England & Fraser Index Calculator
England & Fraser Index Calculator
The original 1973 discriminant function for microcytic anaemia: a negative result favours thalassaemia trait, a positive one iron deficiency. It prioritises who is tested — it does not diagnose either.
England & Fraser Index
MCV, RBC, Hb → functionMCV 60 fL, red cell count 6.2 ×10¹²/L, haemoglobin 11.0 g/dL
Formula
Negative → beta-thalassaemia trait more likely · positive → iron deficiency more likely
- MCV
- mean corpuscular volume in fL — the only term that raises the function, so a very low MCV drives the result negative and toward thalassaemia trait
- RBC
- red cell count in ×10¹²/L. Thalassaemia trait preserves or raises the count, which subtracts more and pushes the function negative; iron deficiency lowers it, which subtracts less
- 5 × Hb
- haemoglobin in g/dL, weighted five-fold — much the heaviest term. A haemoglobin entered in g/L instead of g/dL produces a large negative number and a confident wrong answer, which is the commonest way this index is misused
- the sign is the answer
- there is no numerical cut-off to remember: the function crosses zero. A result near zero is genuinely uninformative rather than borderline, and should be treated as the index declining to answer
Worked example
MCV 60 fL, red cell count 6.2 ×10¹²/L, haemoglobin 11.0 g/dL
5 × 11.0 = 55.0
60 − 6.2 − 55.0 − 3.4 = −4.6
Negative, so beta-thalassaemia trait is the more likely of the two — send haemoglobin electrophoresis or HPLC, and ferritin
Note what drove it: a red cell count of 6.2 ×10¹²/L alongside an MCV of 60 fL is a great many very small cells, which is the pattern the index was built to detect
Enter the haemoglobin as 110 g/L by mistake and the function returns −499.6 — still negative, still confidently reported, and meaningless. Check the unit before the sign
Three discriminant indices on the same patient
| Index | Formula | Inputs needed | Favours thalassaemia trait |
|---|---|---|---|
| Mentzer | MCV ÷ RBC | MCV, red cell count | Below 13 |
| England & Fraser | MCV − RBC − (5 × Hb) − 3.4 | MCV, red cell count, haemoglobin | A negative result |
| Green & King | MCV² × RDW ÷ (Hb × 100) | MCV, RDW-CV, haemoglobin | Below 65 |
What the index is for, and what it is not for
| Question | Answer |
|---|---|
| Can it diagnose thalassaemia trait? | No. It was derived to decide who is sent for confirmatory testing, at a time when that testing was scarce and expensive |
| Can it exclude iron deficiency? | No. Ferritin does that, read against CRP |
| Does it work where both conditions are present? | No. Coexistence pulls the function toward zero, which is exactly where it discriminates worst |
| Does its accuracy travel between populations? | Poorly. It depends on the local prevalence of each condition and on the mix of thalassaemia genotypes present |
| What does a result close to zero mean? | That the index has not answered. Treat it as uninformative rather than as weakly favouring either side, and send both confirmatory tests |
The original discriminant, and the honest limits of all of them
England and Fraser published this function in the Lancet in 1973, and it is the ancestor of every discriminant index that followed. The problem it addressed has not changed: beta-thalassaemia trait and iron deficiency both present as a microcytic hypochromic anaemia, they need entirely different responses, and confirming which is which requires a specific test that in 1973 was scarce. The function was built to decide, from the routine blood count that every patient already had, which of those tests to send.
It combines three observations. The MCV is low in both conditions and lowest in thalassaemia trait, so it raises the function. The red cell count is preserved or raised in thalassaemia trait — the marrow makes plenty of cells, each of them small — and reduced in iron deficiency, where haemoglobin synthesis limits production itself, so subtracting it pushes the trait negative. And the haemoglobin, weighted five-fold, captures the observation that thalassaemia trait spares the haemoglobin more than the degree of microcytosis would suggest. The constant of 3.4 sets the boundary at zero, so the sign of the result is the answer and there is no threshold to remember.
That five-fold weighting on the haemoglobin is worth respecting. It is by far the heaviest term, and a haemoglobin entered in grams per litre instead of grams per decilitre — 110 instead of 11.0 — returns a large negative number that looks like a confident vote for thalassaemia trait. The index will not warn anyone, because a negative result is a legitimate output. Check the unit before reading the sign.
None of these indices is diagnostic. A meta-analysis of 99 studies and more than 135,000 results compared twelve of them and found that none reached the accuracy needed for a definitive diagnosis: this one ranked fifth with an area under the curve of 0.887, Green and King’s seventh, Mentzer’s eighth, all clustered too closely to separate. Performance varies substantially between populations, because it depends on how common each condition is locally. And the failure that matters most is invisible to the arithmetic: iron deficiency and thalassaemia trait frequently coexist, most often in exactly the populations where screening is done, and when they do every index is dragged toward zero and every index misleads. Ferritin and haemoglobin electrophoresis settle this question. The index decides only which is sent first.
Frequently asked questions
What is the England & Fraser index?
A discriminant function calculated as the MCV minus the red cell count minus five times the haemoglobin minus 3.4. A negative result favours beta-thalassaemia trait and a positive one favours iron deficiency. It was published in the Lancet in 1973 and is the oldest index of its kind.
What units does the England & Fraser index use?
MCV in femtolitres, red cell count in ×10¹²/L (identical to ×10⁶/µL) and haemoglobin in g/dL. The haemoglobin term is weighted five-fold, so entering it in g/L instead — 110 rather than 11.0 — produces a large negative result and a confidently wrong answer.
Does a negative result mean the patient has thalassaemia trait?
No. It means thalassaemia trait is the more likely of the two and should be tested for first, with haemoglobin electrophoresis or HPLC. Measure ferritin at the same time: coexisting iron deficiency lowers HbA₂ toward the normal range and can cause electrophoresis to miss the trait.
What does a result close to zero mean?
That the index has not answered. Zero is the boundary, so a function of −0.3 or +0.4 carries no useful information and should not be read as weakly favouring either side. Send both confirmatory tests rather than treating a marginal sign as a result.
How accurate is the England & Fraser index?
In a meta-analysis of 99 studies it reached a diagnostic odds ratio of 34.7 with an area under the curve of 0.887, ranking fifth of twelve indices — useful for deciding who to test and not adequate for diagnosis. Accuracy also varies with the population, and it fails altogether when iron deficiency and thalassaemia trait coexist.
Related calculators
References
- England JM, Fraser PM. Differentiation of iron deficiency from thalassaemia trait by routine blood-count. Lancet. 1973;1(7801):449–452.
- Hoffmann JJML, Urrechaga E, Aguirre U. Discriminant indices for distinguishing thalassemia and iron deficiency in patients with microcytic anemia: a meta-analysis. Clin Chem Lab Med. 2015;53(12):1883–1894.
- Ntaios G, Chatzinikolaou A, Saouli Z, et al. Discrimination indices as screening tests for β-thalassemic trait. Ann Hematol. 2007;86(7):487–491.
Medical Disclaimer: The tools and content provided here are for educational and reference purposes only. They are not intended to substitute for professional medical advice, diagnosis, or treatment. Clinical decisions should always be based on the comprehensive assessment of a qualified healthcare professional.