Public in general and healthcare professionals in particular are confused from unclear and conflicting information in the organ transplant related data. To sort out and clarify such confusions, a statistical methodology is constructed and demonstrated in this article. The gap between the number of organ donors and the number waiting for organ transplant is named shortage. The gap between the number of organ donors and the number of recipients is named illegal organ trade level. The gap between the number of organ recipients and the number waiting for organ transplant is named unmet organ demand. Expressions are derived, based on a statistical methodology, to compute the confidence interval for these true unknown gaps. A few recommendations are compiled and stated in the end to close such gaps for the sake of those waiting for organ transplant to have a quality life.

 

Keywords: Multivariate Gaussian distribution; Confidence Interval; Mahalanobis distance.

What is organ or tissue transplantation? It is replacing a person’s damaged or absent organ by an organ from a living or deceased person. The regenerative medicine allows sometimes to grow tissue from the person’s own stem cells. Organs or tissues that are transplanted within the person’s body are called auto grafts. Transplants that are performed between two subjects of the same species are called allografts. The first and earliest historical transplant was auto grafted skin in nose reconstruction called rhinoplasty by an Indian surgeon Sushruta in the 2nd century B. C. Other noteworthy transplants and their time are summarized below.

 

•       In 1905, a Czech Surgeon, Eduard Zirm performed the first successful cornea transplant.
•       In 1950, an US surgeon, Richard H. Lawler performed the first successful kidney transplant.
•       In 1967, the first successful heart transplant was done by a South Africa’s surgeon Christian Barnard. 
•       In 2005, an Indian surgeon, P. N. Mhatre did the first successful ovarian transplant.
•       In 2008, the first baby was born from a transplanted ovary by US gynecologist Sherman Silber. The donor was her twin sister.

Popularly transplanted organs are heart, kidneys, liver, lungs, pancreas, intestine, and thymus. Commonly transplanted tissues are bones, cornea, skin, heart valves, nerves and veins. Tissue is procured from those who experienced brain death or cessation of heartbeat. Unlike organs, tissues are stored for a short duration, up to five years. The American Association of Tissue Banks estimates that a million tissue transplants occur each year in the United States of America (USA). Bone marrow is a flexible tissue in the interior of bones. Bone marrow constitutes a four percent of the total body mass of humans, supporting the body’s immune system. There are about 25 million people are listed as bone marrow donors worldwide. A practical difficulty in transplants is the recipient’s body rejection of organ/tissue due to antigens. This is resolved using a technique called serotyping, which checks the matching between the recipient and the donor. The World Health Organization (WHO) announced that about 66,000 kidney transplants, 21,000 liver transplants and 6,000 heart transplants were performed globally in 2005. Still, there is a severe shortage of organs or tissues. A purchase or sale of illegal organs from live donors is prohibited in many countries.

 

For a variety of reasons, thousands of persons are waiting for organ transplant. This number has been rising globally over the years, while the number of donors is quite stable. The supply of organs comes from the living or dead persons on voluntarily basis. Of course, the number of donors is trailing far behind the demand for organ transplant. The awareness to donate organs to use ought to increase so that their gap narrows. There might be cultural, religious, ethnic, or economic stumbles for not many donated organs for transplant. At the same time, one wonders whether the demand for organ increases due to deteriorating health among world citizens due to environmental, genetic, or poor quality life practices. A promotion of healthy living might reduce the need for organ transplant.

 

Let us be factual. For a lack of organs, about 22 people die every day. An average of 81 transplants occurs every day in USA. Another person is added to the waiting list in every 10 minutes. About 123,000 people are waiting for an organ transplant. The year 2014 was a record-breaking year for the number of transplants performed and the number of deceased donor transplants. About 29,532 transplants were performed in 2014. It was the first time more than 29,000 transplants were performed in a single year. Only 23,715 transplants were from deceased donors. 

About 3,500 heart transplants are performed annually worldwide. The majority of these (about 2,300) are performed annually in the USA. The lung transplants are risky. It takes about one hour for the pre-operative preparation of the patient. A single lung transplant takes about eight hours, while a double lung transplant takes about twelve hours to complete. A history of prior chest surgery may complicate the procedure and require additional time. A heart-lung transplant is carried out to replace both heart and lungs in a single operation. Due to a shortage of suitable donors, heart-lung transplant is a rarely done, about a hundred each year in USA.

 

Epidemiologists, healthcare professionals, legislative and administrative wings of the society need to pay attention to understand and resolve issues that exist in the transplantation of organs word wide (WHO,2004)[1]. The figure 1 illustrates that there is a wider gap between the number waiting for organ and the number donors of organ. Because the data in Figure 1 do not count tissue transplant, in discussions below, we mention only organs. Surprisingly, the number of persons who received transplants is, however, more than the number of donors. What does this apparent contradictory information mean could this contradiction hint out the under-reporting of data occasionally, family members or friends to alleviate the suffering of loved ones donate organs and it may be not reported. Could a data analysis resolve the conflicting information. The number waiting for organ transplant is much higher than the number of organ donors and it suggests a shortage for organ transplant. The number of organ donors is lesser than the number of recipients and it suggests that there must have been illegal organ trade [2]. The number waiting for organ transplant is higher than the number of recipients and it suggests the existence of unmet demand. This article has developed a statistical methodology to extract and interpret pertinent data information and then compute a confidence interval for shortage, illegal trade, and unmet demand with respect to organ transplantation. In the end, the required rules and regulations to overcome any abuse of human rights or ethics [3,4] are commented. Access to organ transplantation is a reason for rising medical tourism. About 80 percent of all organs are donated and used in the same geographic area. Many patients travel to countries, where organs are obtainable through commercial transactions. The unlicensed international organ trade is forbidden. In 2004, the WHO urged all its member States to protect the poorest and vulnerable groups from the undue exploitation of the transplant tourists seeking a sale of tissues or organs. A few recommendations are compiled and discussed in the end with an intention to promote the supply and implantation of organs.

 

 

 

2. A Statistical Methodology to Analyze and Interpret Transplant Data.

 

An appropriate underlying model for the data is a necessity. What is a model? A model is an abstraction of the reality. Then, a statistical methodology, based on an appropriate model for the data, needs to be constructed to extract pertinent information and interpret. Such an interpretation would be the basis for formulating and implementing policies in relation to organ transplantation.[5] For the importance of policy changes to encourage organ transplantation. The beneficiaries of organ transplantation would certainly have a higher quality life.

To develop an appropriate underlying model for the data, let denote a vector of random variables, in which, , and represent the number of persons waiting, the number of recipients, and the number of donors respectively. Because of the large data size and the well-known central limit theorem, the random vector follows a trivariate Gaussian distribution

       {C}{C}                                (1)

                        , and ) denote respectively the unknown mean vector, variance-covariance matrix, and the Mahalanobis distance. The probability-probability plots in Figure 2 through Figure 4 confirm their Gaussianity. The Mahalanobis distance is a Euclidean distance of an observed mean adjusted three-dimensional vector from the origin . The maximum likelihood estimator (MLE) of the parameters in multivariate Gaussianity (1) is

 

                 ,                          (2)

                           (3)

 

What is disturbing is that the number waiting for organ is about 700 percent more than the number of donors, which is only 46 percent of the number of recipients. How is that more recipients exist than the number of donors. The number of donors must have been under-reported. Close relatives or friends could have donated organ to wipe out the suffering of those recipients. Such a donation is legal but should be reported. Yet, why would it go unaccounted? Hence, the gap,between the number of donors and the number of recipients is the data evidence for the existence of illegal transactions of organ trade. We could formulate a research hypothesis (Q1): Is the gap statistically significant? If so, new regulatory policies against illegal purchase or sale of organs from poor and weaker donors and their implementations are necessities.

 

Likewise, the gap, between the number waiting for organ and the number of donors is  shortage of organs for transplant. Is the shortage statistically significant? If so, there is a need to promote the importance of organ donations. A new organ donation related policy is necessity. We formulate a second research hypothesis (Q2): Should there be a new legislation promoting worldwide organ donation.

 

Next, we formulate a third research hypothesis (Q3): is the gap, {C}{C} between the number waiting for organ and the number of recipients indicating a shortage of organs significant portraying the unmet demand for organ transplant statistically significant? If so, what needs to be done to close the gap?

 

When , there exist illegal transactions of organ trade. When , some donated organs are not transplanted, there must have been wastage of organs. Lastly, we formulate a composite research hypothesis (Q4): Conditional on the removal of illegal organ trade (that is,  ), what might be the expected and volatility of organ shortage?

 

To answer the above questions, we need to develop a new statistical methodology. For this purpose, let us provoke a statistical property of multivariate Gaussian distribution. That is, a contrast transformation,follows a multivariate Gaussian, whereis a chosen matrix of number of P independent contrast coefficients and the inverse of the symmetric    variance-covariance matrix is 

 

                         (4)

In our context, the maximum number of possible       independent contracts is three (that is,). The measure portrays the Mahalanobis distance from the origin in a three dimensional space where the data average , where is the maximum likelihood estimate of the inverse of the variance-covariance matrix (4). [6] for details about inverting a matrix. How much of this distance is covered by a contrast, is . Hence, a relative could be created to indicate the significance of the covered Mahalanobis distance and it is the ratio . This relative index is indicative of higher significance.

We now examine the validity of the research hypothesis Q1. For this purpose, we select . Consequently, an observed illegal organ trade level   follows a univariate Gaussian distribution with mean and variance 

{C}{C}            (5)

Where {C}{C} is the partial correlation between the number of recipients and the number of donors for a fixed number waiting for organ. Hence, a 100(1-) percent confidence interval for the unobserved illegal organ trade or organ wastage level is

 

                                            (6)

Based on (5). How significant is the contrast transformation,  It is indicated by the ratio . The domain for the relative is the and closer this relative to one is indicative of higher significance.

To examine the validity of the research hypothesis Q2, we select. Consequently, an observed shortage gap,  follows a univariate Gaussian distribution with mean   and variance 

  {C}{C}                      (7)

Whereis the partial correlation between the number waiting and the number of donors for a fixed number recipient for organ. Hence, a 100(1-) percent confidence interval for the unknown organ shortage gap is

                         {C}{C}{C}      (8)  

According to (7). How significant is the contrast transformation, It is indicated by the index ratio . The domain for the relative is the and closer this relative to one is indicative of higher significance.

To examine the validity of the research hypothesis Q3, we select . Consequently, an observed unmet demand level,  follows a univariate Gaussian distribution with mean  and variance 

 

                 (9)

Where is the partial correlation between the number waiting and the number of recipients for a fixed number of organ donors. Hence, a 100(1-) percent confidence interval for the unobserved unmet demand for organ is

                                               (10)

Using (9). How significant is the contrast transformation ? It is indicated by the ratio                                                                        .         

The domain for the relative is the and closer this relative to one is indicative of higher significance.

To answer the research hypothesis (Q4), notice that there is no illegal organ trade suggesting that . In such a situation, the underlying model for the random vector () is a bivariate Gaussian distribution

                     ,      (11)

                 

               And                                                        

        (12)

Denote respectively the unknown mean vector, variance-covariance matrix, and the shrunken or stretched Mahalanobis distance under all legal organ trade and no organ wastage. In such a situation, what might be the expected and volatility of the unmet demand for organ transplant? For this purpose, select . Consequently, an observed unmet demand level,  follows a univariate Gaussian distribution with mean   and variance 

                          (13)

Where is the correlation between the number waiting and the number of recipients. Hence, a 100(1-) percent confidence interval for the unobserved unmet demand for organ in the absence of illegal organ trade and waste of organs is

 

                     (14) 

 

How significant is the contrast transformation ? It is indicated by the ratio

   {C}{C}.   (15)

 

The domain for the relative is the and closer this relative to one is indicative of higher significance. Consequently, the difference between (10) and (15) gives an idea about the impact of executing zero illegal organ trade and zero wastage of organs.

 

 

3. Illustration Using WHO’s Transplant data during 1991-2013

In this section, the concepts and expressions are illustrated using the transplant data in Figure 1. First, the number, waiting, the number,of recipients, and the number, of organ donors are Gaussian distributed, according to the Box-Whisker plots in Figure 2, Figure 3, and Figure 4. Also, the three variables are positively correlated (Table 1) meaning that if one variable increases, the other variable is expected to increase among , , and. 

The average number waiting for organ, average number of organ recipients, and the number of organ donors are ,  , and  with variances , , and respectively.  A larger variance is indicative of more volatility. In this sense, the number waiting for organ is more volatile than the number of organ recipients, which is more volatile than the number of donors. In other words, the donors are more stable. For a fixed variable, the correlation between any two variables is partial correlation. See the partial correlations , , and in Table 2. The partial correlations exhibit a shift from the correlations among ,, and .

First, for a fixed number waiting for organ, the partial correlationbetween the number of donors and the number of recipients is 0.92, which is slightly down from their correlation . When there are more donors donating organs, there are more recipients of organ transplant. Secondly, for a fixed number of organ recipients, the partial correlation between the number of donors and the number waiting for organ attains a negative value – 0.41, which is far down from their correlation . This is quite interesting. When more donors come forward to donate organs, there is lesser number waiting for organs. Thirdly, for a fixed number of organ donors, the partial correlation between the number waiting for organ and the number of recipients for organ attains 0.73, which is slightly down from their correlation . The number of donors has a direct impact on the number waiting for organ and on the number of recipients of organ transplant.

With respect to the origin in the Euclidean space, the vector average is situated at a Mahalanobis’ distance of 185.88. According (6), a 95 percent confidence interval for the unobserved illegal organ trade or organ wastage level in the period 1991-2013 is (10,691, 11, 774) worldwide. The relative index, in the expansion of the Mahalanobis’ distance for the illegal organ trade or organ wastage level in the period 1991-2013 is only 8.88, with not much of higher significance.

According (8), a 95 percent confidence interval for the unobserved organ shortage in the period 1991-2013 is (65,023, 66,504) worldwide. The relative index, in the expansion of the Mahalanobis’ distance for the organ shortage in the period 1991-2013 is only 163.12, with much higher significance.

 

 

Figure 2. The number of donors in terms Number waiting for transplant.

 

Figure 3. The number of recipients in terms of donors for transplants.

 

Figure 4. The number of recipients in terms of # waiting for transplants.

 

Table 1. Correlation among the # donors, recipients, and Number waiting (p-value <0.001)

​

 

 

 

According (10), a 95 percent confidence interval for the unobserved unmet demand for organ in the period 1991-2013 is (53,628, 55,433) worldwide. The relative index, in the expansion of the Mahalanobis’ distance for the unmet demand for organ in the period 1991-2013 is only 75.51, with a reasonable higher significance.

 

Lastly, if the illegal organ trade or organ wastage level is totally abolished in the world, with respect to the originin the Euclidean space, the vector average moves far away to a Mahalanobis’ distance of 4,415.54, according to (12). In this hypothetical situation of total abolishment of illegal organ trade or organ wastage, according (14), a 95 percent confidence interval for the unobserved unmet demand for organ in the period 1991-2013 would be (50,552, 58,509) worldwide. This confidence interval under an abolishment of illegal organ trade is wider than what would that otherwise. Paradoxically, the presence of illegal organ trade helps.  However, the relative index,  in the expanded Mahalanobis’ distance shrinks to 0.16 for the unmet demand for organ in the period 1991-2013, with a drastically significant reduction. These findings become possible with the help of the statistical methodology in Section2.

 

More awareness needs to me made among the potential organ donors about the importance of donating organs. Worldwide facilities ought to be established and supported to procure organs soon enough from those who unexpectedly die due to accidents or heart attack. Priorities should be given to air transport the procured organs to the correct destination for transplanting them in those waiting for organs in a world of heavy traffic with congestions. In addition, stocking and preservation of unutilized organs should be encouraged for future implantation. The WHO ought to provide a leadership to promote and implement the above mentioned incentives among the nations.

 

For an example, an English daily paper, Times of India, on 31 July 2015 The Indian Air Force (IAF) recently put one of its special aircrafts, an Embraer, for a unique operation — transporting a kidney and a liver from Pune to Delhi. It was used to save the life of two critically-ill patients, a 56-year-old ex-serviceman with liver cancer and another jawan suffering from kidney failure. Both are doing good post-surgery, said doctors. NEW DELHI: The Indian Air Force (IAF) recently put one of its special aircrafts, an Embraer, for a unique operation — transporting a kidney and a liver from Pune to Delhi. It was used to save the life of two critically-ill patients, a 56-year-old ex-serviceman with liver cancer and another jawan suffering from kidney failure. Both are doing good post-surgery, said doctors. NEW DELHI: The Indian Air Force (IAF) recently put one of its special aircrafts, an Embraer, for a unique operation — transporting a kidney and a liver from Pune to Delhi. It was used to save the life of two critically-ill patients, a 56-year-old ex-serviceman with liver cancer and another jawan suffering from kidney failure. Both are doing good post-surgery, said doctors. NEW DELHI: The Indian Air Force (IAF) recently put one of its special aircrafts, an Embraer, for a unique operation — transporting a kidney and a liver from Pune to Delhi. It was used to save the life of two critically-ill patients, a 56-year-old ex-serviceman with liver cancer and another jawan suffering from kidney failure. Both are doing good post-surgery, said doctors. NEW DELHI: The Indian Air Force (IAF) recently put one of its special aircrafts, an Embraer, for a unique operation — transporting a kidney and a liver from Pune to Delhi. It was used to save the life of two critically-ill patients, a 56-year-old ex-serviceman with liver cancer and another jawan suffering from kidney failure. Both are doing good post-surgery, said doctors. announced that the Indian Air Force (IAF) allowed its special aircraft, an Embraer, for a unique operation for transporting a kidney and a liver from Pune to Delhi to save the life of two critically-ill patients. Both were doing good post-surgery, according to doctors. This incidence cites the importance of promoting the importance of a quick air transporting organ or tissue from a remote place to a destination place worldwide.

 

A lack of public organ donation program cannot be a justification for using organs from executed prisoners. The World Medical Association stated that the prisoners are not in a peaceful frame of thinking to give consent, and hence their organs must not be used for transplantation.

No forced donation must be allowed. Humans have a pair of organs. A human can live with just one organ. An illusionary tendency might exist to sell off one of the organ pairs for a high price. The market value of a kidney, a liver, and a heart are $100,000, $250,000, and $860,000 respectively. This might induce an illegal organ trafficking, which must be stopped by high ethical standards and regulations. [7]

 

Sometimes, the traditionalists believe that the body desecration should be forbidden, and thus reject organ transplant. About 99 million persons in USA are 50 years of age. If they donate organs, how many more lives in the waiting could be saved.[4] Showed that the costs of organ transplantations have decreased due to medical improvements. People of all ages, however, can be organ, eye, and tissue donors. There are ethical issues in the distribution of available organs.

The author thanks the Texas State University for the award of Faculty Development Leave in spring 2015 as it helped to pursue the research work of this article.

1. WHO (2004). Resolution on human organ and tissue transplantation.

2. Cherry MJ (2005) Kidney for sale by owner: human organs, transplantation, and the market. Washington: Georgetown University Press.

3. Halpern SD, Shaked A, Hasz RD, Caplan AL (2008) Informing candidates for solid-organ transplantation about donor risk factors. New England Journal of Medicine 26; 358(26):2832-2837.

4. Kousoulas L, Vondran FWR, Syryca P, Klempnauer J, Schrem H, et al. (2015) Risk adjusted analysis of relevant outcomes drivers for patients after more than two kidney transplants, Journal of Transplantation, ID 712049; 1-9 .

5. Tritaki G, Giannantonio P, Boccia S, (2014) A systematic literature review on the policies and economic evaluation of oragan transplations in EU. Epidemiology Biostatistics and Public Health 11;1-10.

6. Schott JR (2005) Matrix Analysis for Statistics, John Wiley Press Hoboken NJ.

7. N Scheper-Hughes (2003) Keeping an eye on the global traffic in human organs. Lancet 361:1645-8.