Calculates the Maddrey discriminant function from the prothrombin time and bilirubin, to identify severe alcohol-associated hepatitis.
Result
Enter the prothrombin time, the control time and the bilirubin.
Sources
AASLD 2019 · 3 studies
AASLD 2019 DF 32 or more, or MELD above 20, marks severe disease.
3
studies
927
citations
435
PubMed papers
Evidence
Guideline recommendation
“The 2019 AASLD practice guidance on alcohol-associated liver disease uses a Maddrey discriminant function of 32 or more, or a MELD score above 20, to identify severe alcohol-associated hepatitis, the group in which corticosteroids are considered, and recommends the Lille score to judge the response after about 7 days.”
American Association for the Study of Liver Diseases
Hepatology: Journal Metrics Score 6.5, Q1 · cited 975 times
Known limitations
In 66 patients with severe alcoholic hepatitis, defined by a DF above 32 or spontaneous encephalopathy, 11 of 31 on placebo (35%) died within 28 days, against 2 of 35 (6%) on methylprednisolone.
Ann Intern Med: Journal Metrics Score 4.6, Q1 · cited 504 times
In individual data from five trials of patients with a DF of 32 or more or encephalopathy (418 patients), 28-day survival was 80% with corticosteroids against 66% without; the DF, encephalopathy and the Lille score each independently predicted survival.
In the STOPAH trial (1,103 patients with alcoholic hepatitis and a DF of 32 or more), 28-day mortality was 14% with prednisolone against 17% with placebo (odds ratio 0.72, P = 0.06, not significant), with no benefit at 90 days or 1 year and more serious infections (13% against 7%).
N Engl J Med: Journal Metrics Score 29.8, Q1 · cited 853 times
The original paper has been cited 927 times, and 435 PubMed articles mention the Maddrey discriminant function in their title or abstract. Citation counts from OpenAlex and article counts from PubMed, retrieved November 13, 2026. Journal Metrics Scores and quartiles are from this site’s current release; follow the journal name for details.
After the result
DF 32 or more · DF below 32 · Any result
Severe alcohol-associated hepatitis. Not severe by this measure. Make sure the diagnosis fits.
Next steps
Avoid common errors
5 common errors to avoid
and 3 more
When the DF misleads
1INR is not prothrombin time
The formula needs seconds. An INR of 2.0 entered as 2 seconds gives a negative prolongation and a meaningless DF. The calculator refuses values below 5 seconds.
2Laboratory variation
Thromboplastin reagents differ, so the prothrombin time and its control vary between laboratories. A patient can sit above 32 in one laboratory and below it in another.
3The control time
Use the laboratory’s own control or mean normal time. Each second of error moves the DF by 4.6.
4Anticoagulants and vitamin K
Warfarin prolongs the prothrombin time without reflecting liver function; vitamin K given before the test can shorten it. Either makes the DF misleading.
5Hemolysis raises bilirubin
In Zieve’s syndrome and other hemolysis, part of the bilirubin is not from liver failure, which can push the DF up.
Formula
4.6 × (prothrombin time − control time) + total bilirubin in mg/dL; severe at 32 or more.
4.6 × ΔPT + bilirubin
4.6 × (prothrombin time − control time) + total bilirubin in mg/dL; severe at 32 or more.
Formula and cut-off
| Value | Formula |
|---|---|
| Discriminant function | 4.6 × (prothrombin time − control time, seconds) + total bilirubin (mg/dL) |
| Bilirubin in µmol/L | divide by 17.1 to get mg/dL before adding |
| Result | DF | Meaning |
|---|---|---|
| Below 32 | below 32 | Below the cut-off for severe disease. Corticosteroids were not shown to help below 32; follow the trend, since the DF can rise over the first days, and look at the MELD score as well. |
| Severe alcohol-associated hepatitis | 32 or more | A DF of 32 or more marks severe alcohol-associated hepatitis, with a high short-term mortality: in the 1989 trial that set the cut-off, 35% of patients on placebo, more than half of whom also had encephalopathy, died within 28 days. This is the group in which corticosteroids were tested. |
Maddrey 1978
Carithers 1989
Units
Test cases
3 published cases, each also a test case
3 published cases; the calculator reproduces every result.
Worked examples
A 35-year-old woman with alcohol-related cirrhosis who had kept drinking presented with jaundice, ascites and a hemoglobin of 6 g/dL from non-immune hemolysis (Zieve’s syndrome). The prothrombin time was 29.5 seconds against a laboratory reference of 11.4, and total bilirubin was 9.54 mg/dL. The report gives a Maddrey score of 92.
“Maddrey discriminant function score of 92 points”
4.6 × 18.1 + 9.54 = 92.8; the report gives 92. Hemolysis also raises bilirubin, which can inflate the DF; here the very long prothrombin time alone puts it far above 32.
Entered as: Prothrombin time (patient): 29.5 seconds; Control prothrombin time: 11.4 seconds; Total bilirubin: 9.54 mg/dL.
Source: Ribeiro R et al., Cureus 2024 (PubMed · Free full text · DOI)
A 31-year-old man with heavy alcohol use and alcohol-associated hepatitis had a prothrombin time of 19.2 seconds and a total bilirubin of only 6.8 mg/dL; the report gives a Maddrey score of 35.3. He was later found to have Veillonella bacteremia. He started prednisolone; his Lille score at day 7 was 0.577, indicating non-response, and he died within 3 months.
“Maddrey's Discriminant Function score was 35.3 (Prothrombin time 19.2 seconds and total bilirubin 6.8 mg/dL).”
The report does not state the control time; 13.0 seconds reproduces its 35.3 exactly. Most of the score here comes from the prothrombin time, not the bilirubin.
Entered as: Prothrombin time (patient): 19.2 seconds; Control prothrombin time: 13 seconds; Total bilirubin: 6.8 mg/dL.
Source: Lee P et al., Case Reports Hepatol 2021 (PubMed · Free full text · DOI)
A 29-year-old woman with alcoholism (a very high phosphatidylethanol level) and a family history of hemochromatosis had a prothrombin time of 18.6 seconds and a total bilirubin of 8.7 mg/dL. The report gives a Maddrey score of 46.4; she was treated with prednisolone, but her bilirubin and INR rose again, she developed kidney failure and encephalopathy, and she died.
“The patient’s Maddrey’s discriminant function was 46.4”
The report does not give the control time; 10.4 seconds reproduces its 46.4, but is shorter than the INR of 1.5 suggests, so the authors’ control is uncertain. A control of 12.4 seconds would give 37.2, still above 32. The report gives no Lille score; non-response to corticosteroids is usually judged with the Lille score after about 7 days.
Entered as: Prothrombin time (patient): 18.6 seconds; Control prothrombin time: 10.4 seconds; Total bilirubin: 8.7 mg/dL.
Source: Shobi V et al., J Med Case Rep 2021 (PubMed · Free full text · DOI)
FAQ
6 questions and answers
and 4 more answers
Questions
DF = 4.6 × (patient prothrombin time − control prothrombin time, in seconds) + total bilirubin in mg/dL. A prothrombin time of 20 seconds against a control of 12, with a bilirubin of 10 mg/dL, gives 4.6 × 8 + 10 = 46.8. With bilirubin in µmol/L, divide it by 17.1 first.
A discriminant function of 32 or more. Carithers and colleagues enrolled patients with a DF above 32, or spontaneous hepatic encephalopathy, in their 1989 corticosteroid trial; later trials and guidance use 32 or more. In that trial 35% of patients on placebo, more than half of whom also had encephalopathy, died within 28 days. Maddrey’s original 1978 paper used a different version of the formula and a higher cut-off, so the 32 threshold belongs to the modified formula used here.
No. The formula needs the prothrombin time in seconds and the laboratory’s control time. The INR is a ratio; entering it in place of seconds gives a meaningless number. Because thromboplastin reagents differ, the same patient can have a different DF in different laboratories, which is one reason guidance now also uses the MELD score, built on the INR.
Use the laboratory’s control or mean normal prothrombin time, often printed beside the result. If only a reference range is given, its midpoint is a common stand-in; say so when you record the score, since a 1-second difference changes the DF by 4.6.
Not entirely. Patients with spontaneous hepatic encephalopathy were treated as severe in the trials whatever their DF, and the DF can rise over the first days in hospital. Repeat it, and look at the MELD score too.
The DF and MELD both estimate severity at presentation; the 2019 AASLD guidance discusses both, and MELD above about 20 is also used to mark severe disease. The Lille score is different: it is calculated after about 7 days of corticosteroids to see whether the patient is responding.
Further reading
8 references with PubMed and DOI links
8
references
3
free full text
From Maddrey WC et al., Gastroenterology 1978 to the newest case reports.
References
clinical grade of aneurysmal subarachnoid hemorrhage, I to V.
total calcium adjusted for albumin, in mg/dL or mmol/L.
stroke severity from 15 bedside items, 0 to 42.
MAP from systolic and diastolic pressure, against the 65 mm Hg target.
eye, verbal and motor scores for preverbal children, 3 to 15.
oxygenation ratio with the Berlin ARDS severity ranges.
serum sodium corrected for high glucose, Katz or Hillier factor.
sodium − (chloride + bicarbonate), with the albumin-corrected gap.
urea nitrogen to creatinine ratio, in US or SI units.
estimated creatinine clearance with actual, ideal or adjusted weight.
cardiac output and index from oxygen consumption and saturations.
ANC from the white cell count, neutrophils and bands.
insulin resistance from fasting glucose and insulin, in US or SI units.
FENa from plasma and urine sodium and creatinine: prerenal, indeterminate or tubular pattern.
three-item stroke severity screen for large vessel occlusion, 0 to 4.
water deficit in hypernatremia from sodium, weight and body water.
expected PaCO2 in metabolic acidosis, 1.5 × HCO3 + 8 ± 2.
corrected QT interval by Bazett, Fridericia, Framingham or Hodges.
head CT decision rule for children with minor head trauma.
blood loss before hemoglobin or hematocrit reaches a chosen lowest value.
eye, verbal and motor response, 3 to 15, with GCS-Pupils.
Devine ideal body weight and adjusted weight from height and sex.
cuffed and uncuffed tube size and oral depth by age.
calculated osmolality, osmolal gap and ethanol correction.
MELD, MELD-Na and MELD 3.0 for chronic liver disease.
early stroke risk after a transient ischemic attack.
Which published the AASLD guidance, with its current metrics.
Which published the original Maddrey paper, with its current metrics.
Contributed by Dr. Meng Zhao (MD · Former Neurosurgeon · Medical AI Researcher), from the original publications listed here. Last updated November 13, 2026. LinkedIn
The calculator code is tested against every worked example on this page before each release.
This calculator supports, and does not replace, clinical judgment. It is meant for healthcare professionals and is not medical advice for patients. Report an error through the contact page.