Maddrey discriminant function: how to calculate Maddrey's DF

Maddrey's discriminant function (DF) is 4.6 times the prothrombin time difference in seconds, plus total bilirubin in mg/dL. With a patient prothrombin time of 20 seconds, a laboratory control of 12 seconds and a bilirubin of 8 mg/dL, DF = 4.6 × (20 − 12) + 8 = 44.8.

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Liver calculators
Maddrey WC et al. · 1978
The Maddrey DF formula
Worked examples
Maddrey DF reference values
Frequently asked questions

What is Maddrey's discriminant function?

Maddrey's DF is a single number built from two blood tests in alcoholic hepatitis: how far the prothrombin time (PT) is prolonged beyond the laboratory's control value, and the total bilirubin. It's also called the Maddrey score, Maddrey DF, or the discriminant function for alcoholic hepatitis.

The name comes from the statistical method used in the study, discriminant analysis. In the formula, each extra second of PT prolongation adds 4.6 points; each mg/dL of bilirubin adds 1 point.

This page explains the arithmetic. It doesn't give a cutoff, and it doesn't say what a value means for a patient or recommend any therapy.

The Maddrey DF formula

DF = 4.6 × (patient PT − control PT, in seconds)
   + total bilirubin (mg/dL)

Exact expression the calculator uses:

DF = 4.6 * (pt_patient_sec - pt_control_sec) + bilirubin_mg_dl

In words: subtract the control PT from the patient's PT, multiply the difference by 4.6, then add the bilirubin in mg/dL. Magent's calculator reports the result to 1 decimal place.

What each part means

Term	Plain-English meaning	Unit	Accepted range
`pt_patient_sec`	The patient's prothrombin time	seconds	8–120
`pt_control_sec`	The laboratory's control prothrombin time	seconds	8–20
`bilirubin_mg_dl`	Total bilirubin	mg/dL	0.1–40; give this or µmol/L
`bilirubin_umol_l`	Total bilirubin in SI units	µmol/L	2–684, converted ÷ 17.1
`df`	Maddrey discriminant function	points	1 decimal place

How the formula works

Find the PT difference: patient PT minus control PT, in seconds.
Multiply that difference by 4.6.
Put bilirubin in mg/dL. If you have µmol/L, divide by 17.1.
Add the bilirubin to the result of step 2.
Round to 1 decimal place.

The PT term usually carries most of the weight. Eight seconds of prolongation contributes 36.8 points, while 8 mg/dL of bilirubin contributes 8. If the patient's PT equals the control, the PT term is zero and the DF equals the bilirubin.

Units

The formula uses PT in seconds and bilirubin in mg/dL. Two points are worth checking:

Seconds, not INR. The 1978 formula uses the PT difference in seconds against the lab's own control. The calculator doesn't accept an INR or convert one.
Bilirubin units. Bilirubin reported in µmol/L is converted to mg/dL by dividing by 17.1, so 136.8 µmol/L becomes 8.0 mg/dL.

Worked examples

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

Example 1: PT 20 s, control 12 s, bilirubin 8 mg/dL

PT difference: 20 − 12 = 8 seconds
PT term: 4.6 × 8 = 36.8
DF: 36.8 + 8 = 44.8

Example 2: the same values with bilirubin in µmol/L

Bilirubin: 136.8 ÷ 17.1 = 8.0 mg/dL
DF: 4.6 × (20 − 12) + 8.0 = 44.8

Example 3: PT equal to control

PT difference: 12 − 12 = 0 seconds
DF: 4.6 × 0 + 8 = 8.0

Example 3 shows the bilirubin term on its own.

Maddrey DF reference values

These values are computed from the formula and rounded to 1 decimal, as the calculator reports them. They show how the score moves; they aren't targets, reference ranges or severity categories.

Each second of PT prolongation adds 4.6 points, and each 1 mg/dL of bilirubin adds 1 point. With no PT difference, the DF equals the bilirubin: 8 mg/dL gives 8.0. A PT difference of 8 seconds with bilirubin 8 mg/dL gives 44.8.

History of the formula

The formula is credited to W. C. Maddrey and colleagues, in a paper published in Gastroenterology in 1978 (volume 75, issue 2, pages 193–199). The full reference is under Source below.

The abstract describes a randomized, double-blind trial in 55 patients with alcoholic hepatitis. A stepwise discriminant analysis of laboratory factors found that prolongation of the prothrombin time and the height of serum bilirubin at the start of the study were independently associated with death. The DF combines those two measurements.

A 2002 study in BMC Gastroenterology writes the same formula as 4.6 × (patient's PT − control PT) + total bilirubin (mg/dL).[1]

When it's used

Published work describes the DF as a predictor of mortality risk in alcoholic hepatitis.[1] Researchers have compared it with other liver scores, such as MELD, in patients hospitalized with the condition.[1]

Where it's used

In the 2002 comparison, scores were calculated from laboratory values obtained within 24 hours of hospital admission.[1] That study also notes a practical problem: the DF needs the prothrombin time in seconds, which has been largely replaced by the INR and isn't always reported by clinical laboratories.[1]

Who uses it

The DF appears in liver research and in hospital care of alcoholic hepatitis, where it is calculated from routine blood results.[1]

Limits of the calculation

It's a weighted sum of two numbers. It doesn't classify severity, and Magent doesn't recommend corticosteroids or any other therapy.
It uses PT in seconds against the laboratory control, as published in 1978. It doesn't accept or convert an INR.
Later trials used a DF value as a severity line. That is later-trial context, not part of the 1978 formula, and the calculator doesn't return it.
The control PT varies between laboratories and reagents. Use the control value reported with the patient's result.
Inputs outside the accepted ranges are rejected, not estimated.

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

MELD-Na uses bilirubin, INR, creatinine and sodium. It uses INR, not PT in seconds.
FIB-4 estimates liver fibrosis from age, AST, ALT and platelets. It isn't specific to alcoholic hepatitis.

Glossary

Prothrombin time (PT): how many seconds a blood sample takes to clot in a standard test.
Control PT: the laboratory's reference PT, reported alongside the patient's value.
INR: international normalized ratio, a standardized way of reporting PT. The DF doesn't use it.
Total bilirubin: a blood measure of bile pigment, in mg/dL or µmol/L.
Discriminant analysis: a statistical method that weights measurements to separate groups.

Common mistakes

Entering INR instead of seconds. The formula needs PT in seconds for both the patient and the control.
Using a generic control value. The control PT should come from the same laboratory run as the patient's PT.
Forgetting to convert bilirubin. A value in µmol/L is much larger than the mg/dL value. Enter it in the µmol/L field so it's converted.
Adding instead of subtracting the control. The PT term is the difference between the two times.

Source

Maddrey WC, Boitnott JK, Bedine MS, Weber FL Jr, Mezey E, White RI Jr. Corticosteroid therapy of alcoholic hepatitis. Gastroenterology. 1978;75(2):193-199. DOI: 10.1016/0016-5085(78)90401-8

Frequently asked questions

How do you calculate Maddrey's discriminant function?

Subtract the control PT from the patient's PT in seconds, multiply by 4.6, and add total bilirubin in mg/dL. For 20 s, 12 s and 8 mg/dL, that's 4.6 × 8 + 8 = 44.8.

What is a high Maddrey score?

This page doesn't give a cutoff or severity bands. It calculates the score; what a value means depends on the clinical context.

Can I use INR in the Maddrey formula?

No. The 1978 formula uses prothrombin time in seconds, compared with the laboratory control. The calculator doesn't accept INR.

What does 4.6 mean in the Maddrey formula?

It's the weight given to each second of PT prolongation. The 4.6 multiplier is the one used in the modified Maddrey discriminant function, as written in the 2002 study under Further reading.[1]

Can bilirubin be entered in µmol/L?

Yes. The calculator divides µmol/L by 17.1 to get mg/dL.

Who developed the Maddrey discriminant function?

W. C. Maddrey and colleagues, in a 1978 paper in Gastroenterology.