The 'Number Need to Treat': Does It Help Clinical Decision Making?

Home , Number needed to harm, Number needed to treat, Relative risk reduction

Journal of Human Hypertension (1999) 13, 721–724  1999 Stockton Press. All rights reserved 0950-9240/99 $15.00 http://www.stockton-press.co.uk/jhh COMMENTARY The ‘number need to treat’: does it help clinical decision making?

S Ebrahim and G Davey Smith Department of Social Medicine, University of Bristol, Canynge Hall, Whiteladies Road, Bristol BS8 2PR, UK

The number needed to treat (NNT) is an increasingly from pooled absolute risk differences in meta-analysis. popular way of presenting the effects of treatment. How- In general, the NNT should be calculated by applying the ever, the NNT varies markedly depending on the base- relative risk reduction on treatment estimated by trials line risk of patients, the outcome considered, and the or meta-analysis to populations of speciﬁed absolute clinical setting. Furthermore geographic and secular high, average or low risk to illustrate a range of poss- trends make the NNT unstable between places and over ible NNTs. time. Particular caution is needed in deriving the NNT

Keywords: meta-analysis; hypertension; randomised controlled trials

Eight hundred and thirty-three. This is the number ment effects are constant across a wide range of of mildly hypertensive people who must be treated baseline levels of risk. with antihypertensives for a year to avoid one The absolute effects of treatment take account of stroke1 and is widely quoted as an argument for not baseline level of risk and are simply the difference bothering to detect and treat hypertensive people. between intervention and control group rates. From Why has the number needed to treat (NNT) become a clinical and public health standpoint it is useful so popular recently? Is it because it can be used to to have some idea of the amount of effort required highlight the workload and cost implications of to avoid one adverse event. This is given by the treatments? Is it because the trade off between bene- reciprocal of the absolute risk difference—the num- fits and risks of treatment is made more obvious? Or ber needed to treat.4 The absolute effect and the is it just the novelty value of a new(ish) method of NNT will vary—often greatly—according to the expressing the effects of treatment? Despite the pro- baseline level of risk and this means that a single motion of NNT as easier for clinicians to under- measure of effect applicable to different age groups, stand, when presented with a range of measures of for example, cannot be derived. treatment effects, most found NNTs no easier to 2 understand or explain to others than relative risk. Baseline levels of risk vary So far so simple, but the NNT has some rather dis- Describing the effects of treatment turbing characteristics that make it difficult to use The effects of treatment are conventionally in practice. Which baseline level of risk should be expressed in relative terms—the ratio of the event used? In the trials of antihypertensives among older rate in the treatment group divided by the event rate patients without previous cardiovascular disease,5–11 in the control group. Ratios greater than one imply baseline risk varied widely (see Table 1). For total, that treatment is harmful, less than one, that treat- coronary heart disease (CHD) and stroke mortality ment is beneficial. This hides the fact that a small control group rates varied by 5.3, 3.5 and 12-fold relative benefit applied to patients at very high risk respectively. These differences are not due to the will generate more lives saved (and non-fatal events play of chance but are produced by the design avoided) than the same relative benefit applied to characteristics of the trials themselves—the clinical much lower risk patients. However, the relative setting, level of blood pressure, comorbidity, age treatment effect may be dependent on the baseline and sex of the participants. level of risk in the control group. For example, sur- gery for carotid endarterectomy is effective for high The effect of choice of outcome on NNT risk tight stenosis but not for low risk smaller degrees of stenosis.3 It cannot be assumed that treat- As demonstrated in Table 1, not only do baseline levels of risk vary, but so do NNTs, depending on the outcomes considered. If the most common out- Correspondence: Shah Ebrahim, Department of Social Medicine, University of Bristol, Canynge Hall, Whiteladies Road, Bristol come is used (eg, all bad things that can happen to BS8 2PR, UK you, or a combined cardiovascular end-point) then Received 18 May 1999; accepted 22 May 1999 the NNT is lower than if an uncommon, but poten- The ‘number needed to treat’ S Ebrahim and G Davey Smith 722 Table 1 Summary of trials of antihypertensive drugs in older people: variation in baseline risk, odds ratios of treatment effect and numbers needed to treat

Trial (Ref.) Baseline level of risk in control Odds ratios of treatment effects Numbers needed to treat for 5 years group/1000 person years

Total CHD Stroke Total CHD Stroke Total CHD Stroke

Kuramoto5 42.7 18.3 6.1 1.10 1.09 2.22 47a 121a 27a Sprackling6 120b – – 1.00 – – ϱ EWHPE7 76.4 24.1 15.9 0.89 0.61 0.67 24 21 38 Coope8 33.7 13.7 7.3 0.96 0.99 0.29 148 1460 39 SHEP9 22.7 6.8 1.3 0.87 0.81 0.72 68 155 549 STOP-H10 38.7 16.0 9.2 0.55 0.49 0.26 12 24 29 MRC11 24.5 8.6 3.3 0.96 0.77 0.89 204 101 550

aNumber needed to harm as treatment groups had higher rates than control groups; bDuration of follow-up estimated to be 7.5+ years from life tables.

tially more important outcome is used (eg, mortality). Choice of outcome for NNT calculations can make or break the case for using a specific treatment, as can choice of trial to derive baseline risks. NNTs can be easily inflated or deflated by the dur- ation of treatment considered. A single year NNT is five times larger than a 5-year NNT. In mild hypertension, this is the difference between NNTs to pre- vent one stroke of 833 and 167! And if the overall cardiovascular event rate is used as the outcome, rather than stroke, the 1-year and 5-year NNTs fall to 667 and 133.

Ineffective treatments A mathematical quirk of the NNT is that if the treatment has no effect, that is the event rates are identical in both the treatment and control groups, then the absolute risk difference is zero, and 1/zero, the Figure 1 Relationship between absolute risk difference and num- 12 bers needed to treat. When the risk difference is zero, number NNT, is infinity. This is demonstrated by the ϱ Sprackling trial in Table 1 which had identical needed to treat is . death rates in intervention and control groups.6 Thus, a treatment of little effect will have a lower tension trial event rates were much lower than in confidence interval of the absolute risk difference epidemiological studies and for fatal events were that is negative and an upper confidence interval closer to those expected for normotensive men that is positive. If the treatment produces an adverse rather than hypertensive men. These differences effect then a number needed to harm, rather than a reflect the selection bias mentioned above, and raise NNT, is the outcome. If confidence intervals of treat- serious questions about the value of trial-derived ment efficacy overlap a null effect, then the confi- NNTs (see Table 2). Selection bias may work in the dence intervals of the NNT will stretch from a nega- opposite direction occasionally. In the Hypertension tive value (ie, number needed to harm) at the lower Detection and Follow Up Program—a comparison of border, include infinity, and stretch to a NNT at the careful stepped care versus usual care—baseline upper border. It is rather confusing to have a meas- risks of death were very high because the parti- ure of effect with confidence intervals that may cipants were predominately poor, and many were include benefit, harm and infinity! (See Figure 1). black.13 Clinicians who want to use NNTs have to make a judgment about which baseline risk applies Trial participants and patients in routine to their patients and without local epidemiological data this is difficult. clinical practice Patients entered into randomised controlled trials Geographical and secular trends and are a selected group. In most randomised controlled their effects on NNT trials, participants are at lower risk than might be expected because with given eligibility criteria Further concerns in using NNTs are that geographic healthier people are more likely to end up enrolled and secular trends in the baseline risk of cardio- in trials. Thus trial baseline risks may be quite inap- vascular diseases can be marked. For example, propriate to apply in clinical practice. This will tend ischaemic heart disease and stroke mortality rates to inflate the apparent NNT. In the MRC mild hyper- are about twice as high in the north as the south of The ‘number needed to treat’ S Ebrahim and G Davey Smith 723 Table 2 Variation in risk of events among men aged 35–64 years in the MRC mild hypertension trial1 and men aged 45–59 in the British Regional Heart Study (BRHS). Hypertension defined as diastolic blood pressure of 90–109 mm Hg in the MRC trial and systolic/diastolic blood pressure of 160+ and/or 90+ in BRHS

Outcome MRC placebo group BRHS hypertensives BRHS normotensives NNT for 5 years rate/1000 person rate/100 person rate/1000 person years years years Trial derived BRHS derived

Stroke death 0.6 1.1 0.4 667 364 Coronary death 3.9 6.5 3.2 2608a 1200a Fatal and non-fatal 11.9 16.2 4.4 105 77 events aNumber needed to harm as event rates were higher in treated group than placebo for coronary deaths. the Britain.14 Consequently, the relevant cardio- inclusion criteria which is of use to the clinician in vascular disease (CVD) baseline risk for a Scottish making treatment decisions.17 GP will be twice that of a home counties GP, In summary, NNTs may be useful to illustrate the resulting in an NNT for antihypertensive treatment range of workload that is required to achieve bene- that is twice as great in the south of England as in fits from treatments in a rough and ready way. NNTs Scotland. Similarly, CVD variation between coun- are less useful than is often supposed in communi- tries results in NNTs that differ in direct proportion cating effects of individual treatment decisions since to the underlying event rates. they vary between patient groups, clinical settings, Secular trends in stroke produce the same sort of places and over time, in ways which clinicians will effect. Stroke mortality rates are falling dramatically usually not have adequate data to take into account. in most Western countries15 and with this fall, NNTs for antihypertensive treatment will also fall over References time. Table 3 shows the effects that may be expected on NNTs, assuming baseline event rates in hyperten- 1 Medical Research Council Working Group. MRC Trial sives are twice those in the general population and of mild hypertension: principal findings. Br Med J 1985; 291: 97–104. that the relative risk reduction for stroke mortality 2 McColl A, Smith H, White P, Field J. General prac- on antihypertensive treatment is 33%. It is clear that titioners’ perceptions of the route to evidence based NNTs vary widely over time, are higher in women medicine: a questionnaire survey. BMJ 1998; 316: than men—reflecting women’s lower baseline risk— 361–365. and are considerably lower than NNTs derived from 3 Barnett HJ et al for the North American Symptomatic participants in randomised controlled trials.4,16 Carotid Endarterectomy Trial Collaborators. Benefit of carotid endarterectomy in symptomatic patients with moderate or severe carotid stenosis. N Engl J Med Meta-analysis and NNTs 1998; 339: 1415–1425. There is an increasing trend for meta-analyses of 4 Cook RJ, Sackett DL. The number needed to treat: a clinically useful measure of treatment effect. BMJ treatments to provide pooled estimates of NNTs in 1995; 310: 452–454. addition to conventional relative risk estimates of 5 Kuramoto K, Matsushita S, Kuwajima I, Murakami M. 16 effects. Available software, including the Cochrane Prospective study on the treatment of mild hyperten- Library Meta-View package permit absolute risk dif- sion in the aged. Jap Heart J 1981; 22: 75–85. ferences, and hence NNTs, to be calculated easily. 6 Sprackling M, Mitchell JRA, Short A, Watt G. Blood Such pooled NNTs are potentially misleading as pressure reduction in the elderly: a randomised con- they encourage assumptions that clinical patient trolled trial of methyldopa. Br Med J 1981; 283: risk is similar to trial patient risk. They may fail to 1151–1153. allow for different lengths of follow-up in trials, they 7 Amery A et al. Mortality and morbidity results from contravene statistical assumptions in pooling of the European Working Party on High Blood Pressure in the Elderly Trial. Lancet 1985; i: 1349–1354. data, and hide the heterogeneity of NNTs due to trial 8 Coope J, Warrender T. Randomised trial of treatment of hypertension in elderly patients in primary care. Br Table 3 Secular trends in stroke mortality and the effect on num- Med J 1986; 293: 1145–1151. bers needed to treat to avoid a stroke death from 1971 to 1991 9 SHEP Cooperative Research Group. Prevention of stroke by antihypertensive drug treatment in older per- Time period Stroke mortality rate Numbers needed to sons with isolated systolic hypertension. Final results (65–74) per 10000 be treated, 5 years, of the systolic hypertension in the elderly program with antihypertensives (SHEP). JAMA 1991; 265: 3255–3264 (Abstract). to avoid one stroke 10 Dahlof B et al. Morbidity and mortality in the Swedish death trial in old patients with hypertension (STOP- hypertension). Lancet 1991; 338: 1281–1285. Men Women Men Women 11 Medical Research Council Working Party. Medical Research Council trial of treatment of hypertension in 1971 423 297 70 99 older adults: principal results. BMJ 1992; 304: 405– 1981 300 213 98 138 412. 1991 213 153 139 193 12 Altman D. 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