For education and research only. This page explains what the UK liver transplant registry can and cannot show about who should be offered a liver. It must not be used to make or influence decisions about any individual's clinical care, listing or organ offers. Nothing on this page is stored or sent anywhere.

UK liver offering · how the evidence is made

Why it can't just be based on the data

It is tempting to think the fairest way to offer a donated liver is to let the data decide: fit a model to what happened to patients in the past and rank by its predictions. The UK's Transplant Benefit Score is the most thorough attempt at that anywhere in the world.

This page is about why the data alone can never settle it. Not because models are bad, but because the record was made by the scheme it is now asked to judge; because the one thing the waiting-list model needs to know — how each patient would have fared without a transplant — is cut off, for most patients, by the transplant itself; and because people need a liver for far more reasons than any model has room for. The sections follow the statistical assessment in the 2025 review of the National Liver Offering Scheme, with moving diagrams for each step.

What the registry sees: each patient from the day they join the list to the day they leave it.

What a scheme needs: how each patient would have fared with a transplant and without one.

For any one person only one of the two can ever be observed. For about seven in ten, the half the waiting-list model needs ends at the transplant.

1 · The idea

The data describe a scheme, not the patients

The UK Transplant Registry records what happened under the rules in force at the time: who was listed, who was chosen for each liver, who was left waiting, and what became of them. Those outcomes are not a property of the patients alone. They are the joint product of the patients, the clinicians who selected them and the scheme that set the order. Change the scheme and the record changes with it.

Three things a scheme needs that no dataset contains.

A definition of fair

Whether livers should go to those in greatest need, those with the greatest expected gain, or those expected to do best afterwards is a value judgement. The data can estimate each of these; they cannot choose between them. When the review asked, patients and the public put need first (63%), then benefit (21%), then outcome (17%).

NLOS review 2025, survey of about 400 respondents

What was never observed

No one is followed both with and without a transplant. A model of survival without a transplant can only learn from the people who were left on the list — and who was left depended on the old rules. Sections 3 to 7 are about this.

What is too rare to estimate

Dozens of reasons for needing a liver have a handful of registrations a year. A model fits what is common and folds the rest into "other", or leaves it outside the score altogether. Section 2 shows how many there are.

2 · The indications

Dozens of reasons to need a liver; ten boxes in the model

Every word below is an indication for liver transplantation written into the UK selection policy. Size is a rough guide to how many people are registered with it in a year; colour is the route by which they are offered a liver. Tap a word to see how the current scheme treats it, then switch to As the score sees it to watch the words fall into the ten disease groups the Transplant Benefit Score knows — or outside the score altogether.

Tap a word

Each card says which route the indication takes through the offering scheme and, where it is ranked by the Transplant Benefit Score, which of the ten disease groups it is counted as.

Indications from NHSBT POL195/21 (sections 1.1, 1.2, 3.2.1, 3.4, 3.5.2, 3.6.1, 3.10 and Appendices A–G). Sizes: the large adult groups follow the Annual Report on Liver Transplantation 2024/25 (Table 3.2, 939 UK adult elective registrations: alcohol-related 27%, cancer 17%, other 14%, PSC 12%, metabolic 9%, PBC 7%, autoimmune and cryptogenic 6%, re-graft 4%, ACLF 2%, hepatitis B 1%, hepatitis C 1%) and Table 4.1 (100 paediatric registrations); the split within a registry group and the rare indications are illustrative, because no split is published.

The score ranks the majority — adult elective patients with chronic liver disease or hepatocellular carcinoma — and knows each of them as one of ten disease groups plus age, a few blood tests and, for cancer, tumour details. Everyone else is placed by rules and judgement rather than by a survival model: children, acute liver failure, acute-on-chronic liver failure, the variant syndromes, the service evaluations, multi-organ transplants and the appeals panel. Even inside the ten groups the boxes are broad. "Metabolic" spans fatty liver disease, haemochromatosis and Wilson's disease; "other" is whatever is left. A registry with a few hundred registrations a year in its largest group cannot say anything reliable about a condition that appears once or twice, and a scheme still has to find those patients a liver.

3 · What the data can see

Most patients leave the data before the question is answered

The waiting-list half of the score, M1, is a model of survival without a transplant over five years. The registry can only observe that while a patient is on the list. The moment someone is transplanted, what would have happened to them without one becomes unknowable: in the language of the models, they are censored. The review notes that more than 70% of patients on the list receive a transplant within a few years, that the longest follow-up in the HCC cohort was 2.8 years (4.5 years for chronic liver disease), and that in the revised cohort only 1% of HCC patients and 2% of chronic liver disease patients were still on the list at two and a half years.

Twenty patients, five years: what the waiting-list model can see

On the list — observedAfter transplant — survival without a transplant never observed✕Died or removed because their condition deteriorated○Removed for another reason

Patient-years observed–of 100 the five-year model would like

Patient-years unobserved–cut off by a transplant

Still being observed–of 20 patients at year 0

Illustrative patients, drawn to match recent UK proportions: at one year about 64 in 100 adult elective registrations have been transplanted, 8 have died or been removed because their condition deteriorated, 5 have been removed for other reasons and 23 are still waiting; at two years about 72, 10, 8 and 10 (NLOS ninety-six month review). The model is fitted to the solid lines only, and the right-hand half of the picture — where a five-year prediction lives — is almost empty.

4 · Carried flat

Where the follow-up ends, the curve is assumed to stop falling

A five-year prediction needs five years of follow-up. Where follow-up ended earlier, the review found, the TBS assumes that no further deaths occur: the survival curve is carried flat to the five-year horizon. For HCC that means the curve stops moving at 2.8 years. The review's figures for an average HCC patient are striking. Without the correction for censoring described in section 5, predicted survival at 2.8 years was 16%; with it, 57% — and 57% is then also the predicted five-year survival.

An average HCC patient's predicted survival without a transplant

Estimated from the patients observed (16% at 2.8 years)After reweighting for censoring (57% at 2.8 years)Carried flat: no further deaths assumed

Days alive without transplant–area under the curve (M1), of 1,826

Of which assumed–days beyond the last follow-up

Shapes are illustrative; the two anchor points at 2.8 years and the flat tail to five years are the review's. The M1 that enters the score is the area under the amber curve, counted in days.

Why it matters for the score. The TBS is predicted days alive over five years with a transplant minus predicted days alive without one. For the review's average patient, the flat tail at 57% contributes about 460 of the days in M1 — none of them observed — and the gap between the two sides of the subtraction shrinks accordingly. That is one of the routes to the HCC paradox, in which adding a tumour to an otherwise identical patient raises their predicted survival without a transplant and lowers their score.

The same assumption runs the other way for chronic liver disease, where follow-up reached 4.5 years: a flat tail there is less consequential, but the five-year horizon itself is doing work. The review found that only 1–2% of patients were still listed at two and a half years, and recommended that the horizon be reconsidered.

What the data saySurvival to 2.8 years, for the people who were not chosen for a transplant in that time.What the score usesSurvival to five years, for everyone, as if no one had been transplanted.

5 · The correction

IPCW: making the few stand in for the many

Inverse probability of censoring weighting (IPCW) is the standard repair for censoring that is not random, and it is what the TBS developers used to estimate survival as if transplanted patients had not been transplanted. Each patient who remains on the list is weighted by one over their estimated probability of not having been transplanted so far, given their recorded characteristics. Someone who looked very likely to be transplanted but was not is made to count for all the similar patients who were. The reweighted group is then treated as though no one had left.

Reweighting: one patient profile, one year

Still on the list — each dot's size is its weightTransplanted — leaves the data✕Died

Thirty patients who look alike to the model. As they are transplanted, the weights of those left behind grow so that the group still "adds up to" thirty. By the end a few people — and whatever made them the ones not chosen — carry the estimate for everyone.

What the correction has to assume

Nothing that drove selection is missing from the model. Given the recorded variables, being chosen for a liver must be unrelated to how the patient would have fared. But clinicians choose on things the registry does not hold — frailty, how fast someone is deteriorating, what the scans show, what the tumour is doing — and they choose on them precisely because they predict survival. The review lists clinical condition, size matching, competition for organs and rate of change among the unmeasured factors.
Someone must be left. For every kind of patient, some must remain untransplanted long enough to be observed. Where almost everyone is transplanted, a handful of people carry enormous weights and the curve is set by them. A jump from 16% to 57% in the same data is what that looks like.
The weights are a model of the old scheme. The probability of being transplanted is estimated from how centres chose patients under the rules of the time. The "corrected" survival is survival as if those choices had been made without regard to risk — which is the opposite of what the clinicians were trying to do.
Nothing after the last follow-up. Weights cannot create observations beyond 2.8 years. From there the curve is carried flat (section 4).

Try it: when does the correction work?Toy model

How much of the selection depends on things the model cannot see 50%

How quickly patients are transplanted typical

True survival without a transplant (what the score needs)Estimated from those observed, censoring at transplantAfter IPCW using the recorded severity only

True survival at 3 years–if no one had been transplanted

Naive estimate–at 3 years

IPCW estimate–at 3 years · largest weight –

A simulated cohort of 3,000 patients with one recorded severity measure and one hidden one, both of which shorten survival. Clinicians transplant the sicker patients first; the slider sets how much of that choice rests on the hidden measure. The correction uses the recorded measure only, as any real analysis must. When nothing is hidden, IPCW recovers the truth exactly — that is what it is for. As the hidden share grows, both estimates drift optimistic: the people left behind are the ones clinicians were least worried about, and no reweighting of them can recover the others. Numbers are illustrative; the mechanism is not.

6 · Selection hides risk

The same observations, two different truths

Before 2018 livers were offered to centres, and within centres largely by need. The people clinicians were most worried about were transplanted first: the sickest, often the youngest, often those already in hospital. Their survival without a transplant was rarely observed. A model fitted to that record sees that the people left on the list in those groups did relatively well, and concludes that the group is at lower risk. The review's clearest example is admission to hospital: being an in-patient at registration lowered predicted risk in the score, so sicker patients were deprioritised, until the term was set to zero in May 2023. The review warns that the same mechanism may understate the risk of younger, sicker patients generally.

Two groups with the same recorded severity

Ten patients in each group. In the group clinicians prioritised, eight are transplanted early and the two left behind survive the year. In the other, four are transplanted and two of the six left behind die. The record is identical under both truths; only the unobserved half differs. A model can only read the record.

The record cannot tell the two apart. In the first truth the prioritised group really is lower risk. In the second, clinicians were right: the people they transplanted were the ones who would have died, and the two left behind were the exceptions. Both truths produce exactly the same registry. The model learns the first because it is the one the data can see.

Published evidence of the patternUnder the score, patients aged 60 and over are predicted to survive 263 days without a transplant and those aged 25–49 861 days, while predicted survival after transplant is almost identical (1,599 v 1,573 days). After the scheme was introduced, DBD transplants fell by 23% for 25–49-year-olds and rose by 14% for over-60s. The authors attribute the pattern to selection bias and unmeasured frailty in a heavily censored cohort.Attia et al, Lancet Healthy Longevity 2024

Age is not a cause of any of this; it stands in for frailty, comorbidity and what the clinicians of the time could see and the registry could not. The review recommended that age should not be used unadjusted in a future scheme, and that any scheme be modelled group by group before it is deployed.

7 · The loop

Evidence made by the scheme it is asked to judge

Put the pieces together and the record becomes circular. The scheme decides who is chosen; who is chosen decides who remains to be observed; the people who remain are the evidence; the model is fitted to the evidence; the next scheme is built from the model. Nothing in the loop is dishonest. It is simply that the only way to learn how a different scheme would behave is to run one, or to make assumptions and say so.

Scheme → selection → record → model → scheme

Two consequences the review draws out.

The pre-implementation simulations were self-reinforcing. The scheme was tested by replaying past registrations with the score deciding who was transplanted and the model's own predictions deciding who survived. Patients the model predicted would survive without a transplant were not transplanted in the simulation and then, by construction, did not die. The simulations predicted that patients with cancer would receive about a third of transplants while mortality on the list fell from 5.9% to 4.8%, and that under-50s would receive 20% fewer transplants while their mortality fell from 4.5% to 2.9%. These are properties of the model's assumptions, not observations.

Monitoring since 2018 measures clinicians plus the algorithm. Livers are declined, placed by fast-track after the named patients have declined, or allocated by centres (every DCD liver). Centre-based selection accounted for 57% of transplants in 2024/25, up from 39% in the scheme's first year. The outcomes being monitored are the joint product of the score and the people working around it, so a problem in the score can be hidden by the clinicians correcting for it, and credit for an improvement cannot be assigned.

The one source of evidence that comes from outside the loop is a change of scheme. What happened to each patient group when the score was introduced in 2018 is a test that no replay of the old record can provide — and it is the test the age findings above come from.

8 · The band

How far could the truth be from the record?

It helps to see how wide the honest answer is. At one year, about 8 in 100 patients registered for an adult elective transplant have died or been removed because their condition deteriorated, and about 64 in 100 have been transplanted. The record cannot say how those 64 would have fared. If every one of them would have survived the year, survival without a transplant is about 92 in 100. If none would have, it is about 28 in 100. Every model picks a line inside that band by assumption — the TBS through its reweighting, a simulator through its calibration. The band is what the data know on their own.

One hundred patients at one year: what the record knows

Assume this many of the 64 transplanted patients would have survived the year without a transplant 48

Known from the record8 · 5 · 23died or deteriorated · removed · still waiting

Implied survival at one year–in 100, if no one had been transplanted

The band28 – 92in 100 — every point in it fits the record

Rounded one-year outcomes for recent adult elective registrations (NLOS ninety-six month review). Patients removed for other reasons and those still waiting are counted as alive at one year; the arithmetic ignores them for simplicity. The point is the width, not the midpoint.

9 · What follows

So what should it be based on?

Data are necessary and not sufficient. The registry can rank patients within what it has seen; it cannot say what fairness is, cannot see the half of each life it was never shown, and cannot speak for the conditions it holds one case of. A scheme that is honest about this looks different from one that is not.

● What the data can do

Rank need within the observed world. Scores such as UKELD, MELD 3.0 and M1 order patients by how they have fared on the list; the review's own assessment puts the concordance of M1 at about 0.70.
Describe the system. Who is listed, how long they wait, who is offered what, and how outcomes differ between groups and over time — the material of every monitoring report.
Test a change after the fact. A change of scheme is the one experiment the loop allows. Outcomes by age and disease before and after 2018 are evidence no replay can produce.
Feed a simulation, with its assumptions stated. Once the assumptions about the unobserved half are written down, their consequences can be worked through and compared — which is what the group's waiting list simulator is for.

● What has to come from outside the data

The objective. Need, benefit or outcome is a choice; the review recommended a needs-based scheme with utility monitored rather than optimised.
Honest uncertainty. Confidence intervals around a score, and bands of "equivalent priority" inside which geography and waiting time decide, rather than five decimal places and a single ranking.
A route for what cannot be scored. Exception points, an appeals panel and a standardised centre-based fallback for the variant syndromes, rare indications and cancers that no model has data for.
Checks before deployment. An equality impact assessment, modelling by patient group, and a calculator in the open so that clinicians can test the score on the patients in front of them before it is used.
Sensitivity, not a single world. No survival model should be the sole judge of the schemes that are compared with it — including the score's own M1. Each candidate rule should be run under every plausible model of the unobserved half, and the result reported as a range.
Monitoring that was agreed in advance. Pre-specified indicators, by patient group, published and independent — so that the next review does not have to reconstruct what the scheme was meant to achieve.

Companion pages from the same group: the waiting list simulator, the TBS calculator, the liver risk scores calculator and the liver selection policy explainer.

10 · Sources

Where this comes from

NLOS Review Committee. National Liver Offering Scheme (NLOS) Review: Report & Recommendations. NHS Blood and Transplant, October 2025. Statistical assessment of the scheme, pp. 22–25 (limitations of data; age as a proxy for health; historic non-UK data; proportional hazards; learning random variation; asymmetry; model performance; simulation testing; post-implementation evaluation). PDF
NHS Blood and Transplant, Statistics and Clinical Research. National Liver Offering Scheme: ninety-six month review. Paper LAG(26)03, May 2026 (one- and two-year outcomes after registration).
NHS Blood and Transplant. Annual Report on Liver Transplantation 2024/2025. August 2025. Table 3.2 (adult elective registrations by primary liver disease) and Table 4.1 (paediatric registrations). PDF
NHS Blood and Transplant. Liver Transplantation: Selection Criteria and Recipient Registration, POL195/21; and Deceased Donor Liver Distribution and Allocation, POL196/14. Current versions on the NHSBT ODT Clinical site.
Allen E, Taylor R, Gimson A, Thorburn D. Transplant benefit-based offering of deceased donor livers in the United Kingdom. J Hepatol 2024;81:471–478.
Attia A et al. The UK liver allocation algorithm and the HCC paradox. Lancet 2023;401:911–912; and authors' reply, Lancet 2023;402:371–372.
Attia A et al. Effect of recipient age on prioritisation for liver transplantation in the UK: a population-based modelling study. Lancet Healthy Longev 2024;5:e346–355.
Robins JM, Finkelstein DM. Correcting for noncompliance and dependent censoring in an AIDS clinical trial with inverse probability of censoring weighted (IPCW) log-rank tests. Biometrics 2000;56:779–788 (the method behind IPCW).
NHS Blood and Transplant. National Liver Offering Scheme: seventy-two month review, LAG(24)03 (the in-patient term set to zero on 23 May 2023).

The animated figures are illustrations of the mechanisms described in these sources. Where a figure carries a number, the number is the source's; the shapes between the numbers are drawn to make the mechanism visible, not estimated from data.