In many clinical trials, we are interested in dichotomous outcomes such as death or no death, disease or no disease, remission or no remission. We then want to know whether treatment reduces or increases the risk of the outcome of interest. The term “risk” as used in this context refers to the probability of an event occurring. “Risk” can measure the likelihood of both a good outcome, for example a person with active Crohn’s disease going into remission, or a bad outcome, for example a person with meningococcal septicaemia dying.

Communicating risk to patients and the general public can be a challenging task. One reason for this is that there are so many ways in which risk can be presented, and the interpretation of risk measures can be a daunting task. Moreover, not all the various ways of reporting risk clearly show the benefits or otherwise of treatments in a clinically useful way, and many of these measures are frequently misunderstood. In this article, data from table 1 will be used to explain some of the risk measures that are commonly used to report the results of clinical trials. The data summarise the efficacy results of a recent multi-centre, double-blind, placebo-controlled trial which evaluated the efficacy and safety of ondansetron, a selective serotonin receptor antagonist in the prevention of post-operative vomiting following surgery under general anaesthesia.1 In this trial, 670 children (aged 1–24 months) were randomised to receive a single dose of either 0.1 mg/kg intravenous ondansetron prior to surgery or placebo. The main outcome measure was the prevention of vomiting within 24 h post-operatively. For the purpose of these discussions, we will assume that we have already satisfied ourselves of the internal validity of the trial.

RISK

In the statistical sense, risk is the probability that an event will occur.2 Risk can describe either a beneficial event or an adverse event depending on the outcome of interest.3 Risk is calculated as the number of people in a group who experience the outcome of interest divided by the total number of people in the group. From the data in table 1, the risk of vomiting for patients in the ondansetron group is 38/335 or 11%, and the risk of vomiting for patients in the placebo group is 93/335 or 28%.

Relative risk and relative risk reduction

Relative risk (RR) or risk ratio is the ratio of the risk in the treatment group to the risk in the control group. From the data in table 1, the RR of vomiting post-operatively for patients receiving ondansetron compared to those receiving placebo is 11/28 or about 0.39. This means that the risk of vomiting for children receiving ondansetron is 0.39 times less than that of children receiving placebo.

Relative risk reduction (RRR) is the reduction in risk to the treatment group compared to the control group expressed as a percentage. There are two ways of calculating RRR. If the RR is known, RRR is simply calculated by subtracting the RR from 1 (1−RR). Thus from the data in table 1, RRR is 1–0.39 = 0.61 or 61%. This means that the risk of a child vomiting post-operatively is reduced by 61% in the ondansetron group compared to the placebo group. RRR can also be computed as [(Pc−Pt)/Pc]×100%, where Pc is the risk in the control group, and Pt is the risk in the treatment group. From the data in table 1, RRR may also be calculated as [(28−11)/28]×100% = 61%.

Although the relative risk measures (RR and RRR) are usually used to summarise the results of studies, their clinical usefulness as measures of treatment effect is very limited.4 They do not take account of the baseline risks of patients and can be misleading as they tend to exaggerate the benefits of an intervention. Absolute risk measures such as the number needed to treat (below) are more useful as clinical measures of the effects of treatments.

Absolute risk reduction and number needed to treat

Absolute risk reduction (ARR) is one of the simplest risk measures and is also one of the most useful. It is simply the arithmetic difference between the risk in the treatment group and the risk in the control group. From table 1, the ARR with regard to vomiting post-operatively for patients receiving ondansetron compared to those receiving placebo is simply the difference between the two risks which is 28%−11% or 17%. The interpretation of this is that, compared to placebo, ondansetron reduced the risk of post-operative vomiting by 17%.

Despite its simplicity, it is not always easy for patients and healthcare professionals to conceptualise what ARR actually means in clinical practice.5 For instance, from our example above, what does a 17% reduced chance of vomiting actually mean for an individual patient? Is 17% reduction clinically important?

Fortunately, a major advantage of the ARR is that it can be converted into a related measure called the number needed to treat (NNT), which is more easily understood.6 The NNT is defined as the number of people who need to receive a treatment in order to achieve the required outcome in one of them. The NNT is simply calculated as the reciprocal of the ARR. In the above example, we calculated ARR as 17% or 0.17. The NNT is therefore 100/17 or 1/0.17≈6. This means that for every six children given ondansetron, one case of post-operative vomiting would be prevented.

The NNT is the most useful measure of benefit as it allows risk to be expressed in a more clinically relevant way. For instance, when given two treatments with similar side effect profile and costs, we would be more comfortable prescribing a treatment with an NNT of 5 (needs to be given to five people in order to achieve the required outcome in one) than using another treatment with an NNT of 200 (needs to be given to 200 people in order to achieve the required outcome in one).

Factors to consider in the interpretation of NNTs

While the NNT is a very useful measure of treatment effect, a number of important factors need to be considered in its interpretation and in its application to individual patients.4 7 Some of these points are discussed below.

NNTs vary with baseline risk

One of the advantages of the absolute risk measures is that they reflect baseline risk and more accurately indicate the magnitude of the treatment effect. However, because they vary according to the baseline risk of the population, all the absolute risk measures including the NNT are of limited generalisability. It is, for instance, inappropriate for published NNTs from one population to be applied directly to a patient with a different baseline risk of the outcome been assessed.4 Published ARR and NNT apply only to populations whose baseline risk is similar to the baseline risk of patients in the study. For example, the calculated NNT of 6 from the data in table 1 can be directly applied to your own group of patients aged 1–24 months having surgery under general anaesthesia if their baseline risk of vomiting post-operatively is similar to the baseline risk (risk of the control group) of patient’s in the study by Khalil et al, which is about 28%.

Fortunately, there are at least three methods which allow us to estimate NNTs for our own patients based on published NNTs. One simple method (called the f method) for estimating our individual patient’s NNT has recently been described.8 The f method requires comparing an estimate of our patient’s risk of the outcome being assessed (if our patient was to receive only the “control” intervention) to the risk in the control group in the study which reported the NNT. These risks are then expressed as a ratio called f. Using our ondansetron example, if we estimate that without any treatment, our patients are half as likely to vomit post-operatively compared to the control group patients in the study, then f = 0.5, and if they are twice as likely, then f = 2. Based on the assumption that RRR is stable across different baseline risks,4 the NNT for our patient is simply calculated by dividing the reported NNT by f (NNT/f). As an example, you may recall from table 1 that in the ondansetron study, the NNT was 6. If we estimate that our own group of patients (aged 1–24 months) having surgery under general anaesthesia have half the risk of vomiting compared to the control group in the study, then the NNT for our patients is calculated as 6/0.5 or 12. If, on the other hand, we estimate our patients’ risk to be twice that of the control group in the study, then the NNT for our patients will be 6/2 or 3. Thus the NNT for our own patients will vary according to their baseline risk of vomiting post-operatively. The NNT is lower for patients at higher risk of the outcome of interest and vice versa.

The second method is slightly more cumbersome and involves estimating an ARR for our patients. If the baseline risk (Po) of our patient is known, one can take advantage of the fact that the published RR is likely to be similar across different levels of baseline risk, and calculate ARR for our patient using the formula: ARR = Po×(1–RR) or Po×RRR.4 The reciprocal of the calculated ARR will then be the NNT for our patient. Po may be estimated from local data or from clinical experience, or may be assumed to be similar to that of an untreated group of patients from a published study.

The third method is to use a nomogram devised by Chatellier et al.9 On this nomogram, a straight line drawn through your patient’s baseline risk and the published RRR will intersect with the NNT for the patient.

Consider adverse events associated with treatment

NNTs convey the likely benefits that may be derived from a treatment. However, we always have to bear in mind that effective treatments may also be associated with adverse events. It is important that the severity and frequency of the adverse events are taken into consideration and discussed with patients. To determine the effect of adverse events, the number needed to harm (NHH) is calculated.

Number needed to harm

The number needed to harm (NNH) is the number of patients who need to receive an intervention in order for one of them to suffer a specified adverse event.10 The NNH is analogous to the NNT and is calculated as the reciprocal of the absolute difference in adverse event rates between the treatment group and the control group. The data in table 2, also adapted from the study by Khalil et al, show the number of children experiencing an adverse event following treatment with ondansetron or placebo.1 You can notice that slightly more patients developed adverse events in the ondansetron group compared to the placebo group. Thus there was an increase in risk of adverse events for the treated group. Absolute risk increase (ARI) is analogous to ARR, and this term is used when the risk of an event is increased in the treatment group. From table 2, the risk of an adverse event is 5/335 or 1.5% in the placebo group compared to 6/335 or 1.8% in the ondansetron group. Thus the ARI of adverse events for patients receiving ondansetron is 1.8%−1.5% or 0.3%. This means that children receiving ondansetron had an 0.3% increased risk of developing adverse events compared to children receiving placebo.

The NNH is simply the reciprocal of the ARI and is calculated as 100/0.3 or 333. This means that we would need to treat 333 children, such as those in the study by Khalil et al, with ondansetron prior to surgery for one child to develop an adverse event.

NNHs also vary with baseline risks. Just as we did for NNTs, the f method can be used to individualise NNHs for our patients. For instance, if we estimate that our own patients are 3 times as likely to develop an adverse event with ondansetron compared to the control group patients in the study, then f = 3, and the NNH for our patients will be 333/3 or 111. This means that we would need to treat 111 children at a higher risk of developing adverse events with ondansetron prior to surgery for one of them to develop an adverse event.

Likelihood of being helped or harmed

While both the NNT and NNH are useful in conveying information about the potential benefits and harms of treatments to patients, they do not clearly convey to the individual patient their unique benefit–risk ratio of the treatment. For instance, what does it mean if a patient is told that the NNT of a treatment is 4 and the NNH is 9? One statistic which allows us to combine benefits and harms into a single ratio is the “likelihood of being helped or harmed” (LHH).8 10 To calculate LHH, 1/NNT ( = ARR) and 1/NNH ( = ARI) are combined into an aggregate ratio, that is: LHH = 1/NNT:1/NNH.

For instance, for a patient who is similar to those in the study by Khalil et al and who also has similar baseline risks of vomiting post-operatively and developing adverse events, we can calculate his LHH using the NNT and NNH figures calculated from the study to be: LHH = 1/6:1/333 = 56 to 1 in favour of ondansetron.

What this means is that this patient is 56 times more likely to benefit from ondansetron than to be harmed.

Applying LHH to individual patients

In considering whether the benefits of a treatment offset the risk of adverse events for an individual patient, it is important that we take into account that patient’s baseline risks and first calculate an individualised NNT and NNH for him before calculating that patient’s unique LHH. In this way, we take account of our patient’s own specific potential benefits and harms.10

As an example, consider a patient of yours aged 10 months who is going to have surgery under general anaesthesia. You are considering whether to administer ondansetron to this patient prior to surgery in order to prevent post-operative vomiting. If, based on our patient’s unique circumstances, we estimate that his baseline risk of post-operative vomiting is twice that of the patients in the study by Khalil et al, we can use the f method to calculate our patient’s unique NNT by dividing the NNT for Khalil et al’s population by 2, that is our patient’s unique NNT = 6/2 = 3.

In the same way, if we estimate that the our patient’s risk of developing an adverse event is three times that of patients in the study by Khalil et al, we can calculate our patient’s unique NNH by dividing the NNH for Khalil et al’s population by 3, that is our patient’s unique NNH = 333/3 = 111.

We can then use these individualised NNT and NNH values to calculate our patient’s own LHH, that is our patient’s unique LHH = 1/NNT:1/NNH = 1/3:1/111 = 37 to 1 in favour of ondansetron.

We can then tell the parents of the patient that the patient is 37 times more likely to benefit from ondansetron than to be harmed.

NNTs should be reported with confidence intervals

The NNT, NNH, LHH and indeed all the other risk measures discussed above represent different ways of expressing estimated benefits or harms of treatments. As with all statistical estimates, the uncertainty in the estimated value should be accompanied by a confidence interval.4

Consider the applicability of the results to your patient

Before applying the results of any clinical trial to patients, it is important to consider the extent to which the results are applicable to your own patient or group of patients (external validity). One other important issue to consider is the values and preferences of the patient. Another advantage of the LHH statistic described above is that it is possible to also incorporate a patient’s (or parents’) values and preferences into the statistic. LHH can therefore allow the combination of treatment benefits, treatment harms and patients preferences into one single statistic. Methods which allow the patient-specific LHH to be adjusted to take account of the patient’s (or parents’) unique values will not be discussed in this article, but readers are referred to an excellent description of this process.10 11

Other issues to consider before deciding to apply the results to your patients are the cost of the treatment and availability of the treatment in your clinical setting.

CONCLUSIONS

It is important for clinicians to understand the interpretation of the various risk measures which are used to describe the benefits and harms of treatments. Relative risk measures do not take baseline risks into account and tend to exaggerate the benefits of treatments. Measures derived from the ARR such as NNT, NNH and LHH are much more useful clinically. Taking account of the patient’s own circumstances, individualised NNTs, NNHs, and LHHs could be calculated for patients.