How this instrument works
The Model for End-Stage Liver Disease score turns three routine blood tests — bilirubin, INR, and creatinine — into a single figure that predicts three-month mortality in someone with advanced liver disease. Each lab value passes through a natural logarithm, gets multiplied by its own weight, and the three products are summed: 3.78 times the log of bilirubin, 11.2 times the log of INR, 9.57 times the log of creatinine, plus a constant of 6.43. Logarithms compress a wide spread of lab chaos into a scale that behaves like a genuine risk index rather than a raw sum of milligrams and ratios.
Two guardrails keep that arithmetic honest. Any of the three values below 1.0 is floored up to exactly 1.0 before it reaches the logarithm — an unfloored bilirubin of 0.4 or an INR of 0.9 would otherwise produce a negative log and subtract points from a patient who is, if anything, doing reasonably well. Creatinine carries a second rule on top of the floor: it's capped at 4.0 mg/dL, and for a patient on regular dialysis (twice weekly or more, or 24 hours of continuous therapy) it gets set to 4.0 automatically regardless of the measured lab value, because dialysis itself clears creatinine from the blood far more efficiently than failing kidneys would on their own.
Kamath, Wiesner, Malinchoc, and colleagues published this exact equation in Hepatology in 2001, derived from patients undergoing an elective procedure to relieve portal hypertension. It displaced the older Child-Pugh classification, which leaned on subjective clinical signs like the severity of ascites or the degree of confusion. What follows is that original three-variable formula exactly as written — worth understanding on its own terms even though it is no longer what decides a real transplant waitlist position.
- Enter Bilirubin in mg/dL from the most recent metabolic panel.
- Enter INR — the standardized prothrombin ratio, not raw clotting seconds — from the same blood draw.
- Enter Creatinine in mg/dL, then set the dialysis toggle to Yes if the patient receives regular dialysis (twice weekly or more, or continuous 24-hour therapy); the calculator overrides your entry to 4.0 automatically when that toggle is on.
- Read the resulting score alongside the three adjusted values the formula actually used, so you can see exactly which floor or cap rule fired.
Worked example — bilirubin 3.0, INR 2.0, creatinine 2.5
A patient with bilirubin 3.0 mg/dL, INR 2.0, and creatinine 2.5 mg/dL — none of the three needs flooring or capping. The bilirubin term: 3.78 × ln(3.0) = 3.78 × 1.099 = 4.15. The INR term: 11.2 × ln(2.0) = 11.2 × 0.693 = 7.76. The creatinine term: 9.57 × ln(2.5) = 9.57 × 0.916 = 8.77. Add the constant of 6.43 and the total reads 4.15 + 7.76 + 8.77 + 6.43 = 27.1 — a level tied to meaningfully elevated short-term mortality without a transplant.
Now picture the same patient with bilirubin 0.5, INR 0.9, and creatinine 1.0, but on dialysis twice a week. Bilirubin and INR both sit below 1.0, so each floors up to 1.0, and ln(1.0) is zero — those two terms vanish from the sum entirely. The dialysis rule then overrides creatinine to 4.0 no matter that 1.0 mg/dL was actually measured. What remains is 9.57 × ln(4.0) + 6.43 = 9.57 × 1.386 + 6.43 = 13.27 + 6.43 = 19.7 — a substantial figure built almost entirely from the dialysis override rather than the patient's own labs.
Questions
Is this the formula transplant programs actually use to allocate organs today?
No. This is the original equation exactly as Kamath, Wiesner, Malinchoc, and colleagues published it in Hepatology in 2001 (PMID 11172350). Real-world liver allocation has moved on twice since: MELD-Na added serum sodium when the OPTN adopted it in January 2016, and MELD 3.0 (Kim WR et al., Gastroenterology, 2021) layered in sex and albumin on top of that. This calculator is the foundation those revisions were built from, not a substitute for a current waitlist score.
Why are the lab values floored at 1.0 before taking the logarithm?
Because the natural log of anything below 1.0 is negative, and a negative term would subtract points from a patient whose bilirubin or INR happens to sit below that line — the opposite of what a severity score is supposed to do. Flooring each value at 1.0 guarantees every logarithm is zero or positive, so an unusually favorable lab result can only contribute nothing, never actively pull the total down.
Why does creatinine get capped at 4.0 mg/dL, and why does dialysis override it?
Two rules stack here. Values measured above 4.0 stopped adding useful predictive weight in the original derivation, so the equation simply stops counting past that ceiling. Separately, anyone on regular dialysis — twice weekly or more, or continuous 24-hour therapy — has creatinine set to 4.0 automatically, whatever the lab actually reports, because dialysis is already scrubbing creatinine from the blood; a measured value in that setting reflects how well the dialysis is working, not how sick the kidneys are.
What does a resulting score around 27 actually mean?
Broadly, higher tracks with worse short-term outlook: figures under 10 are associated with comparatively low three-month mortality without transplant, while anything above 30 sits at the sharp end of the scale. A value near 27, like the worked example above, falls in a range where waitlist mortality is meaningfully elevated — though the exact percentage a clinician would quote comes from a validated mortality table, not from this equation in isolation.
Does this version account for sodium or albumin?
No — that omission is precisely why this is labeled the 2001 original rather than a current allocation tool. Low sodium and low albumin both independently worsen a cirrhosis patient's real prognosis, and neither term appears anywhere in this equation. MELD-Na folds in sodium; MELD 3.0 folds in sodium, albumin, and a sex adjustment together. A patient with unremarkable bilirubin, INR, and creatinine but dangerously low sodium will look healthier here than they truly are.
What's the difference between INR and raw prothrombin time?
INR is prothrombin time already standardized against a reference reagent, so a reading of 2.0 means the same thing regardless of which lab or which clotting-time reagent produced it. Enter INR directly here, not seconds — plugging in raw prothrombin-time seconds instead of INR would produce a meaningless result.
References
- Kamath PS, Wiesner RH, Malinchoc M, et al. A model to predict survival in patients with end-stage liver disease. Hepatology. 2001;33(2):464-470 (PubMed)
- Kim WR et al. MELD 3.0: The Model for End-Stage Liver Disease Updated for the Modern Era. Gastroenterology. 2021 (PubMed)
- UNOS — Policy and system changes adding serum sodium to MELD calculation (effective Jan 11, 2016)
Read this first: This instrument computes a screening figure from population formulas — it is not a diagnosis, and it cannot see the whole picture a clinician can. Use it to inform a conversation, not to replace one.