In France, the waiting time for a kidney transplant is increasing. In order to avoid this long wait, some patients find someone who is willing to give them a kidney. Nevertheless, the patient could be incompatible with this potential willing donor. To deal with this issue, kidney exchange programs have been developed. In this project we aim at understanding the poor preformance of the french program and to propose some changes in order to improve those performance.
Two main reasons explain the poor performance of the French Kidney Exchange Program : 1- the practices that are allowed are too restrictive (only pairwise exchanges are authorized) ; and 2- too few pairs are participating. Starting from these observations we propose an evaluation of the impact of introducing new practices, on the one hand, and increasing participation, on the other hand, on the number of transplants. We have considered three new practices. First, an increase in the size of the exchange cycles with the introduction of three-way and four-way exchanges (in which, respectively, three pairs and four pairs are involved). Second, the introduction of chains of tansplants initiated by a deceased donor. One important specificity of these chains, with respect to exchange cycles, lies in the fact that chains are not closed (the last donnor in a chain does not have to donate to a patient registered in the program). Due to this specifity more transplants can be performed through chains compared to cycles. In most of the countries authorizing those chains, they are initiated by an « altruistic » living donor. However, this is unlikely to be accepted in France in the short term. Hence, we have to consider chains initiated by a deceased donor. In practice, the donor of a pair registered in the program could initiate a chain in exchange of a high priority on the deceased donor list for her or his intended patient. Third, we consider the impact of authorizing blood type incompatible transplants within the exchange program. The rational for this proposal lies in the fact that, for some patients, those transplants are comparable to a compatible graft in terms of graft and patient survival. Moreover, few of these blood type incompatible grafts are likely to increase the total number of compatible transplants, in particular for hypersensitized patients, for whom very few compatible donors exist.
Our quantification of the impact associated with the introduction of new practices within the exchange program is based on data provided by the Agence de la Biomédecine. A first dataset gathered information about the characteristics of all the pairs having participating to the program since the begining. Using tese data we performed some counterfectual analyses enabling us to determine the number of additional grafts that would have been obtained if more flexible policies have been introduced. By their very nature, these analyses have been performed why considering the participation of the exchange program as unchanged. In order to evaluate the impact of an increase in the participation to the program, we also performed data based simulation. To do se, we have decomposed the set of pairs having participated to the program in different biological types. Then, we built simulated pools by assuming that the arrival of each type follows a poisson distribution with parameter equals to the average inflows of this type of pairs in the data times a scale parameter. If this scale parameter is equal to one, we reproduce, on average, the composition of pairs having participated to the program. However, we can also increase this parameter in order to simulate an increasing participation and to evaluate its impact on the effect of alternative practices. A finer analysis was needed in order to study the consequences of the introduction of chains. Indeed, we have to ensure that the receiver of the pair initiating a chain receives a « sufficiently good » deceased donor kidney in reasonable time. Hence, we used a second dataset concerning all the kidneys from deceased donors offered during the period. Based on those data we are able to determine, for each patient in the program, the average number of offers from a deceased donor he/she could expect per year. We can also filter these offers according to objective quality criteria.
We conclude from our counterfactual analysis that the introduction of cycles of size three (exchange cycles in which three pairs are involved) would have increase the total number of transplant by 20%. Starting from this point, the impact of the introduction of cycles of size four is much more limited. Further, the introduction of one chain per year, initiated by a deceased donor kidney with a standard quality, would have allow for a rise in the number of transplant per 50% even in the case in which only pairwise exchanges are allowed. Moreover, those chains basically exhaust all the gains that could have been expected from an increase in the size of exchange cycles. Being given the relative abundance of deceased donor kidneys in France, the introduction of those chains is likely to significantly improve the performance of the french program. Finally, authorizing blood-type incompatible transplants within the program has also a huge positive impact on the number of transplants (this number increases by 150% when only pairwise exchanges are allowed). However, this impressive result has to be interpreted as an upper bound since we lack of precise information on the possibility or not, for each patient having participated to the program, to receive such kind of incompatible graft. The results of our simulations lead us to conclude to a more than proportional impact of an increase in the participation to the program on the total number of transplant (in the situation in which only paiwise exchanges are allowed, doubling the participation translates into a number of transplant multiplied by 2.46). Finally, we conclude that the positive impact, on the percentage of patients receiving a kidney, associated with the introduction of new practices, is ehnanced as the participation increases.
Our counterfactual exercices and our simulations fail to capture the fact that the introduction of new practices and the increase in participation are likely to be linked. Indeed, if these new practices increase the probability to get a graft within the program, they could lead more incompatible pairs to join the program. If it is the case, our assessment of the impact of the indtroduction of these new practices is somehow under-estimated. In order to tackle this issue we would like to propose a discrete choice model in which the patients of each pair face different options : wait on the deceased donor list, receive an incompatible graft from her/his own donor or join the exchange program. Then, using the data provided by the Agence de la Biomédecine, we will estimate the model and, in particular, the sensitivity of the decision of entering or not in the program to the probability to get a graft in the program. Based on this estimation we will be able to assess the total effect of the introduction of new practices and to decompose this totalt effect into a direct effect (considering the participation as given) and an indirect effect (taking into account the induced change in participation).
Millions of people across the world suffer from kidney diseases. The number of patients on the waiting list for a kidney transplant from a deceased donor is steadily increasing. To address this shortage, kidney paired donation programs have been launched. They allow patients with living but biologically incompatible donors to “exchange” donors. This project will consider kidney exchange programs from both a theoretical and empirical perspective. The starting point of our proposal comes from our analysis of a data set provided by the Agence de la Biomédecine comprising, among other things, the pairs of patients-donors in the pools of exchange from the beginning of the exchange program in France. So far, the program in France is restricted to pairwise exchanges. Based on preliminary analysis, we observed that three ways exchanges can increase by 20% the total number of transplantations achieved while exchanges of larger sizes only yield modest improvements. However, three ways exchanges involve an important logistical burden since each requires six simultaneous surgeries. Importantly, we observed that chains from non-directed donors (donors with no associated patient getting a kidney from the exchange pool) can yield large improvements over the current practice and exhaust all the gains that one can achieve by using exchanges larger than two ways. These chains do not involve any logistical burden as the associated transplantations can be realized sequentially. Our exploration also points out three additional elements that are at the core of this project. First, it is well-known that there are patients who are hard to match (hyper sensitive and/or of blood type O) and these are over-represented in the pool. Our counter-factual analysis puts into relief that these patients can benefit from relaxing the rules in the exchange program. Importantly, there is in general a trade-off between targeting these patients and the possible overall number of transplants. We first observed in our data analysis that this trade-off tends to vanish as the size of the pool increases and as policies get more permissive. Second, the advantage of chains increases as the size of the pool becomes larger. Finally, we observed a basic phenomenon: reducing slightly the size of the chain implemented at a given date can allow getting much longer chains in the future. Several projects come out from these observations. After further analysing the data set, we plan to get a better understanding of the trade-off between efficiency (i.e., total number of transplants achieved) and fairness (the number of transplants achieved for hard to match patients). We will theoretically investigate how the cost of imposing fairness can decrease as the size of the pool increases and as the policies become more flexible, in particular, when allowing for chains. Since the size of the pool is a critical variable to get better performances both in terms of efficiency and fairness, we will also try to get a better understanding of the type of policies that must be run in order to give incentives to different countries to merge exchange programs. We claim that this is a non-trivial issue as some countries may lose by joining a common pool if the policy is not properly designed. Finally, our last empirical observation suggests that it is important to consider the future when deciding which transplant to make today and that there may exist a tension between static and dynamic optimization. We plan to understand theoretically how we can design simple policies that would take into account this tension and maximize efficiency and fairness in an intertemporal perspective. Clearly, our project aims at going back and forth between the theoretical results and the empirical analysis. In particular, based on our results, we are eventually planning to provide recommendations on the way to design the kidney exchange program in France.
Monsieur Victor Hiller (LABORATOIRE D'ECONOMIE MATHEMATIQUE ET DE MICRO-ECONOMIE APPLIQUEE)
The author of this summary is the project coordinator, who is responsible for the content of this summary. The ANR declines any responsibility as for its contents.
LABORATOIRE D'ECONOMIE MATHEMATIQUE ET DE MICRO-ECONOMIE APPLIQUEE
Help of the ANR 153,088 euros
Beginning and duration of the scientific project: - 48 Months