Liver waiting list simulator

Simulated patients join a waiting list, synthetic donors give livers each week, and a needs score decides who is offered them, and who dies waiting.

What this is and how to use it

A simulation, not real data. This is a model of the UK adult liver transplant waiting list. Every simulated patient and every donor is synthetic. The starting settings come from NHS Blood and Transplant's 2025/26 figures, so on average the simulated list behaves like the real one: about 610 simulated patients waiting, roughly 64% transplanted and 8% dying or becoming too unwell within a year of listing.

What it is for. Seeing how allocation rules and supply play out over years: who gets offered livers, who waits, and who is removed. It cannot predict what will happen to any real patient and must not be used for clinical decisions.

  1. Watch. A UK-sized run is already loaded. Press Play above the plot to see the list week by week.
  2. Read the plot. Each dot is a simulated patient. New simulated patients wait in Joining on the left; the middle shows everyone on the list (height = their score, across = time waiting); on the right, simulated patients drop into Transplanted, Died or too unwell or Removed. Hover or tap a dot for that simulated patient's story.
  3. Change one thing. Open a group in Settings (for example Who gets the liver to rank by UKELD instead of the Transplant Benefit Score) and press Run simulation. The plot clears and the new run starts at week 0.
  4. Compare fairly. One run has a lot of chance in it. Open the 2 · Compare strategies tab, pick one thing to change (for example the ranking rule) and up to three versions of it, and run them all on the same 10–50 numbered seeds, beside NHSBT's figures.

Questions to try: does sickest-first (UKELD or MELD 3.0) mean fewer deaths than the TBS? What happens to simulated HCC patients under each rule? How much does a higher DCD share or fewer livers change waiting? Who waits longer with weight matching?

How it works

A teaching model. The simulated patients are fictitious and most inputs are illustrative assumptions. It is not NHSBT data or the National Liver Offering Scheme, and it does not predict any real patient's wait. It opens on the UK-sized preset: a starting list of 613 simulated elective patients including ACLF and variant syndrome (the size of the UK list on 31 March 2026), simulated super-urgent patients on top, and DBD livers ranked by the Transplant Benefit Score. Simulated patients can be suspended from the list (on by default). Paediatric, split-liver, multi-organ and fast-track offering and living-donor transplants are not modelled.

Each simulated patient

  • Drawn from synthetic UK-style registrations: disease group, age, listing bloods and HCC details come from one row of the synthetic recipient file.
  • Sex, blood group, severe ascites and urea are added by the model (the file does not hold them).
  • At listing they are given a death week from the chosen death model. Their bloods worsen over the 26 weeks before it, on top of slow drift and weekly noise.
  • UKELD, MELD 3.0, GEMA-Na and TBS v2 M1 are all recalculated from the same bloods every week.

Each week

  1. New simulated patients register and wait in Joining.
  2. Listed simulated patients' bloods and scores update.
  3. Simulated patients reaching their death week die; a few leave for other reasons. If suspension is on, some are suspended or return to the active list.
  4. Livers arrive from synthetic donors and are offered to active (not suspended) simulated patients. Some are not usable for anyone, more often from older and DCD donors (NHSBT 2025/26 rates). DBD livers go down the ranked list; DCD livers to a randomly ordered compatible simulated patient. Each offer may be declined (DBD 55%, DCD 38% by default); after declines a liver is not used.

Calibration

  • The UK-sized preset (the default) matches 2025/26 activity: a starting list of 613 elective patients (31 March 2026), 68 elective (chronic liver disease and HCC) registrations a month, 90 variant syndrome, 24 ACLF and 50 super-urgent patients a year, 83.5 retrieved livers a month (about 66 transplanted), 48% DCD, weight matching ±20 kg and removal for improvement (NHSBT annual report 2025/26; NLOS 96-month review; Annual Report on Organ Utilisation 2025/26).
  • With that preset and "Calibrated to UK outcomes", every death model gives about 63% transplanted, 8% died, 5.5% removed (about 15 a year as improved) and 23% still waiting 1 year after listing; at 2 years 75%, 10%, 7% and 8%. NHSBT: 63%, 8%, 4% and 26% for 2023/24 registrations; 64%, 8%, 5% and 23% for 2024/25.
  • Over a 5-year run the elective list (chronic liver disease, HCC, ACLF and variant syndrome, active and suspended) stays at about 610: about 510 active and 100 suspended (UK, 31 March 2026: 613, with 512 active and 101 suspended). Simulated super-urgent patients are listed separately. Median waiting time to transplant, measured as NHSBT does (Kaplan-Meier, censoring deaths and removals, excluding time suspended), was about 137 days before the 27 October refit, against NHSBT's 130 for 2023–25 registrations.
  • As published, M1 gives 11% deaths at 1 year, UKELD 9%, MELD 3.0 and GEMA-Na 7%.
  • How the death-risk factors work, and their limits, are explained under "Model for death without transplant → Death risk" in the settings. In short: one fixed multiplier per death model, fitted once to 8% deaths at one year on the default UK run, the same for every run you make.
  • Known gaps: living-donor transplants (33 in 2025/26) and re-transplant listings are not modelled separately.
  • The rate of change in bloods, the 26-week worsening before death and the suspension rates are assumptions. Decline chances and the share of livers not usable come from NHSBT's Annual Report on Organ Utilisation 2025/26; see the "+" next to each setting.

Strategies and seeds

Scores and death models

UKELD5.395 ln INR + 1.485 ln creatinine + 3.13 ln bilirubin − 81.565 ln sodium + 435 (NHSBT; creatinine capped at 400).
MELD 3.0OPTN 2023 formula with sex, bilirubin, sodium, INR, creatinine and albumin; bounded 6–40, left unrounded.
GEMA-NaGEMA (bilirubin, INR and RFH-GFR from creatinine, urea, INR, age, sodium, sex and ascites) with the sodium term.
TBS M1 needExpected days alive within 5 years without a transplant, from the TBS v2 waiting-list (M1) models and baseline survival. Recalculated against your synthetic file's M1 values: they agree to within 0.004 days.
Deaths: TBS M1S0(t)exp(LP) with the v2 baseline survival; year-5 hazard beyond 5 years.
Deaths: UKELD1-year survival exp(−exp(0.181 × UKELD − 11.25)), through UKELD 49 = 9% and 60 = 50% mortality; constant hazard.
Deaths: MELD 3.090-day survival 0.946exp(0.17698 × MELD 3.0 − 3.56); constant hazard.
Deaths: GEMA-NaThe MELD 3.0 equation applied to GEMA-Na points (no GEMA-Na survival equation is published).

Model inputs

Disease groups (from the simulated patient pool, median at listing)

Blood groups (assigned)

Synthetic donors

Variant syndrome categories (NHSBT POL195 section 3.2.1; mix illustrative)

Every variant syndrome registration needs a UKELD under 49; in the simulator a variant syndrome patient whose UKELD reaches 49 or more moves to the chronic liver disease list (setting under "Simulated super-urgent, ACLF and variant syndrome patients"). * POL195 allows an exception for severe or very severe hepatopulmonary syndrome. Diuretic-resistant ascites and chronic hepatic encephalopathy are variant syndromes in the context of chronic liver disease, registered under the chronic liver disease criterion.

Blood group compatibility: O livers can go to anyone; A to A and AB; B to B and AB; AB to AB. New registrations and livers per week follow a binomial approximation to a Poisson process. Every input is in the CSV files in data/; edit them and rebuild to change the model.

Sources: synthetic recipient and donor files (Edinburgh Organ Allocation Research Group); NHS Blood and Transplant, POL195/20 Liver transplantation: selection criteria and recipient registration; NHS Blood and Transplant, National Liver Offering Scheme: ninety-six month review, LAG(26)03, May 2026; Barber K et al., UKELD, Transplantation 2011; Kim WR et al., MELD 3.0, Gastroenterology 2021; Rodríguez-Perálvarez M et al., GEMA, Lancet Gastroenterol Hepatol 2023; TBS v2 coefficients and baseline survival as used in the TBS calculator.

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