Example
The ARR is therefore the amount by which your therapy reduces the risk of the bad outcome. For example, if your drug reduces the risk of a bad outcome from 50 per cent to 30 per cent, the ARR is:
ARR = CER - EER = 0.5 - 0.3 = 0.2 (20 per cent)
therefore NNT = 1/ARR = 1/0.2 = 5
The following table is taken from Chapter 3 of the book, How to Practice and Teach Evidence-Based
Medicine. It shows an abstract of the diabetes control and complications trial examining the
effectiveness of intensive diabetes therapy on the development and progression of neuropathy.
Derivation of clinically useful measures of therapy:
| The occurrence of neuropathy | Event Rates (diabetic neuropathy) | RRR
(CER-EER)/CER | ARR
(CER-EER) | NNT
(1/ARR)
|
| Usual insulin regimen CER | Intensive insulin regimen EER
|
|---|
| in the actual trial | 0.096 | 0.028 | (0.096-0.028)/0.096
= 71% | 0.096-0.028
=
0.068 | 1/0.068
= 14.7 or 15
|
high hypothetical
case A | 0.96 | 0.28 | (0.96-0.28)/0.96
= 71% | 0.96-0.28
=
0.68 | 1/0.68
= 1.47 or 2
|
low hypothetical
case
B | 0.0096 | 0.0028 | (0.0096-0.0028)/
0.0096
=
71% | 0.0096-0.0028
= 0.0068 | 1/0.0068
= 147
|
Click here for more samples.
Converting Odds Ratios to NNTs
The formula for converting ORs to NNTs is:
NNT = (1-(PEER*(1-OR))) / ((1-PEER)*(PEER)*(1-OR))
The formula for converting ORs to NNHs (Numbers Needed to Harm) is:
NNH = ((PEER*(OR-1))+1) / (PEER*(OR-1)*(1-PEER))
This table can be used to convert odds ratios to NNTs:
Deriving NNTs from a treatment's Odds Ratio and
the observed or expected Event Rates of untreated groups or individuals:
| CER or PEER | Odds Ratios
|
|---|
| 0.5 | 0.55 | 0.6 | 0.65 | 0.7 | 0.75 | 0.8 | 0.85
| 0.9 | | 1.5 | 2 | 2.5 | 3 | 3.5 | 4 | 4.5 | 5 | 10
|
|---|
| NNTs for efficacy | | NNHs for harm
|
|---|
| 0.05 | 41 | 46 | 52 | 59 | 69 | 83 | 104
| 139 | 209 | | 43 | 22 | 15 | 12 | 9 | 8 | 7 | 6 | 3
|
|---|
| 0.1 | 21 | 24 | 27 | 31 | 36 | 43 | 54 | 73 | 110
| | 23 | 12 | 9 | 7 | 6 | 5 | 4 | 4 | 2
|
|---|
| 0.2 | 11 | 13 | 14 | 17 | 20 | 24 | 30 | 40 | 61
| | 14 | 8 | 5 | 4 | 4 | 3 | 3 | 3 | 2
|
|---|
| 0.3 | 8 | 9 | 10 | 12 | 14 | 18 | 22 | 30 | 46
| | 11 | 6 | 5 | 4 | 3 | 3 | 3 | 3 | 2
|
|---|
| 0.4 | 7 | 8 | 9 | 10 | 12 | 15 | 19 | 26 | 40
| | 10 | 6 | 4 | 4 | 3 | 3 | 3 | 3 | 2
|
|---|
| 0.5 | 6 | 7 | 8 | 9 | 11 | 14 | 18 | 25 | 38
| | 10 | 6 | 5 | 4 | 4 | 3 | 3 | 3 | 2
|
|---|
| 0.7 | 6 | 7 | 9 | 10 | 13 | 16 | 20 | 28 | 44
| | 13 | 8 | 7 | 6 | 5 | 5 | 5 | 5 | 4
|
|---|
| 0.9 | 12 | 15 | 18 | 22 | 27 | 34 | 46 | 64 | 101
| | 32 | 21 | 17 | 16 | 14 | 14 | 13 | 13 | 11
|
|---|
PEER - Patient's Expected Event Rate; CER - Control Event Rate
Note that the entries under efficacy are NNTs; those under harm are NNHs
Click here to comment on
NNTs