An economic analysis of productivity in organ transplantation in Brazil just before and after the COVID-19 pandemic

We evaluate the productivity of the Brazilian states and the Federal District in transforming potential organ donors into actual donations in the years immediately before and after the COVID-19 pandemic (2019-2022). The Brazilian National Health System (SUS) which is one of the largest public transplant systems in the world, provides full coverage of all costs involved in organ donation, transplants, and post-transplant. We applied Ordinary Least Squares Regression in data from 2019-2022 and the results indicate that there is signi ﬁ cant room for improvement in terms of converting potential donors into actual donors. The number of donors with organs transplanted decreased during the pandemic as the productivity of the transplant was affected, although it seems that the structure of the Brazilian transplant system and its technology were not signi ﬁ cantly affected permanently.


Introduction
Brazil has one of the most extensive public transplant programs in the world, and the Brazilian National Transplantation System (Sistema Nacional de Transplantes -SNT) provides full coverage of all costs involved in organ donation, transplants, and post-transplant [1].This country carried out 137,387 transplants in 2022 [2].Despite the relevance of the subject and the shortage of organs for transplants, transplantation process productivity assessments are still uncommon in Brazil and all over the world [3].
SNT faces great challenges since the mean waiting times are very long, the shortage of organs is permanent and a great backlog of patients has been observed.In absolute numbers, Brazil holds the fourth largest kidney and third liver transplant programs in the world [2].It is disturbing to realize that the number of potential donors is systematically above the number of transplants performed but, on the other hand, in 2022 there were 33,742 people on the waiting list for a transplant in Brazil [2].These fi gures are clear demonstrations of the existence of a lack of productivity in the Brazilian SNT.
A signifi cant problem in Brazil is the discrepancy between the number of potential donors and the number of transplants performed.To address the issue of evaluating productivity in carrying out the organ donation-transplantation process in the SNT, we chose to work with data from the years 2019-2022.The year 2019 was chosen because it was the year immediately before the COVID-19 pandemic, which brought serious disruption to transplantation activities in Brazil [4,5].
The year 2022 is the most recent year with available data after the end of the pandemic.Apparently, the SNT has recovered next section makes a brief digression on the econometric approach for evaluating the donation-transplant process.The third section presents our empirical results.Then we discuss and compare our results with other studies that evaluate the impact of the COVID-19 pandemic on organ transplants in other countries.In the last section, we offer some suggestions for further research and some concluding remarks.

The economic model
The process of transforming organs available from living donors or cadavers into organs transplanted into recipients is complex and hard to describe in economic terms.This process is made up of multiple steps.For an economic description of this process see Marinho and Araujo [3].The economic approach assumes that it would be desirable to produce as many transplants as possible from available organs.This assumption, conditioned by the complexity of the donationtransplant process, leads us to work within a framework that considers the search for improved productivity.
As we said above, we do not know a production function that represents the organ transplant process well.But it is possible to represent this process in a very general way.
Let us assume n inputs and m outputs.The vector of n inputs is x={x 1 ,....., x n }R n + and the vector of m outputs is y={y 1 ,....., y m }R m +.The technology set  is the set of combinations of inputs and outputs such that the inputs can actually produce the outputs:  ={(x, y)| x can produce y}.We rely on a few usual textbook assumptions: all production requires the use of some positive input quantities; free disposability of inputs and outputs; and some nature of returns to scale.

The empirical strategy and data collection
Our basic procedure is to run Ordinary Least Square Regressions (OLS) where the number of deceased that effectively donates organs is assigned as a dependent variable that is explained by the number of brain death notifi cations.
However, there are important heterogeneities in the sample as we will see in the data so the assumption of the existence of a linear relationship between the regressor and the dependent variable does not seem reasonable.To face the problem of nonlinearity we also performed a log-log regression model that converts the original data into a series of multiplicative terms, expressed on a logarithmic scale.This allows for better results when dealing with data featuring non-linear relationships between input and output variables.Furthermore, as there are large heterogeneities in the sample, the application of a loglog model helps to reduce possible effects of heteroskedasticity [6].Additionally, we executed a quadratic regression which is a regression used to fi nd the equation of the parabola that best fi ts a sample.A quadratic equation regression displays a U-shape curve that is either concave down or concave up.
It is important to clarify that a donor can donate several organs and tissues (heart, cornea, sclera, liver, intestine, bones, pancreas, skin, lung, kidney, etc.), which means that an effective donor can generate several transplantable grafts.
Then, we register each potential donor as an input unit and each effective donor as an output unit, in each Federation Unit in the years 2019-2022.As in Marinho e Araujo [3] our approach -of evaluating the transformation of potential donors into effective donors who had organs transplanted -is different from an alternative that involves evaluating the total number of transplants performed.With this option, we avoid the problem of also having to investigate the capacity for fi nal use (transplantation) of the different organs and tissues of each donor.This comprehensive task is a multifactorial problem, given that each organ and tissue has its own characteristics.
In short, in this paper, each cadaver that has had an organ transplanted will be an output unit, whatever the number of transplants of the different organs it generated.
It is worth noting that a notifi cation of brain death, which is a necessary (but not suffi cient) condition for transplants in Brazil [3], may not become an effective donor for several reasons: family refusal, transportation problems, lack of an adequate receptor in a timely manner (most organs only last a few days), problems with organ extraction and maintenance, medical contraindication, etc. [3,7].Morais, et al. [8] point out that the ratio between potential and actual donations in Brazil was only 35.5%, mainly due to medical contraindications.
According to the ABTO [9], the main causes of losses are family refusal, medical contraindication, cardiac arrest, and unconfi rmed brain death.

Data were collected from offi cial documents -the Brazilian
Transplantation Registry of the Brazilian Organ Transplant Association (ABTO), (available at https://site.abto.org.br/conteudo/rbt/).The data were analyzed using the free software environment R (R Development Core Team R) [10] A language and environment for statistical computing.R Foundation for Statistical Computing) Version 4.2.2.The data and the relevant summary statistics are presented in Table 1.
The variable TX represents the number of deceased who effectively donate organs after a brain death is notifi ed and the variable NOTIF represents the number of brain death notifi cations in both years under analysis.

Results
The transplant activities in Brazil may be subject to regional and state-size heterogeneities as can be seen in Table 1.The large differences in the number of transplants and notifi cations of brain deaths between the states are refl ected in the summary statistics presented in the fi nal rows of Table 1.These discrepancies refl ect the large socioeconomic differences between the states in the most developed regions It should be noted that the aforementioned differences between the states and regions of the country do not show a signifi cant downward trend in the period studied.For example, the Coeffi cient of Variation (CV) of donors with organs transplanted (TX) went from 1.30 in 2019 to 1.32 in 2022.The total number of notifi cations increased from 11,395 to 13,195, that is, approximately 16 %, but in the opposite direction, the number of donors with organs transplanted decreased from 3,211 to 2,905 a drop of 9.5 % which indicates a loss of productivity in the system that may have been caused by the COVID-19 pandemic [1,4,5].The productivity in the transformation of donors into transplants, which can be measured by the TX/ NOTIF ratio, fell from 28.2% in 2019 to 22.1% in 2022.transformation allows us to calculate the elasticities in econometric models [6].Elasticity is an economic measure of how sensitive one economic variable is to changes in another.
If a variable changes more than proportionally when another increases or decreases the relationship between them is said to be elastic.Otherwise, the relationship is said to be inelastic.
More specifi cally, in our case, a 1% increase in the notifi cation rate (NOTIF) would imply an increase of 1.4% in donors with organs transplanted (TX) in the year 2019 and an increase of almost 1.5% in the year 2022.In summary, the increase in the amounts of donors with organs transplanted is approximately 40% to 50% greater than the increase in the number of notifi cations, which allows us to conclude that efforts to increase the notifi cation rate may be highly rewarding.This     Brazilian transplant system.The parameters of the econometric models did not undergo major changes, remaining statistically signifi cant and with few quantitative variations.Apparently, the drop in performance was caused by various restrictions imposed by the pandemic on the healthcare system, as we will in the following section [11,12].

Discussion
Brazil carried out 137,387 transplants in the year 2022.
Despite this, 33,742 people were on the waiting list for organ and tissue transplants in the country at the end of 2022, with waiting times lasting years, depending on the case.One of the main obstacles to carrying out transplants and reducing this backlog is the loss of transplantable organs, that is, the failure to carry out transplants in organs available from cadaver donors.
The literature reports that the COVID-19 pandemic caused negative impacts on transplantation activities and there was an increase in the number of people on transplant waiting lists around the world [1,13,14].Brazil was also negatively affected       Our study is limited by the great disparity in the capacity to carry out transplants between Brazilian states, as seen in Table 1.As the sample is small each year (n = 26), it would not be

Productivity (%): TX/NOTIF
from the damage caused by the COVID-19 pandemic, and there are no signifi cant differences in terms of capacity to transform potential donors into effective donors before and after the pandemic, but this recovery capacity has not yet been refl ected in the overall performance of the SNT.The remainder of this paper is organized as follows.The 002 Citation: Marinho A (2023) An economic analysis of productivity in organ transplantation in Brazil just before and after the COVID-19 pandemic.Arch Organ Transplant 8(1): 001-007.DOI: https://dx.doi.org/10.17352/2640-7973.000021 of the country (South and Southeast regions -mainly the State of São Paulo) and poorer regions (Northern and Northeastern regions), which is refl ected in the ability to detect brain deaths, preserve corpses and perform transplants.This is all despite the fact that the Brazilian National Transplant System is part of the Brazilian public health system, the Unifi ed Health System (SUS), which is a reference among public health systems in the world.Citation: Marinho A (2023) An economic analysis of productivity in organ transplantation in Brazil just before and after the COVID-19 pandemic.Arch Organ Transplant 8(1): 001-007.DOI: https://dx.doi.org/10.17352/2640-7973.000021

Figures 1 ,
Figures 1,2 below show that brain death (NOTIF) and Transplants (TX) are highly correlated in the years 2019 and conclusion indicates that there is room to expand the number of transplants with quantitative results in donors with organs transplanted proportionally greater than the augmentation in the number of notifi cations.Obviously, in strictly economic terms, the costs of increasing notifi cations should be compared with the value of added transplants, but this is an exercise thathas not yet been carried out in Brazil.Tables 2,3 below also show that in our quadratic models, the variable NOTIF^2 presents coeffi cients with negative and statistically signifi cant signs, indicating the presence of convexity and decreasing returns to scale only in 2019, that is, before the pandemic increases in transplant production less than proportional to the increase in notifi cations.However, as the NOTIF^2 parameter ceased to be statistically signifi cant from 2020 onwards, this effect could no longer be observed in subsequent years, which means that the presence of decreasing returns to scale ceased to exist in the sample.When comparing the two regressions in the year immediately before the pandemic (2019) and the year immediately after (2022) we see that the elasticity increased slightly, from 1.40 in 2019 to 1.49 in 2022 but, on the other hand, the quadratic term (NOTIF^2) which was negative and statistically signifi cant in 2019 is no longer signifi cant in 2020-2022.However, as we saw productivity measured by the ratio (TX/NOTIF) fell from 28.18% to 22.02% in the period.Therefore, we cannot rule out the hypothesis that the capacity to transform actual donors into potential donors after the pandemic is not very different from what was achieved before it.We can observe that notifi cations fell from 11,695 to 10,639 (a drop of 9.0%) between 2019 and 2020, while donors who originated transplants fell from 3,211 to 2,789 (a drop of 13.1%).In 2021, notifi cations rose to 12,215, surpassing the performance of 2019 (pre-pandemic) but transplants rose to just 2,695, still below the pre-pandemic year.In 2022 we observed notifi cations reached 13,195 but only 2,905 transplants were performed.In Figure 5 below, we see that productivity (TX/NOTIF) fell from 28.2% in 2019 to 22.1% in 2022.At the end of 2022, the Brazilian transplant system had not yet fully recovered from the impacts of the COVID-19 pandemic.In Figures 6-9 and Table 3 below, we can see that the pandemic, which peaked in the years 2020 and 2021, did not signifi cantly affect the ability -or the technologyto transform potential donors into effective donors in the

[ 1 , 4 , 5 ,
10,15].Aubert, et al. [13] compared transplant activities in 2020 from the date of the 100th reported cumulative COVID-19 case to Dec 31, 2020 (or the end of follow-up, whichever was earlier) to the same period of time in 2019 and reported an
possible to resort to stratifi cation or the creation of clusters and still use linear regression models.Carrying out separate studies for each type of transplantable organ and tissue (kidney, liver, heart, lung, cornea, etc.) would be recommended but was not possible in the present text, given the size limitations of a study of this type.It is also recommended that longer-term monitoring be carried out with data after the pandemic to assess possible effects that have not yet been detected.Such effects include lessons that have not yet been fully explored, which did not manifest themselves immediately but which may be important in the future performance of the Brazilian National Transplantation System.Conclusion Apparently, Brazil recovered its capacity to transform potential donors into effective donors after the negative impact of the COVID-19 pandemic, but at the end of 2022, the country's transplant activity had not yet returned to the levels observed in 2019.

Table 1 :
Number of deceased that effectively donate organs (TX); number of brain death notifi cations (NOTIF) and summary statistics.