A discrete event simulator for policy evaluation in liver allocation in Eurotransplant

TL;DR

The paper presents ELAS, a discrete-event simulator tailored to Eurotransplant liver allocation, addressing the need for quantitative policy evaluation across eight European countries. It details the DES design, input streams, and modular components (match list, obligation, exception score, graft offering, post-transplant), plus verification and validation against 2016–2019 ET data. Demonstrations include BeLIAC’s Belgian exception-score policies and a ReMELD-Na based policy, illustrating potential improvements in fairness and reductions in waiting-list mortality under policy changes. Limitations such as registry data gaps and assumptions about center behavior are discussed, with future directions including data enhancements and recalibration as transplantation practices evolve.

Abstract

We present the ELAS simulator, a discrete event simulator built for the Eurotransplant (ET) Liver Allocation System (ELAS). Eurotransplant uses ELAS to allocate deceased donor livers in eight European countries. The simulator is made publicly available to be transparent on which model Eurotransplant uses to evaluate liver allocation policies, and to facilitate collaborations with policymakers, scientists and other stakeholders in evaluating alternative liver allocation policies. This paper describes the design and modules of the ELAS simulator. One of the included modules is the obligation module, which is instrumental in ensuring that international cooperation in liver allocation benefits all ET member countries. By default, the ELAS simulator simulates liver allocation according to the actual ET allocation rules. Stochastic processes, such as graft offer acceptance behavior and listing for a repeat transplantation, are approximated with statistical models which were calibrated to data from the ET registry. We validate the ELAS simulator by comparing simulated waitlist outcomes to historically observed waitlist outcomes between 2016 and 2019. The modular design of the ELAS simulator gives end users maximal control over the rules and assumptions under which ET liver allocation is simulated, which makes the simulator useful for policy evaluation. We illustrate this with two clinically motivated case studies, for which we collaborated with hepatologists and transplantation surgeons from two liver advisory committees affiliated with Eurotransplant.

Figures (8)

• Figure 1: Event handling flowchart for the ELAS simulator. Inputs and parameters are represented using parallelograms. D, deceased on the waiting list; ELAS, Eurotransplant Liver Allocation System; FES, Future Event Set; MELD, Model for End-Stage Liver Disease; R, waiting list removal.
• Figure 2: Estimated event probabilities for transplant recipients, per country for different time horizons. An event was defined as re-transplantation or waiting list death, whichever occurred first. Probabilities were estimated from real data and simulated data with the Kaplan-Meier estimator, using time since transplantation as the timescale.
• Figure 3: Distribution of (N)SE MELD scores for exception candidates (left) and laboratory MELD scores for non-exception candidates (right) at transplantation in ELAS simulations. Only transplantations based on recipient-driven offers are shown. Boxplots and distributions were calculated over 50 simulations.
• Figure A1: Estimated re-listing rates for transplant recipients, per country for different time horizons. Relisting rates were estimated with the Kaplan-Meier estimator, using time since transplantation as the timescale.
• Figure C2: Estimated survival probabilities estimated in the cohort, with (blue) and without (orange) Inverse Probability Censoring Weighting to correct for informative censoring by transplantation.