# What is number needed to harm (NNH)?

BMJ 2013; 347 doi: http://dx.doi.org/10.1136/bmj.f4869 (Published 02 August 2013) Cite this as: BMJ 2013;347:f4869- Philip Sedgwick, reader in medical statistics and medical education

- p.sedgwick{at}sgul.ac.uk

Researchers investigated whether 10 mg, 25 mg, or 50 mg metoclopramide combined with 8 mg dexamethasone, given intraoperatively, was more effective in preventing postoperative nausea and vomiting than 8 mg dexamethasone alone. A four armed, parallel group, double blind, randomised controlled trial was performed. The intervention consisted of 8 mg dexamethasone alone (no metoclopramide) or 8 mg dexamethasone plus 10 mg, 25 mg, or 50 mg metoclopramide. Participants were 3140 patients who received balanced or regional anaesthesia during surgery.1

The main outcome measures were postoperative nausea and vomiting within 24 hours of surgery, plus occurrence of adverse drug reactions. The table⇓ shows the proportion of patients experiencing postoperative nausea and vomiting plus number needed to treat for each treatment group. The most common adverse drug reactions were hypotension and tachycardia; the table also shows the proportion of patients experiencing these adverse events plus number needed to harm for each treatment group.

The researchers concluded that the addition of 50 mg metoclopramide to 8 mg dexamethasone (given intraoperatively) is an effective, safe, and cheap way to prevent postoperative nausea and vomiting. It was suggested that a reduced dose of 25 mg metoclopramide intraoperatively, with additional postoperative prophylaxis in high risk patients, might be equally effective and cause fewer adverse drug reactions.

Which of the following statements, if any, are true?

a) Number needed to harm is a measure of the harm (adverse drug reactions) caused by the intervention when compared with 8 mg dexamethasone alone

b) It is estimated that on average, for every 11 patients given 50 mg metoclopramide one would experience an adverse drug reaction

c) The larger the value of the number needed to harm, the lower the risk of adverse drug reactions caused by treatment with metoclopramide compared with 8 mg dexamethasone alone

d) The number needed to harm depends on only the absolute difference in risk of adverse drug reactions between treatment groups

## Answers

Statements *a, c and d* are true, whereas *b* is false.

The aim of the trial was to test the effectiveness of metoclopramide when combined with 8 mg dexamethasone, given intraoperatively, in preventing postoperative nausea and vomiting. Patients were randomised to one of four doses of metoclopramide: 0 mg, 10 mg, 25 mg, or 50 mg. The results (table) suggest that the proportion of patients experiencing postoperative nausea and vomiting declined as the dose of metoclopramide increased. The benefit of the intervention is indicated by the number needed to treat for each dose compared with 0 mg (8 mg dexamethasone alone). The number needed to treat has been described in a previous question.2 The dose of 0 mg metoclopramide (8 mg dexamethasone alone) is referred to as the reference category and indicated by the number 1 in the number needed to treat column.

The results (table) suggest that the proportion of patients experiencing adverse drug reactions (hypotension and tachycardia) increased as the dose of metoclopramide increased. The number needed to harm (NNH), sometimes referred to as number needed to treat to harm (NNTH), is a measure of the harm caused by an intervention (*a* is true). For obvious reasons, the number needed to harm is typically used to describe the extent of the side effects of treatment. To derive the number needed to harm, the effects of the intervention in each treatment group are compared with one of the other treatment groups—typically the control or standard treatment—which in this example was 8 mg dexamethasone alone. As for number needed to treat, the treatment group that received 8 mg dexamethasone alone (no metoclopramide) is referred to as the reference category and indicated by the number 1 in the number needed to harm column.

To illustrate the calculation of number needed to harm, consider treatment with 50 mg metoclopramide. Adverse drug reactions (hypotension and tachycardia) were reported for 17.9% of patients in the treatment group that received 50 mg metoclopramide versus 8.8% of those in group that received 8 mg dexamethasone alone (no metoclopramide). This represented an increase of 9.1% (0.091) in adverse drug reactions due to intervention with 50 mg metoclopramide. The number needed to harm was calculated as the reciprocal of this increase in risk—that is, 1÷0.091, which equals 10.99. The number needed to harm is the average number of patients who needed to be treated with 50 mg metoclopramide for one extra patient to experience adverse drug reactions (hypotension or tachycardia) than if the same patients had been treated with 8 mg dexamethasone alone. On average, if 10.99 patients were treated with 8 mg dexamethasone alone, then 0.96 (8.8%) of them would be expected to experience adverse drug reactions, whereas if the same patients were treated with 50 mg metoclopramide then 1.96 (17.9%) of them would experience adverse drug reactions. To have direct clinical relevance, the derived number needed to harm was rounded up to 11 patients.

Statement *b* is a common misinterpretation of number needed to harm—that is, on average, for every 11 patients treated with 50 mg metoclopramide, one would experience an adverse drug reaction (*b* is false). The statement is indicative that, on average, for every 11 patients treated with 50 mg metoclopramide, one would develop an adverse drug reaction whereas the remaining 10 would not. As indicated above, this is obviously not the case. As a measure of the harm of intervention with 50 mg metoclopramide, number needed to harm indicated the harm of treatment compared with 8 mg dexamethasone alone.

The importance of the size of the number needed to harm must be decided on clinical grounds. Nonetheless, the larger the value of the statistic the better, because the greater the number of patients who need to be treated with metoclopramide for one additional patient to experience an adverse drug reaction when compared with 8 mg dexamethasone alone (*c* is true). This is in contrast to number needed to treat, where smaller values are better because they indicate greater therapeutic benefit of the intervention compared with the control.2

As with other estimates, it is important that the uncertainty in the number needed to harm is assessed by a confidence interval. The 95% confidence interval for number needed to harm is derived in a similar way to the statistic itself. The reciprocal of the limits for the 95% confidence interval of the absolute risk difference are derived and then reversed, giving the limits of the 95% confidence interval for number needed to harm. For example, the absolute risk increase in adverse drug reactions between 50 mg metoclopramide and 8 mg dexamethasone alone was 0.091 (95% confidence interval 0.058 to 0.124). The reciprocal of these limits when reversed give the 95% confidence interval for number needed to harm—that is, 1÷0.124=8.1 and 1÷0.058=17.2 (95% confidence interval 8.1 to 17.2). The 95% confidence intervals for number needed to treat (table) were calculated in a similar way.

The increase in absolute risk of adverse drug reactions between 10 mg metoclopramide plus 8 mg dexamethasone and 8 mg dexamethasone alone was 0.24 (95% confidence interval −0.006 to 0.054). The number needed to harm was 1÷0.24; that is, 41.7. Because the 95% confidence interval for the difference in risk of adverse drug reactions straddled zero, the difference was not statistically significant at the 5% level of significance. Therefore, it was not conclusive that 10 mg metoclopramide increased adverse drug reactions when compared with 8 mg dexamethasone alone. For that reason the number needed to harm for 10 mg metoclopramide is indicated as “not significant” (table). When the difference in risk between two treatments is not statistically significant, the confidence interval for the number needed to harm is difficult to interpret. The 95% confidence interval for the number needed to harm for 10 mg metoclopramide cannot simply be the reciprocal of the confidence limits for the absolute risk difference in adverse drug reactions—that is, −176.9 and 18.6—because the number needed to harm of 41.7 lies outside this range. In effect, the confidence interval consists of all values outside the range—that is, −∞ to −176.9, and 18.6 to +∞—that represent intervals of benefit and harm.

The challenge is how the estimate of uncertainty from a confidence interval for number needed to harm can be incorporated into clinical decision making. The interval estimate for the population parameter for 50 mg metoclopramide (95% confidence interval 8.1 to 17.2) is relatively narrow, suggesting the sample estimate of number needed to harm was relatively precise. By contrast, the 95% confidence interval for number needed to harm for 25 mg metoclopramide compared with 8 mg dexamethasone alone was wide (13.9 to 100.0), suggesting an inaccurate estimate. Nonetheless, it is conclusive that 25 mg metoclopramide will significantly increase adverse drug reactions compared with 8 mg dexamethasone alone.

The value of number needed to harm depends only on the difference in risk of adverse drug reactions between the intervention groups (10 mg, 25 mg, or 50 mg metoclopramide) and 8 mg dexamethasone alone treatment group (*d* is true). For example, a number needed to harm of 11 would have been obtained for the comparison of 50 mg metoclopramide with 8 mg dexamethasone alone regardless of the absolute risks for the two treatment groups, so long as the absolute risk difference between them was 0.091. Therefore, it is important that other measures of risk, including the absolute risk of adverse events for each treatment group, are presented alongside the measure of number needed to harm. Unfortunately, the statistic number needed to harm is not reported as often as number need to treat. However, it is suggested that this statistic is always presented so that the risks of intervention can be fully assessed.

## Notes

**Cite this as:** *BMJ* 2013;347:f4869

## Footnotes

Competing interests: None declared.