# Getting NNTs

Calculating NNTs
from raw data - use the formula
from published odds ratios - use the Table
from published relative risk - use the nomogram
L'Abbé plots
Using NNTs
Systematic reviews of randomised controlled trials provide the highest level of evidence of efficacy of treatments - though in other circumstances, such as adverse events or diagnostic tests, randomised trials may not always provide the best evidence. Commonly accepted levels of efficacy evidence are shown below.

### Type & Strength of Efficacy Evidence

1. Strong evidence from at least 1 systematic review of multiple well-designed randomised controlled trials
2. Strong evidence from at least 1 properly designed randomised controlled trial of appropriate size
3. Evidence from well designed trials without randomisation, single group pre-post, cohort, time series or matched case-controlled studies
4. Evidence from well-designed nonexperimental studies from more than 1 centre or research group
5. Opinions of respected authorities, based on clinical evidence, descriptive studies or reports of expert committees

### Output from systematic reviews

The evidence provided in systematic reviews can take various forms. Often it is statistical - an odds ratio, relative risk, hazard ratio or effect size. These show statistical superiority of one treatment over another, or over no treatment, but they are a bit difficult when we try and relate them to clinical practice. Bandolier has favoured the number-needed-to-treat [1] as a useful way of looking at results of reviews or trials for at least two reasons. It is easy to calculate, and provides the treatment-specific result in a form which we can handle. Using NNTs is a bit trickier. Bandolier has started thinking of the NNT in two ways.

### Black bag evidence

Firstly - and this is where most systematic reviews are useful - it can help us to make decisions between treatment options. If the NNT for treatment A is lower (better) than treatment B, then, all other things being equal, choosing A over B makes sense. Here the choice is what to put in the black bag. A would go into the black bag, B would not.

The other way to use an NNT is when you make choices for an individual patient, perhaps whether to treat or not. The choice here is whether or not to take A out of the black bag and use it.

There are, of course, many nuances to all this. Bandolier recommends a new book from David Sackett & colleagues - Evidence-based Medicine: how to practice and teach EBM - as a cheap and worthwhile acquisition for any thinking doctor, nurse, scientist or manager in the NHS [2].

Readers who find NNTs helpful, but who are not entirely comfortable with them, have asked Bandolier to work through some examples of how to obtain and use NNTs. To do this from existing reviews can be difficult, since not all the information is to hand. So Bandolier has done its own systematic review comparing proton pump inhibitors (PPIs) and H2-antagonists (H2As) in the short-term healing and long-term maintenance of reflux oesophagitis. The full text of the review and associated tables and graphs is available on the Bandolier Internet pages. The information from that review will be used to show how NNTs can be calculated in different ways. NNTs can be calculated from raw data using a formula, from odds ratios, or from relative risk reduction and expected prevalence.

## NNT can be calculated by

• raw data - use the formula
• published odds ratios - use the Table
• published relative risk - use the nomogram

### 1. Calculating NNTs

The NNT calculation is given below.
We need to distinguish between treatments , such as aspirin as an analgesic, and preventative measures , such as aspirin preventing further cardiac problems after myocardial infarction. Using the number outputs from systematic reviews is different depending on which you are looking at. The distinction is between treatment and prophylaxis. For prophylaxis, where fewer events occur in the treated group, the calculation shown will produce negative NNTs. You can use those (the number will be correct), or you can switch the active and control groups around to provide NNTs with a positive sign.

The NNT for prophylaxis is given by the equation 1/(proportion benefiting from control intervention minus the proportion benefiting from experimental intervention), and for treatment by 1/(proportion benefiting from experimental intervention minus the proportion benefiting from control intervention).

NNTs for treatment should be small. We expect large effects in small numbers of people. Because few treatments are 100% effective and because few controls - even placebo or no treatment - are without some effect, NNTs for effective treatments are usually in the range of 2 - 4. Exceptions might be antibiotics. The NNT for Helicobacter pylori eradication with triple or dual therapy, for instance, is 1.2 ( Bandolier 12 ).

NNTs for prophylaxis will be larger, few patients affected in large populations. So the difference between treatment and control will be small, giving large NNTs. For instance, use of aspirin to prevent one death at five weeks after myocardial infarction had an NNT of 40 (Bandolier 17).

#### Using absolute risk reduction

The absolute risk reduction (ARR) is the difference between the event rate in the experimental group and the event rate in the control group. It is the denominator in the NNT calculation. Many reviews and trials provide this information, so if you have it and convert it into a proportion, then you can get the NNT by dividing 1 by the ARR:

NNT = 1/ARR

#### Confidence Intervals

The 95% confidence intervals of the NNT are an indication that 19 times out of 20 the 'true' value will be in the specified range. An NNT with an infinite confidence interval is then but a point estimate; it includes the possibility of no benefit or harm. It may still have clinical importance as a benchmark until further data permits finite confidence intervals, but decisions must take this into account. A method for calculating confidence intervals was given in Bandolier 18.

### 2. Using odds ratios

When it is legitimate and feasible to combine data the odds ratio is the accepted statistical test to show that the experimental intervention works significantly better than control. If a quantitative systematic review produces odds ratios but no NNTs, you can derive NNTs from the Table [3].

#### Working out the NNT from a published odds ratio (OR)

Prevention OR Treatment OR
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
0.05 41 46 52 59 69 83 104 139 209 43 22 15 12 9 8 7 6 3
Control 0.1 21 24 27 31 36 43 54 73 110 23 12 9 7 6 5 4 4 2
Event 0.2 11 13 14 17 20 24 30 40 61 14 8 5 4 4 3 3 3 2
Rate 0.3 8 9 10 12 14 18 22 30 46 11 6 5 4 3 3 3 3 2
(CER) 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

Odds ratios are on the top line and control event rates (CER) down the left hand side. NNTs are in the boxes. So if you have an odds ratio (eg 0.6) and a CER (eg 0.5), then the NNT will be found where they cross (NNT = 8).

A caveat here is that odds ratios should be interpreted with caution when events occur commonly, as in treatments, and odds ratios may over-estimate the benefits of an effect when event rates are above 10%. Odds ratios are likely to be superseded by relative risk reduction because relative risk reduction provides better information in situations where event rates are high [3, 4].

### 3. Relative risk reduction

Chatelier and colleagues published a useful NNT nomogram in the BMJ last year [5]. Relative risk reduction - the percentage reduction in risk between the experimental and control group - is used to calculate the NNT for any group in whom the risk of an event happening was known.

This is probably most likely to be used in prophylaxis. If you have a review or paper which gives a RRR (in percent) and you know the susceptibility of your patient for a bad outcome (usually called the 'patient expected event rate', or PEER), then you can find out the NNT of an intervention.

RRR is calculated by dividing the difference between the rate of events in experimental and control group by the rate of events in the control group. So if 10% of patients have a bad event in controls, and only 9% with some intervention, the RRR is (10-9)/10 = 10%. Relative risk reductions happen in prophylaxis. With treatments we have relative risk increase because we expect more good events. The method works either way.

Say the RRR is 50%, and the PEER is 50%. Then the NNT from the nomogram is 4. But if the RRR is 10% and PEER is 10% then the NNT is about 90.

### L'Abbé plots

A paper [6] by Kristen L'Abbé and colleagues written ten years ago is regarded by Bandolier as one of the most sensible and understandable ever written on systematic reviews. The authors suggest a simple graphical representation of the information from trials. Each point on a L'Abbé scatter plot is one trial in the review. The proportion of patients achieving the outcome with the experimental intervention is plotted against the event rate in controls. Even if a review does not show the data in this way, you can do it yourself if the information is in the review.

For treatment, trials in which the experimental intervention was better than the control will be in the upper left of the plot, between the y axis and the line of equality. If experimental was no better than control then the point will fall on the line of equality, and if control was better than experimental then the point will be in the lower right of the plot, between the x axis and the line of equality.

For prophylaxis this pattern will be reversed. Because prophylaxis reduces the number of bad events - such as death after myocardial infarction by the use of aspirin - we expect a smaller proportion harmed with treatment than with control. So if experimental is better than control the trial results cloud should be between the x axis and the line of equality.

These plots give a quick indication of the level of agreement among trials. If the points are in a consistent cloud, that gives some confidence that what we are seeing is a homogenous effect. But if points are spread all over the graph, and especially if they cross the line of equality, then that should make us concerned about the intervention, or the patients being treated and their condition. This can also be called heterogeneity.

The important point about a L'Abbé plot is that it shows all of the extant data on one piece of paper. When combined with numbers in the trial, and a summary measure like NNT, it is a neat way to summarise lots of information.

## Using NNTs

### Variation in treatment and control

One of the things that plotting information from systematic reviews in L'Abbé plots teaches you is just how variable are the effects of both treatment and control in randomised trials. It is legitimate to be surprised, but after quite a short time it seems that this is the norm.

The reasons are probably complex, but much of the variability will be just random chance. In many circumstances patients can have quite wide patterns of response to a treatment, but trial size for treatments is often relatively small, because trials are hard to do. Gathering data together in systematic review and meta-analysis gives much more power than the single trial in almost all circumstances, and especially for reviews of treatments. Seeing such variability also teaches caution when you are faced with a single trial with apparently excellent (or hopeless) results.

### Comment

There will be circumstances where systematic reviews will not yield information to generate L'Abbé plots, NNTs, relative risk, or even odds ratios. There are times when the information for quantitative systematic review is just not available. Where they are available, then we can use information in our practice.

### Using NNTs for particular patients

The choice of what goes into the black bag will also reflect the choice of what comes out of it. Simplistically, if we are convinced by the evidence shown from page 5 on that omeprazole is better than ranitidine for healing reflux oesophagitis, then we might use omeprazole, though there will be arguments over the value of stepped treatment.

Bandolier will use the example of dog-bite infection (the subject of a recent BMJ editorial [7] and a previous Bandolier review in issue 16) as an example of how NNTs can be used to make judgements on a specific patient.

### Dog bite infection

Suppose a woman presents with a dog bite. Her immune system is compromised by steroid therapy for asthma. Should we give prophylactic antibiotics to prevent infection? We know from a quantitative systematic review of RCTs [8] that there is evidence for benefit with an overall NNT of 16. How can we apply this to our patient?

She is immunocompromised, so her risk of becoming infected is many times higher than the non-compromised patients in the review. We estimate her increased risk (usually called F), to be 5 times greater than the 16% average rate of infection in the review (though in individual studies risk varied between 3% and 46%). Assuming a constant relative risk, the estimated NNT corresponding to an F of 5 is then NNT/F = 16/5 = 3 [2].

So while prophylactic antibiotic treatment of dog bite to prevent infection may not be worthwhile for all patients (NNT of 16), it may well be so for our particular patient (NNT of 3).

Suppose we live in Middlesborough? We know from an RCT that infection rates there are about 50%, so we might be likely to treat all patients. For patients in Middlesborough, the "patient expected event rate", or PEER, is 0.5 compared to the 0.16 average found in the review. The review gave us an odds ratio of 0.6 for prophylactic antibiotics.

If we look down the line of 0.6 in the Table of odds ratios and NNTs, stop at a control event rate (our PEER) of 0.5, we find an NNT of about 8. Now if half our patients bitten by a dog are going to get an infected wound, and by using antibiotics we can stop that happening just once in every eight times, then we save six patients in every 100 having an infected bite.

So even in Middlesborough our prophylactic antibiotics won't stop every infection, but perhaps enough to make it worthwhile. Perhaps changes in practice and knowledge will make it more likely that we want to intervene in this way [7].

### NNTs to inform patients?

This is a difficult area. Because an NNT is treatment-specific, it will not include all the power of an intervention - a placebo response, for instance. Patients want to know their chance of getting better or being harmed, and that includes influences from all sources. The best analgesics have NNTs of 2 for at least 50% pain relief (a high hurdle), which implies that half the patients will achieve at least 50% pain relief because of the analgesic. But the placebo effect will add perhaps another 20% to this, so that reality is that 70% achieve at least 50% pain relief with the analgesic, which sounds better and reflects the reality.

But that is a simple example. Most circumstances are more complex. The LBBH (likelihood of being helped or harmed) has been suggested as one way of presenting information to patients [9], but there is a clear need for more empirical research to provide evidence on how best to do this.

### References

1. Cook RJ, Sackett DL. The number needed to treat: a clinically useful measure of treatment effect. British Medical Journal 1995 310:452-4.
2. DL Sackett, WS Richardson, W Rosenberg, RB Haynes. Evidence-based Medicine: how to practice & teach EBM. Churchill Livingstone. ISBN 0-443-05686-2.
3. Sackett DL, Deeks JJ, Altman DG. Down with odds ratios! Evidence Based Medicine 1996 1:164-6.
4. Sinclair JC, Bracken MB. Clinically useful measures of effect in binary analyses of randomized trials. J Clin Epidemiol 1994 47:881-889.
5. G Chatelier et al. The number needed to treat: a clinically useful nomogram in its proper context. British Medical Journal 1996 312: 426-9.
6. L'Abbé KA, Detsky AS, O'Rourke K. Meta-analysis in clinical research. Ann Intern Med 1987 107:224-33.
7. F Moore. I've just been bitten by a dog. British Medical Journal 1997 314: 88-9.
8. P Cummings. Antibiotics to prevent infection in patients with dog bite wounds: a meta-analysis of randomized trials. Annals of Emergency Medicine 1994 23: 535-40.
9. I Chalmers. Applying overviews in meta-analysis at the bedside. Journal of Clinical Epidemiology 1995 48: 67-70.

previous or next story in this issue