''Number Needed to Treat'': a Tool for Summarizing Treatment Effect, And

Home , Number needed to harm, Number needed to treat

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Current Anaesthesia & Critical Care (2005) 16, 173–179

www.elsevier.com/locate/cacc BASIC SCIENCE ‘‘Number needed to treat’’: A tool for summarizing treatment effect, and its application in anaesthesia and pain management

J. Poulosa, P.C.A. Kamb,Ã aDepartment of Anaesthesia and Pain Management, University of Sydney, Royal North Shore Hospital, St Leonards NSW 2065, Australia bDepartment of Anaesthesia, University of New South Wales, St George Hospital, Kogarah, Sydney NSW 2217 Australia

KEYWORDS Summary Number needed to treat (NNT) has become an increasingly used method Number needed to of reporting study outcomes. It incorporates baseline risk as well as relative risk treat; reduction to provide a whole number that indicates the effort which must be Measure of expended to obtain one additional beneﬁcial outcome. Variations of NNT have been treatment effect; developed to account for harmful effects of treatment, and to improve the clinical Number needed to utility of NNT. NNT provides clinicians with a means of comparing efﬁcacy of harm; different treatments which is more clinically useful and can help guide the provision Measures of risks and distribution of health resources. However, NNT has the potential to mislead the clinician if its limitations are not appreciated. NNT has been increasingly used in the reporting of outcomes from trials and systematic reviews in anaesthesia, pain management, and clinical medicine. & 2005 Elsevier Ltd. All rights reserved.

Introduction clinical practice. Clinicians also need a readily understandable tool for weighing the risks of various 1–3 The need to express estimates of risk in an under- treatments. Ideally this should be feasible without standable manner is a challenge faced regularly by recourse to complicated statistical concepts. The those who work with the results of epidemiological concept of rate difference is converted into a number research and who need to convey their meaning to of individuals, a more intuitively understandable clinicians. Traditional statistical measures from sys- quantity. This quantity was named ‘‘number needed tematic reviews cannot be immediately applied to to treat’’ (NNT). NNT is becoming a popular measure of treatment effect. This number can be calculated ÃCorresponding author. Tel.: +61 2 9350 2180; easily from raw data or from statistical estimates and fax: +61 2 9350 3959. can be applied to different end points (treatment E-mail address: [email protected] (P.C.A. Kam). efﬁcacy, harm, and other outcomes).

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The aims of this review are to summarize the over relative risk in terms of sampling distribution, value and limitations of ‘‘NNT’’ as a measure of it is preferred in meta-analyses.3–5 ORs are often treatment effect in randomized controlled trials. been used as approximations of RRs.3 This association is generally considered valid as long as the event is relatively rare (incidence less than 10%). As Traditional measures of treatment effect the incidence of the event increases, this relation- ship breaks down and OR tends to overestimate 6 The traditional measures of treatment effect are benefits and harms of treatment. relative risk, odds ratio (OR) and absolute risk It is important to note that RR, RRR and OR reduction (ARR). Table 1 summarizes the results of represent measures of treatment effect relative to a study of a new treatment for prevention of the control event rate and do not reflect changes in postoperative nausea and vomiting (PONV) against the baseline risk of an event. A RRR of 40% may be a control (existing treatment). significant, but if the baseline risk of the event in the population is very small, potential toxicity and cost of the treatment may not justify its use. Relative risk (RR)

Relative risk (also known as the ‘‘risk ratio’’) is Absolute risk reduction (ARR) defined as the probability of an event in the study group divided by the probability of an event in the ARR is the absolute difference in risk of an event control group.4 Mathematically in the above study between the experimental and control groups.3 In it is the above example, ARR is mathematically equal to: b=ðb þ dÞa=ða þ cÞ. ARR represents the num- a=ða þ cÞ . ber of events (in this case PONV) prevented as a b=ðb þ dÞ proportion of all patients treated. In contrast, the It expresses the relative probability that an event RRR expresses the number of events prevented as a will occur when the two groups of patients are proportion of the number of events expected.7 It compared.1 The complement of relative risk (1-RR) does not reflect the risk of the event without is known as relative risk reduction (RRR). RRR is an treatment, and cannot discriminate large treat- estimate of the percentage of baseline risk that is ment effects from small ones.8 The ARR incorpo- removed by the treatment.5 A RRR of 0 indicates no rates the baseline risk of the event without therapy benefit or harm from the treatment compared to and the risk reduction with therapy.3 It, like RR, the control group, whereas a RRR of 1 indicate a RRR, and OR, is not an intuitively easy means by ‘‘100% benefit’’.4 which clinicians can assess treatment effect in trial reports and apply them at the bedside.3 Odds ratio (OR) Number needed to treat (NNT) ‘‘Odds’’ expresses the probability that a particular event will occur against the probability it will not 1 In the context of randomized trials on the desirable occur. In the above example, the odds of PONV are effects of treatment, Sackett proposed a method of a/c in the study group and b/d in the control group. converting rate differences into a more intuitive The OR is defined as the odds of an event in the quantity called ‘‘NNT’’. NNT is the ‘‘number of study group divided by the odds of an event in the 4 patients one would need to treat with the experi- control group. OR is the traditional epidemiologi- mental therapy in order to prevent one additional cal expression of the relative likelihood of an 3,9 3,6 adverse event or attain one additional benefit’’. outcome. Because OR has statistical advantages Mathematically it is calculated as 1/ARR. NNT is usually expressed as a whole number (as its point estimate) and can be obtained for any trial that has Table 1 Standard 2 2 table demonstrating reported a binary outcome (i.e. event or no occurrence of postoperative nausea and vomiting event).10 Alternatively, NNT may be calculated (PONV) in study and control group. using the risk of the event in the control group and the RRR as follows: PONV No PONV NNT ¼ 1=ðPc RRRÞ Study group ac Control group bdwhere Pc is the risk of the event (PONV in the above example) in the control group {ie: Pc ¼ b=ðb þ dÞ}. ARTICLE IN PRESS

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A nomogram has been proposed to simplify calcula- where OR is the odds ratio provided by the tion of NNT at the bedside for individual patients.11 case–control study, and UER is the unexposed event The NNT defines the treatment-specific effect of rate. NNTH is a measure of absolute risk because it an intervention or therapy. An NNT of 1 means that takes into account the background risk of the the treatment is effective in all patients. Most outcome occurring in unexposed people, unlike the treatments or interventions will have an NNT higher OR that measures relative risk. NNTH is a composite than 1 because they are effective in some but not measure that takes into account the OR and the all the patients. An NNT of 2–3 indicates that a unexposed event rate. Consequently, it provides a treatment or intervention is quite effective. How- better estimate of risk that corresponds with the ever, NNT must not be used in isolation; the data clinical situation (reality). A major limitation of from which it is derived should also be considered NNTH is that it is not always possible to find a study as heterogeneity of data alters NNT; and we need that provides an approximate estimate of the to consider age, epidemiological and others fac- unexposed event rate (which can be estimated tors. In prophylactic interventions, such as adding from the controls in randomized controlled studies aspirin to streptokinase to reduce the reinfarction or the unexposed subjects in cohort studies). rate following acute coronary syndromes, the NNT may be as high as 20–40 but may still be considered clinically effective. Number needed to screen (NNS)

Number needed to harm (NNH) NNS is defined as the number of people that need to be screened for disease (for a given duration) to 14 The NNH is a similar concept proposed by Sackett prevent one death or one adverse event. It can be and colleagues to express the probability of calculated in trials that directly test the effectiveness of a screening strategy by finding the additional adverse events occurring in clinical trials 14 because of the treatment. The absolute difference reciprocal of the ARR. It may also be estimated in risk of harm between the experimental group in clinical trials measuring the benefit of treating and control group is known as the Absolute Risk risk factors. In this case, the prevalence of Increase (ARI). The reciprocal of ARI is the ‘‘NNH’’ unrecognized and untreated disease that can be for that therapy. NNH is defined as the number of detected must be known. NNS is calculated by patients who must be treated with a therapy in dividing the NNT for treating risk factors by the prevalence of disease that was unrecognized or order to have one additional patient suffer an 14 adverse effect compared with the control treat- untreated. ment.12 However, undesirable effects often become apparent only after a treatment or intervention has become part of clinical practice. Time to the event It may therefore be not possible to study them in a randomized controlled trial, making it necessary to Implicit in studies with binary outcomes is the resort to phase 4 studies or the less ideal case– dimension of time. The differences between event control study. Bjerre and LeLorier proposed the rates in experimental and control groups are term ‘‘number of patients needed to be treated for specific for the period of follow-up.8,15 Conse- one additional patient to be harmed’’ (NNTH) quently, the NNT for a study will vary depending on which is derived from case–control studies.13 The the length of follow-up. Comparisons of outcomes NNTH is ‘‘the number of people exposed to a given between treatments cannot be directly made if the treatment such that on average and over a given follow-up times are different. Direct comparison of follow-up period one additional person experiences NNT for studies of different follow-up times the adverse effect of interest because of the assumes that the relative benefit of the treatment treatment.’’ It expresses the additional absolute is constant over time (i.e. the RRR is constant). The risk of an adverse effect produced by the treatment NNT for at least one of the studies is then time- and does not express the total risk attributable to adjusted so as to conform with the time period of the combination of the background risk and the risk the study with which it is compared.8,15 This is due to exposure. It is calculated by the following achieved by applying the following formula: formula: 1 NNTðtime adjustedÞ ¼ NNTðactualÞðActual follow up time NNTH ¼ , ½ðOR 1ÞUER =comparative follow up timeÞ, ARTICLE IN PRESS

176 J. Poulos, P.C.A. Kam where comparative follow-up time is the follow-up the risk reduction associated with treatment is time to which the NNT is to be adjusted. constant for all levels of risk.22,23 Presentation of study data in terms of NNT as opposed to RRR results in a more conservative appraisal of treat- Confidence intervals for NNT ment effectiveness. It is a more intuitive, relevant, and easily memorized approach for clinicians than 4,21,24 A means of reporting the precision of study results ratios (e.g. RRR, ARR). is necessary when using NNT. This is usually expressed as the 95% confidence interval (95% CI) for the ARR and is given by Limitations of NNT ARR 1:96 SEðARRÞ, where SE(ARR) is the standard error of the absolute NNT has limitations like all other measures of risk reduction.15 The 95% confidence interval for treatment effect. The ability of NNT to combine NNT is the reciprocal of the values defining the baseline risk and RRR into a single number can be a 3 confidence interval for ARR.16 For example, if in a disadvantage. This is best illustrated with an trial the ARR is 10% and the 95% CI is 5–20%, the example. A treatment to prevent an event with a NNT becomes 10 (1/0.1) with 95% CI of 5–20 (1/ low baseline risk of 20% has a RRR of 50%. Hence the 0.2–1/0.05). The 95% confidence interval of NNT NNT is 10. However, a treatment with a high indicates that 19 out of 20 times the ‘‘true’’ value baseline risk of 80% but a smaller RRR of 12.5% will will be in the specified range. An NNT with an also give a NNT of 10. An NNT of 10 tells us that, on infinite confidence interval is a point estimate and average, 10 patients must be treated to prevent includes the possibility of no benefit or harm. one additional event. This, however, does not provide any information about the fate of the other 9 patients. In the situation of the low baseline risk, far fewer of the 9 remaining patients Modifications of number needed to treat are at risk of the event than the 9 in the situation of high baseline risk. It must be appreciated that NNT A number of variations and extensions of NNT have reflects the average number of patients that must been proposed to improve its utility. These include be treated to prevent an event and it does not adjusting NNT for Utility and Timing of Benefits and 17 indicate the fate of the other patients or virulence Harms, NNT Unqualified Success and Unmitigated 3 18,19 20 of the disease process. Furthermore, NNT of 10 Failure and ‘‘threshold NNT’’. However, these means that 9 of the 10 patients either do not modifications are not used in anaesthesia, critical require therapy or will not respond to treatment.3 care medicine and pain medicine literature, and It is suggested that presenting treatment effec- will not be described. tiveness in terms of NNT may adversely affect patient compliance in that NNT underscores the fact that the benefit is actually obtained by only Advantages of NNT one patient of several treated.25 NNT can be calculated by pooling absolute risk There are numerous advantages in using NNT to differences from trials in meta-analyses.26 Such express study outcomes. NNT expresses the efficacy pooled NNT may be misleading because baseline of a treatment in a manner which incorporates risk may vary between the different trials consid- baseline risk without therapy and the risk reduction ered. Changes in secular trends over time (exam- with therapy.3 For example, a treatment which ple: changes in disease severity) may also influence reduces mortality rate from an illness from 1 per the NNT generated, as can differences in the million to 0.5 per million represents a RRR of 50% clinical settings in which the trials were con- but a NNT of 2 million. Hence NNT quantifies the ducted.26 In calculating the pooled NNT, it is baseline risk as well as the RRR.21 suggested that a pooled estimate of ARR (or One of the strengths of NNT is that it is a simple increase) is obtained first, from which NNT can and intuitive estimate measure of effectiveness of then be calculated, rather than combining NNT interventions and is easier to comprehend com- values directly.27 This avoids meaningless results pared with other statistical descriptors.3,22 It has that may otherwise result.28 the advantage that it conveys both statistical and NNT for a treatment is time dependent, and if clinical significance. Furthermore, it can be used to the treatment produces a constant RRR over time, extrapolate published findings to a patient when one can expect that NNTwill decrease as the length ARTICLE IN PRESS

Number needed to treat 177 of follow-up increases.3 Therefore, when compar- likely to be healthier than the general population ing NNT for different studies, the length of follow- as a result of inclusion and exclusion criteria of the up must be standardized to allow direct compar- studies. This would have the effect of inflating the ison. Calculation of NNT for studies involving apparent NNT.34,35 chronic diseases must take into account of the fact that mortality does not cluster in time, and that the duration of follow-up is rarely sufficiently long Examples of applications of number to record the outcome in all patients.29 The NNT calculated thus depends on the point in time at needed to treat which the difference in risk is measured. In contrast, studies of acute conditions (e.g., acute Anaesthesia myocardial infarction) where mortality does cluster in time (usually within the follow-up period).29 It is NNT has been a useful measure to report results of proposed that NNT should be uniformly calculated studies in prevention and treatment of PONV. One independently of duration of follow-up for chronic systematic review of prevention of vomiting after conditions. To achieve this, the NNT in such studies paediatric strabismus surgery reported NNTs for the efficacy of various anti-emetic medications based is calculated as the reciprocal of the hazard 36 difference, where hazard is expressed as mortality on randomized controlled trials. Adverse effects per unit of person-time. The NNT then expresses (such as extrapyramidal symptoms, sedation, drow- the amount of person-time of follow-up required in siness, and the oculocephalic reflex in the case of propofol) also had their corresponding NNHs re- each arm that results in exactly one less death in 36 the treated arm.29 This NNT does not depend on the ported. A systematic review of the efficacy of duration of follow-up as long as the hazard ondansetron in the treatment of established PONV difference is constant across time.29 NNT has also reported a NNT of approximately 4, with no significant difference between doses of 1, 4, and been shown to be sensitive to crossover between 37 treatment arms, and adjustments for such occur- 8 mg. A meta-analysis of randomized controlled rences in trials have been proposed.29 NNT analysis trials to assess the efficacy of droperidol and 5-HT3- of results may be misleading in studies that receptor antagonists alone and in combination for prophylaxis of PONV used pooled data to generate compare treatments which have effects on differ- 38 ent subsets of the population, or where the corresponding NNTs. In this case, there was no treatments exert effects over different periods of statistically significant improvement in antiemetic time.30 effect when droperidol and 5-HT3-receptor antagonists were combined compared with droperidol Other criticisms of NNT include the possibility 38 that NNT may be higher in a study comparing alone. This was reflected in the confidence N treatment with placebo than when comparing intervals of the NNTs which included . The treatment with no treatment due to the placebo authors noted the dependence of NNT on the effect itself.31 NNT and NNH do not capture the baseline risk of the event studied and suggested patients’ individual likelihood of benefit and harm.8 that combinations of droperidol and 5-HT3-receptor antagonists be used only on patients at very high Methods have thus been described where the 38 baseline risk of an event for a particular patient risk of PONV. can be estimated from trial data, hence generating The concept of NNH was used in a review of the 32 causation, frequency, and severity of bradycardia a patient-specific NNT and NNH. The patient’s 39 likelihood of being helped versus harmed ratio with propofol use. In controlled clinical trials, the (LHH) can be calculated as 1/NNT (or ARR):1/NNH NNH was 11.3 (95% CI 7.7–21). In other words, one (or ARI). This ratio tells the patient the likelihood would have to administer propofol to approxi- that the treatment will help as opposed to harm mately 11 patients to cause one additional brady- him/her. The patient’s own values and preferences cardia which would not have occurred if another regarding benefits and harms can be incorporated (control) anaesthetic agent had been used instead. 32 The NNH for bradycardia in paediatric strabismus into this ratio. 39 The variation in baseline risk has prompted surgery was 4.1 (95% CI 3–6.7). suggestions that RRR is advantageous in outcome reporting (as opposed to NNT) as it is independent Pain management of baseline risk and thus has the same value in all patients.33 The issue of baseline risk has also been Systematic reviews have been conducted to eval- cited as limitation in terms of trial design. It is uate the efficacy of various analgesic agents in suggested that participants in studies are more postoperative pain. The NNT for paracetamol ARTICLE IN PRESS

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1000 mg to achieve at least 50% pain relief 7. Davies HT. Interpreting measures of treatment effect. Hosp compared with placebo was 4.6.40 Paracetamol Med 1998;59(6):499–501. 600/650 mg plus codeine 60 mg had a NNT of 3.6. 8. Sackett DL, Straus SE, Richardson WS, Rosenberg W, Haynes The authors noted that comparison with NNTs for RB. Evidence-based medicine: how to practice and teach EBM. 2nd edition. New York: Churchill-Livingstone; 2000. other analgesics (obtained by quantitative systema- 9. Cordell WH. Number needed to treat (NNT). Ann Emerg Med tic reviews) was possible and thus a ladder of 1999;33(4):433–6. analgesic efficacy could be devised.40 A systematic 10. Altman DG. Clinical trials and meta-analyses. In: Altman DG, review with meta-analysis for single-dose ketorolac Machin D, Bryant TN, Gardner MJ, editors. Statistics with and pethidine in acute postoperative pain reported confidence. 2nd ed. London: BMJ Books; 2000. p. 120–38. 11. Chatellier G, Zapletal E, Lemaitre D, Menard J, Degoulet P. that the NNT to produce at least 50% pain relief was The number needed to treat: a clinically useful nomogram in 2.9 (95% CI 2.3–3.9) with intramuscular pethidine its proper context. Br Med J 1996;312(7028):426–9 Erratum 41 100 mg. The numbers needed to harm for pethi- in: Br Med J 1996;312(7030):563. dine at this dose for drowsiness and dizziness was 12. Sackett DL, Haynes RB. Summarizing the effects of therapy: 2.9 (2.2–4.4) and 7.2 (4.8–14), respectively.41 In a new table and some more terms. ACP J Club 1997; the case of intramuscular ketorolac 30 mg, NNT was 127(1):A15–6. 13. Bjerre LM, LeLorier J. Expressing the magnitude of adverse 3.4 (2.5–4.9), and for oral ketorolac 10 mg, NNTwas effects in case–control studies: ‘‘the number of patients 41 2.6 (2.3–3.1). The NNH for any adverse effect needed to be treated for one additional patient to be with oral ketorolac 10 mg was 7.3 (4.7–17).41 harmed’’. Br Med J 2000;320(7233):503–6. 14. Rembold CM. Number needed to screen: development of a statistic for disease screening. Br Med J 1998; 317(7154):307–12. Conclusion 15. Altman DG, Andersen PK. Calculating the number needed to treat for trials where the outcome is time to an event. Br NNT provides a means by which study data may be Med J 1999;319(7223):1492–5. presented in a way considered by many to be more 16. Altman DG. Confidence intervals for the number needed to treat. Br Med J 1998;317(7168):1309–12. clinically useful than other methods. It can be 17. Riegelman R, Schroth WS. Adjusting the number needed to extended to improve its utility and allow better treat: incorporating adjustments for the utility and timing of planning and distribution of health resources. NNT benefits and harms. Med Decis Making 1993;13(3):247–52. can also be modified to guide treatment decisions 18. Schulzer M, Mancini GB. ‘Unqualified success’ and ‘unmiti- for individual patients. 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The number needed to treat: a J Psychiatry 1996;169(1):113. clinically useful measure of treatment effect. Br Med J 25. Artalejo FR, Banegas JR, Artalejo AR, Guallar-Castillon P. 1995;310(6977):452–4 (Erratum in: Br Med J 1995; Number-needed-to-treat to prevent one death. Lancet 310(6986):1056). 1998;351(9112):1365. 5. Jaeschke R, Guyatt G, Shannon H, Walter S, Cook D, Heddle 26. Smeeth L, Haines A, Ebrahim S. Numbers needed to treat N. Basic statistics for clinicians: 3. Assessing the effects of derived from meta-analyses—sometimes informative, usual- treatment: measures of association. CMAJ 1995;152(3): ly misleading. Br Med J 1999;318(7197):1548–51. 351–7 (Erratum in: Can Med Assoc J 1995;152(6):813). 27. Pickin M, Nicholl J. Number needed to treat. Number who 6. Sackett DL, Deeks JJ, Altman DG. Down with odds ratios!. benefit per unit of treatment may be a more appropriate Evidence—Based Med 1996;1:164. measure. Br Med J 1995;310(6989):1270. ARTICLE IN PRESS

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28. Lesaffre E, Pledger G. A note on the number needed to 36. Tramer M, Moore A, McQuay H. Prevention of vomiting after treat. Control Clin Trials 1999;20(5):439–47. paediatric strabismus surgery: a systematic review using the 29. Lubsen J, Hoes A, Grobbee D. Implications of trial results: numbers-needed-to-treat method. Br J Anaesth 1995;75(5): the potentially misleading notions of number needed to 556–61. treat and average duration of life gained. Lancet 37. Tramer MR, Moore RA, Reynolds DJ, McQuay HJ. A 2000;356(9243):1757–9. quantitative systematic review of ondansetron in treatment 30. Wu LA, Kottke TE. Number needed to treat: caveat emptor. of established postoperative nausea and vomiting. Br Med J J Clin Epidemiol 2001;54(2):111–6. 1997;314(7087):1088–92. 31. de Craen AJ, Vickers AJ, Tijssen JG, Kleijnen J. Number- 38. Eberhart LH, Morin AM, Bothner U, Georgieff M. Droperidol needed-to-treat and placebo-controlled trials. Lancet and 5-HT3-receptor antagonists, alone or in combination, 1998;351(9099):310. for prophylaxis of postoperative nausea and vomiting. A 32. McAlister FA, Straus SE, Guyatt GH, Haynes RB. Users’ guides meta-analysis of randomised controlled trials. Acta Anaes- to the medical literature: XX. Integrating research evidence thesiol Scand 2000;44(10):1252–7. with the care of the individual patient. Evidence-Based 39. Tramer MR, Moore RA, McQuay HJ. Propofol and bradycar- Medicine Working Group. J Am Med Assoc 2000;283(21): dia: causation, frequency and severity. Br J Anaesth 1997; 2829–36. 78(6):642–51. 33. Jain BP. Number needed to treat and relative risk reduction. 40. Moore A, Collins S, Carroll D, McQuay H, Edwards J. Single Ann Intern Med 1998;128(1):72–3. dose paracetamol (acetaminophen), with and without 34. Ebrahim S, Smith GD. The ‘number need to treat’: does it codeine, for postoperative pain. Cochrane Database Syst help clinical decision making? J Hum Hypertens 1999;13(11): Rev 2000(2):CD001547. 721–4. 41. Smith LA, Carroll D, Edwards JE, Moore RA, McQuay HJ. 35. Newcombe RG. Conﬁdence intervals for the number needed Single-dose ketorolac and pethidine in acute postoperative to treat. Absolute risk reduction is less likely to be pain: systematic review with meta-analysis. Br J Anaesth misunderstood. Br Med J 1999;318(7200):1765–7. 2000;84(1):48–58.