The number needed to treat statistic is a clinically useful measure of treatment effect, conveying both statistical and clinical importance to the treating doctor.1,2 This information, however, is limited to clinical decision making and lacks a public health perspective. We propose two new statistics, which should allow the impact of an intervention to be seen in the context of the broader population.
The number needed to treat is defined as the number of patients who must be treated to prevent one patient from experiencing the adverse effects of the disease being studied.3 For example, treating five diabetic patients with intensive therapy may result in one fewer patient who dies or has a macrovascular event.4 This gives an immediate and simple understanding of the impact of the intervention. The number needed to treat statistic, however, relates only to those people actually treated and does not give an appreciation of how many people with the disease in question, or of the total population, will benefit from applying the intervention. Our proposed new statistics offer this population perspective to the number needed to treat.
We propose two statistics, the disease impact number and the population impact number. The disease impact number provides a population perspective by taking account of the number of people in the population with the disease, not just those eligible for the intervention according to the entry criteria for the trial from which the evidence of benefit is derived or those who actually have access to treatment. It is defined as “the number of those with the disease in question among whom one event will be prevented by the intervention.” It is given by the formula 1/(absolute risk reduction × proportion of people with the disease who are exposed to the intervention) where the absolute risk reduction is the absolute difference in event rates between experimental and control patients in a trial.5 The number needed to treat is 1/absolute risk reduction, hence the disease impact number is analogous to the number needed to treat for all the people with disease.
The population impact number provides a population perspective by taking into account the number of people in the population from which the patients with the disease are drawn. It is defined as “the number of those in the whole population among whom one event will be prevented by the intervention.” It is given by the formula 1/(absolute risk reduction × proportion of people with the disease who are exposed to the intervention × proportion of the total population with the disease of interest). Hence the population impact number is analogous to the disease impact number for the total population.
Summary points
The number needed to treat statistic is a clinically useful measure but lacks a population perspective
The disease impact number takes account of the number of people with the disease and is “the number of those with the disease in question among whom one event will be prevented by the intervention”
The population impact number takes account of the number of people in the population from which the patients with the disease are drawn and is “the number of those in the whole population among whom one event will be prevented by the intervention”
The disease impact number and population impact number allow an assessment of the wider impact of a treatment or service on the generality of people with the disease and the population from which they are drawn
Number needed to treat from a population perspective
Interventions after stroke and thrombolysis after acute myocardial infarction are examples of how these new statistics provide an interpretation of the results of interventions in clinical trials from a population perspective.
Interventions after stroke
Several interventions have been shown to improve the outcome after stroke.6 Among these, thrombolysis has the largest efficacy in reducing death or dependency in terms of relative risk reduction, although it may be feasible for only around 4% of the population of people with stroke.7 Aspirin, however, has a lower efficacy but could be used for about 70% of patients with stroke6 (because some patients die before coming to medical attention and others have contraindications to aspirin). Table 1 shows how combining this information can help us understand the impact of these interventions from different perspectives.
Table 1.
Aspirin | Warfarin | Organised stroke unit | Thrombolysis | |
---|---|---|---|---|
Absolute risk reduction* | 0.031 | 0.042 | 0.050 | 0.159 |
Proportion of stroke population treated† | 0.70 | 0.29 | 0.70 | 0.04 |
Number needed to treat | 33 | 24 | 20 | 7 |
Disease impact number | 46 | 83 | 29 | 158 |
Population impact number ‡ | 35 450 | 63 160 | 21 980 | 120 950 |
From a systematic review.6
Comprises those for whom treatment can be provided based on access, suitability, and availability (will vary according to economic and geographical setting6).
Annual rate of first cerebral infarction taken as 1.3/1000 (Oxford community stroke study).8
For each intervention, the disease impact number and the population impact number are higher than the number needed to treat. Where the proportion of the stroke population who can access treatment is high, the disease impact number is not much higher than the number needed to treat. Where only a small proportion of the population can access the treatment— for example, for thrombolysis—the disease impact number (158) is considerably higher than the number needed to treat (7). A particular intervention may prevent one death or disability from ischaemic stroke from among many thousands of the population—the population perspective of the value of thrombolysis after stroke changes from a number needed to treat of 7 to a population impact number of over 120 000.
Benefits of thrombolysis after acute myocardial infarction
The efficacy of thrombolysis after acute myocardial infarction differs by age.9 Because the rate of the disease is also heavily age dependent, it is likely that the impact of thrombolysis will have different implications for different age groups. Table 2 shows that the proportion of patients with acute myocardial infarction who are likely to receive thrombolysis is lower in the highest age category—this results in a high number of older patients with the disease among whom current treatment policies would be expected to save one life (disease impact number). Conversely, the low disease mortality in the youngest age group produces a high number of the population among which one life will be saved (population impact number). By considering the components of the disease impact number and population impact number, the effects of alternative treatment policies can be assessed. For example, if the proportion of patients aged 65-74 who receive thrombolysis were increased from 40% to 50%, the disease impact number would decrease from 93 to 75, and the population impact number would decrease from 6100 to just over 4800. If more aggressive secondary prevention were able, however, to reduce the event rate in this age group to, for example, that in the age group below (760/100 000) and 40% received thrombolysis, the population impact number would increase to over 12 000.
Table 2.
Age (years)
|
|||
---|---|---|---|
<55 | 55-64 | 65-74 | |
Absolute risk reduction9 | 0.011 | 0.018 | 0.027 |
Proportion of population with acute myocardial infarction eligible for treatment* | 0.54 | 0.49 | 0.40 |
Event rate of acute myocardial infarction per 100 000† | 137 | 760 | 1523 |
Number needed to treat | 91 | 56 | 37 |
Disease impact number | 169 | 113 | 93 |
Population impact number | 123 000 | 14 900 | 6100 |
Assumes 77%, 70%, and 66% of patients in each ascending age group are admitted to hospital (due to deaths occurring before reaching hospital: WHO MONICA project monitoring trends and determinants in cardiovascular disease study, unpublished) and proportions given thrombolysis in hospital are 0.7, 0.7, and 0.6 in each ascending age group (New South Wales acute cardiac care study, unpublished).
Based on mortality data from Australian Institute of Health and Welfare10 and morbidity data from Australian Institute of Health and Welfare national morbidity database.
Discussion
The number needed to treat statistic is sensitive to the absolute risk in the non-treated group, which may be misleading when the data are derived from a meta-analysis.11,12 Our measures are also sensitive to this issue as our calculations start from the same basis as the number needed to treat. The actual numbers we have calculated depend on several other assumptions in terms of the proportions of the population with disease who can access treatment as well as the proportions of the total population with the disease of interest.
The number needed to treat statistic has been modified by Rembold who has suggested the number needed to screen.13 He divided the number needed to treat by the prevalence of unrecognised or untreated disease. This has a similar goal to our statistics, in that it adds a population dimension to the number needed to treat statistic.
Public health implications
The number needed to treat has been developed for helping clinical decision making—that is, how many patients would have to be treated with the intervention in question to save one patient having the outcome of interest? These data can only come from an appropriately rigorous estimate of benefit, and this is usually a randomised controlled trial. For many reasons, only a subset of patients with the disease are usually evaluated by such a trial. Assume that of 100 patients with an acute myocardial infarction, 70 reach hospital as 30 have died before reaching medical assistance (table 2, age 55-64 years). Any intervention on these 70 patients that might save one or two lives, based on the number needed to treat of 56, is to be welcomed by the patient and doctor but should be seen in the public health context of the 30 who died before reaching hospital. These new statistics help to offer this public health perspective. Assume that there was a certain amount of resource to commit to the treatment of stroke. The number needed to treat statistic would provide attractive incentives for the funds to go to treatment with thrombolysis, as the clinician only has to treat seven patients to avoid death or dependency in one of them. The resources used in introducing thrombolysis (including urgent admission to hospital and computed tomography as well as the drug cost) will only save one person from a population of 120 000 from dying or becoming dependent (as identified by the population impact number statistic). This compares with the smaller amount of resources used in giving aspirin to stroke survivors, which would save one person from a population base one fifth of the size of that needed for thrombolysis.
These statistics can also be extended to examine disease causation, and we are separately presenting the way of calculating the statistics for cohort and case-control studies where the focus is on the number of people who need to be exposed to a risk factor to result in the development of disease in one person.
Acknowledgments
We thank Drs John Page and John Attia who suggested a modification of our original formula for the population impact number.
Footnotes
Competing interests: None declared.
References
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