined.

Assuming Y=1.0257x and R2=0.9846, and considering how the virus evolved in China and recent local data, the results using the equa on, with 98% confidence, create some possible op mis c and cri cal scenarios. The model was built to es mate these scenarios at 5 days and not daily (as in Spain or Italy) given the fewest 2 confirmed infected in Mexico .

While it is interes ng to use models that are easy to understand, using values of direct interpreta on, the proposed index ("COVID-19 Burden Index") seems to us to be oversimplified. This, because the authors minimize the impact of three relevant situa ons that are substan al issue of the integral process: First, in rela on to a contextual jus fica on, they use the assump on that different country-reali es are comparable. Second, rela ve to the equa on, they use a numerator greater than the actual one. Finally, in rela on to the denominator, they do not incorporate fundamental clinical-epidemiological variables. All this leads to a possible overes ma on of the total, with a risk of bias in the interpreta on and applicability of the results. We will briefly develop these three elements in the same order in which we have just presented them.

Three reali es (South Korea, United States of America and Chile) are put as comparable considering data related only to the COVID-19 incidence. It is not taken 3 into account that South Korea is a small country with just over 100,000 km² (109° according to land surface globally), with four ci es (Seoul, Busan, Incheon and Daegu) concentra ng just over a third of the country's 4,5 total popula on; United States of America is a federal country with almost 10 million Km² (4°), in which the fi een most populous ci es do not account 6 for even 10% of the country's total; while Chile is a highly centralized country with approximately 750,000 Km² (38°) in which a single city (San ago) concentrates one third of the country's total popula on (Table N° 1 ).

Analyzing and comparing the incidence of a disease, without considering the geographical and popula on reali es of three very different territories cons tutes a methodological limita on, too important not to be considered in the development of a model. Since the measures being implemented will be different according to geographical reali es, the ini al rate of contagion will be different, and the distribu on of resources available to deal with the disease will be different. In the Mexican example, the total N of confirmed cases reached a value less than the daily N confirmed in Spain and Italy, in the same me elapsed since "case one". That is why we think it is correct to compare similar reali es, especially in terms of popula on concentra on according to territorial area, and according to the distribu on of cri cal resources that exist in a given place and me.

Next, the numerator (15% of the confirmed popula on), equates to between 3 and 6.5 mes the es mated number of people that will require 7 mechanical ven la on . There is no jus fica on for why this high percentage was used. Had it ini ally been decided that the total N of confirmed cases were going to develop severe pneumonia? However, in most hospitals in La n America -including Chile-this type of pa ent does not necessarily recharge intensive care beds, but specialized beds. This is a major factor to refine in the proposed model. Correc ons that would bring the model closer to reality would be:

Or, in any case:

N confirmed × 0.05

In sta s cal terms, the problem is to use all of the N observa ons to obtain op mal es mates of the ˆθi of the θi, considering the uncertainty introduced by the observa on errors. This is a problem that Gauss describes as "the most important of the applica on of 2 mathema cs to natural philosophy" .

Finally, with regard to the denominator, the following elements should be well thought-out: The distribu on of clinical resources that each country has to deal with a situa on such as the current one, beyond the gross N. Relevant in all cases, is especially relevant in c o u n t r i e s w i t h s t r o n g o r g a n i z a o n a l a n d administra ve centralism, as La n Americans: The distribu on of resources is heterogeneous and does not have to relate to a par cular N of contagions in the same place and me. On the other hand, there is a set of variables that makes a comparison between countries more complex. Beyond the effect that certain measures implemented may have generated on the shape of the infec on, lethality and recoverability curves, there will always be popula onspecific variables that will end up affec ng the development of these curves: gene c, nutri onal and idiosyncra c elements. Variables of this type should be considered and quan fied to be included in the denominator in the form of a correc ve factor.

It is possible that the proposed index, with current data, could be useful in geographically and administra vely narrowed places. But it is inaccurate to be applied throughout the process and in places as broad as American countries: Today, the reality in Chile shows that for several days we would be with a result "1" which, according to the model, should be interpreted as "collapse of the health system", which is s ll far from happening. It would be ideal to correct and refine the presented model, bearing in mind the concepts described, to take advantage of the proposal and generate a more accurate response, which can serve as an input both in the implementa on of measures and in the predic on of the behavior of a pandemic like the current one. However, what we propose is to improve the accuracy of the model in terms of quan es and applicability, agreeing with the concept of "stay at home".

In conclusion, we believe that the approach between complementary areas of knowledge should be the door that we must open to generate the new evidence we need. Mathema cs should not dispense clinical sciences, and the result of mutual synergy will always exceed the mere sum between the two. As long as evidence is built, we must avoid venturing conclusions that can promote or result in hasty decisions. 

Is a COVID19 Quarantine justified in Chile or USA right now?

Gauss's contributions to statistics

Food and Agriculture Organization of the United Nations

Clinical Characteristics of Coronavirus Disease 2019 in China