MELD score (Kamath 2001 original): how the formula works

The MELD score in this calculator is the original Model for End-Stage Liver Disease published by Kamath and colleagues in 2001. It combines the natural logs of bilirubin, INR and creatinine with a term for the cause of liver disease, then rounds to a whole number. It is not MELD-Na or MELD 3.0.

Not a medical device. Not a diagnosis or dosing recommendation.

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Liver calculators
Kamath PS et al. · 2001
The MELD formula
Worked examples
Frequently asked questions

What is the MELD score?

MELD stands for Model for End-Stage Liver Disease. The 2001 paper by Kamath and colleagues in Hepatology presented it as a model to predict survival in patients with end-stage liver disease. It uses three laboratory values: total bilirubin, the international normalized ratio (INR) and serum creatinine. A fourth term records whether the liver disease is cholestatic or alcoholic.

Several later versions also carry the MELD name. They add rules that the 2001 paper doesn't have, such as raising low lab values to 1.0, a dialysis rule, sodium, or a cap on the score. Magent's calculator is the 2001 original, with none of those additions. Its result can therefore differ from a MELD number taken from another source, and this page doesn't compare them.

This page explains the arithmetic. It doesn't say what a score means for a particular person.

The MELD formula

MELD = 3.8 × ln(bilirubin, mg/dL)
     + 11.2 × ln(INR)
     + 9.6 × ln(creatinine, mg/dL)
     + 6.4 × etiology                 etiology = 0 if cholestatic or alcoholic, otherwise 1
rounded to the nearest whole number

Exact expression the calculator uses:

meld = round(3.8 * ln(bilirubin_mg_dL) + 11.2 * ln(INR) + 9.6 * ln(creatinine_mg_dL) + 6.4 * etiology)

Inputs

Input	Meaning	Range accepted
`bilirubin_mg_dl`	Total bilirubin, mg/dL	0.1 to 40
`bilirubin_umol_l`	Total bilirubin, µmol/L (use instead of mg/dL)	2 to 684
`inr`	International normalized ratio	0.8 to 10
`creatinine_mg_dl`	Serum creatinine, mg/dL	0.1 to 20
`creatinine_umol_l`	Serum creatinine, µmol/L (use instead of mg/dL)	9 to 1768
`cholestatic_or_alcoholic`	true if the liver disease is cholestatic or alcoholic	true or false

Give bilirubin and creatinine in one unit each, not both.

How the calculation works

Convert units if needed. Creatinine in µmol/L is divided by 88.42. Bilirubin in µmol/L is divided by 17.1.
Set the etiology term. 0 if the disease is cholestatic or alcoholic, 1 otherwise.
Take natural logs of bilirubin, INR and creatinine.
Multiply and add. 3.8 times the bilirubin log, 11.2 times the INR log, 9.6 times the creatinine log, and 6.4 times the etiology term.
Round to the nearest whole number.

What the calculator does not do matters as much:

There are no floors. Bilirubin, INR and creatinine below 1.0 are used as entered, not raised to 1.0.
There is no creatinine cap.
There is no dialysis rule.
There is no cap at 40 on the score.
There is no sodium term.

Because values below 1.0 aren't raised, the log of such a value is negative, and very low inputs can give a low or even negative result.

Units

The formula is defined for bilirubin and creatinine in mg/dL. If you have µmol/L values, the calculator converts them: creatinine ÷ 88.42 and bilirubin ÷ 17.1. INR has no units. The logs are natural logs.

Worked examples

These use Magent's own expected values for the calculator.

Example 1: cholestatic or alcoholic disease

Creatinine 1.9 mg/dL, bilirubin 4.2 mg/dL, INR 1.2, cholestatic or alcoholic.
Etiology term 0.
MELD 14.

Example 2: the same labs, other cause

Creatinine 1.9 mg/dL, bilirubin 4.2 mg/dL, INR 1.2, not cholestatic or alcoholic.
Etiology term 1, which adds 6.4 before rounding.
MELD 20.

Example 3: bilirubin below 1.0

Creatinine 1.9 mg/dL, bilirubin 0.8 mg/dL, INR 1.2, cholestatic or alcoholic.
Bilirubin is used as 0.8, not raised to 1.0.
MELD 7.

Example 4: creatinine in µmol/L

Creatinine 168 µmol/L, bilirubin 4.2 mg/dL, INR 1.2, cholestatic or alcoholic.
Creatinine is converted by dividing by 88.42.
MELD 14, the same as Example 1.

History of the MELD score

The calculator cites Kamath and colleagues, Hepatology, 2001, titled "A model to predict survival in patients with end-stage liver disease". The formula the calculator uses, with its coefficients of 3.8, 11.2, 9.6 and 6.4 and the cholestatic or alcoholic etiology term, is the one in that paper. Lab floors, the dialysis rule, the cap and the sodium term that appear in later versions came afterwards and aren't part of it.

When it's used

The original MELD formula is used when the 2001 Kamath version is specifically needed, for example to reproduce figures from work based on that paper.

Where it's used

The inputs come from routine blood tests, so the formula can be worked out wherever bilirubin, INR and creatinine are available.

Who uses it

The person using the calculator enters the three lab values and the cause of liver disease. The calculator converts units, applies the formula and rounds.

Limits of the calculation

It is the 2001 original. It isn't MELD-Na or MELD 3.0.
It has no floors at 1.0, no creatinine cap, no dialysis rule and no cap at 40.
It isn't a transplant listing or allocation order, and doesn't produce a place on any list.
Whether disease is cholestatic or alcoholic is decided by the person entering the data.
This page doesn't say what to do with a result.

Clinical decisions belong to a qualified clinician who knows the patient.

MELD-Na adds serum sodium and later rules. It is a different formula, so its number isn't interchangeable with the 2001 original.
MELD 3.0 adds further terms. It is also a different formula.
Child-Pugh score adds points for lab values and clinical findings rather than using logs.

Glossary

Bilirubin: a breakdown product of red blood cells, cleared by the liver.
INR: international normalized ratio, a standardized measure of how long blood takes to clot.
Creatinine: a breakdown product of muscle, cleared by the kidneys.
Cholestatic: liver disease in which bile flow is blocked or reduced.
Natural log (ln): the logarithm to base e.

Common mistakes

Applying floors at 1.0. The 2001 formula uses values as entered.
Adding a dialysis rule or a cap. Neither is part of the original.
Setting the etiology term the wrong way round. Cholestatic or alcoholic disease gives 0; other causes give 1.
Comparing the result with a MELD-Na number. They are different formulas.

Source

Kamath PS, et al. A model to predict survival in patients with end-stage liver disease. Hepatology. 2001;33(2):464-470. DOI: 10.1053/jhep.2001.22172. PMID: 11172350

Frequently asked questions

What is in the original MELD score?

Bilirubin, INR, creatinine and whether the liver disease is cholestatic or alcoholic.

Is this the MELD used for the transplant waiting list?

No. This is the 2001 Kamath formula. It isn't MELD-Na or MELD 3.0, and it isn't a listing or allocation order.

Does the calculator raise values below 1.0?

No. Bilirubin, INR and creatinine are used as entered.

Why does the cause of liver disease change the score?

The 2001 formula adds 6.4 when the disease is not cholestatic or alcoholic. With the same labs, Examples 1 and 2 give 14 and 20.

Is there a maximum score?

The calculator has no cap at 40 or any other cap.