Florian Bayer Dr. Christian Jacquelinet Benoit Audry

Transcription

1 1 Using a gravity model for allocation o of livers to transplant Florian Bayer Dr. Christian Jacquelinet Benoit Audry

2 2 a -Introduction Study Objectives Global context : What can be the contribution of spatial analysis and Geography to improve organ allocation? How to improve the liver allocation scheme?

3 3 a -Introduction Contents 1. The context : the french allocation rules of liver grafts 2. The integration of these rules in the gravity model 3. The results 4. Conclusion 5. Future works

4 1 -The context The biomedecine Agency Born with the bioethics law of August 6, 2004 French public body Spread of abilities : - organ allocation - medical assisted procreation - human embryology - genetics

5 1-The context 5 The biomedecine Agency Access to dialysis centres Acces to IVF in France Transplantation teams evaluation

6 1-The context 6 The biomedecine Agency Organ allocation rules, the national waiting list and refusal list are under its responsability : To ensure a fair distribution and seeking the best recipient To make a compromise between efficiency, equity and feasibility In liver transplant, this compromise takes into account : Specific recipient condition (i.e. urgency) The graft quality/safety The distance between donor and transplant centres (cold ischemia time)

7 1-The context 7 Liver Score The Liver Score was introduced in March 2007 To submit a liver for the best recipient, by a "just-in-time" optimization

8 1-The context 8 Liver Score Set of function based on : 1. An estimate of risk to die on waiting list, using the MELD (Model for End- Stage Liver Disease) ( points) 2. His time spent on the waiting list (0-300 points) Accelerating access to transplantation before the patients exceed his best «transplantability t»time 3. The distance between donor and transplant centres (0-300 points) To reduce teams shipment To reduce cold ischemia To take into account the teams location (frontier effect)

9 1-The context 9 Liver Score application 1/ Local network : choosing help In 2009, 21 liver s transplantation teams. Some are related to local retrieval teams Local Network. 50 km Organ retrieval team Transplantation team with n patients on its waiting list When a graft is available in this network, it is proposed in priority to the local transplantation center This team has the choice of the patient. The Liver Score is just a choosing help. The distance doesn t matter When a graft is retrieved outside a local network or when the offer is declined by the transplantation team, then the graft is allocated nationally.

10 1-The context 10 Liver Score application 2/ National : sort of the waiting list Where is the higher Liver Score? The Liver Score is used to sort all suitable recipents that are on the waiting list Take into account the medical functions and the distance between donor and transplantation teams The distance matters

11 1-The context 11 Disparity of local networks in hepatic transplantation Some of the transplantation teams have large regional network. The others have only one (themselves) or sometimes two members in the same city.

12 1-The context 12 Percentage of transplantation issued from a local network, by team

13 1-The context 13 The distance in the Liver Score It fulfilled its role by limiting the teams movement and cold ischemia time. This model continues to favoured local network, but we face big discrepancies between teams. Sicker patients but more distant from the graft or out of these networks could benefit from it, but they don t. - The just-in-time principle of the Liver Score is only partial - Equity problem

14 1-The context 14 Objectives 1. Optimizing the distance function in the current Liver Score by linking the key decision factors of liver transplant : The distance between donor and transplant team The recipient health The graft quality 2. To show that an alternative to local network is conceivable Without reducing the organ retrievment and transplant activity

15 2- The integration of these rules in the gravity model 15 The principles of spatial interaction 1 st : size effect At equal distance, the importance of relations between two places is equal to their ability to transmit and receive 2 nd : distance effect At equal weight, the importance of relations between two places is inversely proportional to their distance Size (population) High Low Attractivity

16 2- The integration of these rules in the gravity model 16 Some principles of spatial interaction The use of this model in geography and geomarketing A B

17 2- The integration of these rules in the gravity model 17 The «basic» model Aij = Mj X Mi / Dij α Mj the mass of the patient on the waiting list Liver Score without distance component Mi the mass of the graft status At this time, no consensus for its evaluation. Mi = 1 Distant Dij between i et j Euclidean metric in an isotropic area The last parameter is α, the distance decay (entropy). It has to be calibrated and Arcview has been used for this operation. A VBA tool has been developped for the day-to-day simulation.

18 2- The integration of these rules in the gravity model 18 Methodology Data : liver transplant ( ) VBA Arcgis Geocoding Day to day simulation Geographic data Arcview Arcview Exploratory approach Setting parameters Annual simulation Arcview Simulation platform

19 3- The results and improvement 19 Results : day to day with Arcgis Liver score Patient Actual Liver Gravity without Rank Score model distance 1 Bordeaux Bordeaux Bordeaux 2 Paris 1 Paris 1 Paris 1 3 Paris 2 Paris 2 Paris 2 4 Marseille Rennes Rennes 5 Lyon 1 Caen Marseille 6 Rennes Paris 3 Lyon 1 7 Toulouse Marseille Paris 3 8 Paris 3 Besançon Caen 9 Besançon Toulouse Toulouse 10 Caen Lyon 1 Besançon 11 Strasbourg Strasbourg Strasbourg 12 Montpellier Montpellier Lyon 2 13 Lyon 2 Lyon 2 Montpellier

20 3- The results and improvement Florian Bayer, Source : Agence de la biomédecine Areaofcertitudetobethefirstonthewaitinglist,for each patient according to its severity score and the model used (same list as before) Current Liver Score Gravity model V1 more local competition p2 p10 p3 p2 p11 p6 p9 p5 p1 p1 p4 Patient area of certitude to get the graft (2 areas) Patient area of certitude to get the graft (9 areas) px Patient rank (score without distance) px Patient rank (score without distance)

21 3- The results and improvement Areaofcertitudetobethefirstonthewaitinglist,for each patient according to its severity score and the model used (same list as before) Gravity model V2 local competition ++ Gravity model V3 local competition +++ p10 p3 p10 p3 p6 p2 p11 p6 p2 p11 p9 p9 p13 p5 p5 p1 p1 p7 p12 p4 p7 p12 p4 Patient area of certitude to get the graft Patient area of certitude to get the graft (11 areas) (12 areas) px Patient rank (score without distance) px Patient rank (score without distance) 21 Florian Bayer, Source : Agence de la biomédecine 2009

22 3- The results and improvement 22 Distribution of the distance between donor and transplant team (March, 6th ) Observed Simulation with actual liver score Simulation with gravity model

23 3- The results and improvement 23 Meld distribution for transplanted patients with cirrhosis (March, 6th ) futile (too early) transplantation : Observed = 91 Liver Score = 39 Gravity model = 30 Observed Simulation with actual liver score Simulation with gravity model

24 3- The results and improvement 24 Too-sick or dead patient delisting rate (March, 6th ) Observed Simulation with actual liver score Simulation with gravity model

25 4- Conclusion 25 Summary Currently local networks can favored patients whose health is less "urgent" than other outside these networks Applying the gravity model without changing current allocation rules allows slightly improving access to transplantation for the most urgent patients The integration of this gravity model in the Liver Score shows that the principle of local priority can be circumvented : simulate a local network for the sufficiently critical patient

26 4- Conclusion 26 Limits Readability by physicians/clinicians Acceptability by transplantation teams Some transplantation teams with local network are affraid of losing their authority on the choice of the recipient Advantages Optimization of the liver graft allocation Scalability of the number of liver transplantation performed from close donors Increase grafts pooling for a better just-in-time distribution Reducing of 15% the too-sick or dead patient delisting rate

27 5- Future works 27 1/ Integrate the health of the donor 2/ Varying the model parameters depending on the distance Others distance functions Relativist models

28 5- Future works 28 Model modifications Results Actual liver Score

29 5- Future works 29 Model modifications Standard gravity model

30 5- Future works 30 Model modifications Gravity model with modified distance function (modified exponential 1 )

31 5- Future works 31 Model modifications Gravity model with modified distance function (modified exponential 2 )

32 5- Future works 32 Distance function : negative exponential

33 5- Future works 33 Distance function : gaussian

34 5- Future works 34 Gravity model variation function of the distance and Liver Score without distance Actual gravity model Relativist model 1

35 35 Publication : Bayer F., Jacquelinet C., Audry B., Modélisation et optimisation spatio-temporelle temporelle de l'accès aux greffons dans le Score Foie. Géomatique expert n 60 (octobre 2008) Many thanks to Dr. Christian Jacquelinet, Benoit Audry, Emilie Savoye, all biomedecine Agency members and transplantation teams. Joël Boulier, Hélène Mathian, Antonine Ribardière from Paris 1 Panthéon-Sorbonne University Claude Grasland, Christine Zanin from Paris 7 Diderot University Francis Dhée from ENSG ESRI Health and ESRI France

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