90 Journal of The Association of Physicians of India ■ Vol. 65 ■ August 2017

STATISTICS FOR RESEARCHERS Number Needed to Treat NJ Gogtay, UM Thatte

Introduction synonymously for benefit (NNT authors evaluated the efficacy of –B) while the “Number Needed to intravenous Zolendronic acid vs. When any patient is treated Harm”(NNH)is used to indicate placebo in preventing fractures with a drug, device, vaccine, or the NNT - H. We also discuss in in a double-blind, randomized undergoes surgery or even an this paper, a lesser-known metric, controlled trial. They randomized investigation with a diagnostic the Number Needed to Screen [NNS], n = 1199 men with primary or test in a clinical research setting, one that is useful for policy makers hypogonadism-associated two broad outcomes are possible for the use of screening tests in osteoporosis who were between 50 -the patient gets better[benefit] or populations. and 85 years of age to receive either the patient gets worse [harmed]. 5 mg of intravenous Zolendronic An important aspect of research History and Origins of the acid or placebo at the beginning is to meaningfully summate data Number Needed to Treat of the study and at 12 months. obtained in terms of measures [NNT] The endpoint of interest was the of effect that can readily be proportion of patients with one or understood and used by physicians The concept of NNT was first more new morphometric fractures and researchers alike. A measure introduced in 1988 by Laupacis over a period of 24 months. that is a single number that can be A et al,3 who defined it as “the The results of the study were 1 used to compare both benefits and number of patients a clinician as follows – 28/574 [4.87%] men harms of two or more preventive, should treat in order to prevent who received placebo developed diagnostic, therapeutic, or one adverse outcome”. Its original fractures over 24 months compared rehabilitative approaches would be intended use was for benefit. The to 09/553 [1.68%] men who extremely useful. One such single NNT concept is essentially one received Zolendronic acid, with number is the “Number Needed to based on noting the frequency of the difference being statistically Treat” (NNT) and is defined as occurrence of an outcome [benefit significant [p = 0.002]. the number of patients that need or harm] measured as a cumulative What the authors have done here to be treated with an intervention incidence of that outcome per is really evaluate the association [relative to another intervention] number of patients followed up between the use [or lack thereof] of in order for it to have an impact 4 over a given time period of time. Zolendronic acid and the reduction [benefit or harm] on one patient. This will result in a proportion of in number of fractures. From a Since the NNT applies in equal patients with the outcome over previous article on Measures of measure to both benefit (B) and time [out of the total number Association,6 you would remember harm (H), the terms NNT-B and followed up], which we then write the 2 x 2 table that we use to present 2 NNT-H are used to indicate them. as a percentage. this type of binary [fracture/no We have used this convention Understanding NNT- B, fracture] data. We will use the same throughout this article. However,in table now to calculate the NNT- B literature, the reader may find how it is Calculated and its [Table 1] in three steps. that the term “NNT” is used Clinical Applications Step 1 Table 1: The association between number of patients with Simply put, NNT equals the We first calculate the Absolute fracture and treatment with reciprocal of the Absolute Risk Risk [AR] of getting fracturesin either placebo or Zolendronic Reduction [ARR]. Let us understand both groups. We use AR1 to acid the calculation and application of indicate the risk of fractures with placebo and AR2 for the risk with Number Number Total NNT using the example of a paper of men of men by Boonen and colleagues.5 The Zolendronic acid. This measure with without fractures fractures Placebo 28 546 574 Department of Clinical Pharmacology, Seth GS Medical College and KEM Hospital, Mumbai, Maharashtra Zolendronic 09 544 553 Received: 03.07.2017; Accepted: 07.07.2017 acid Journal of The Association of Physicians of India ■ Vol. 65 ■ August 2017 91 would be calculated as a proportion [rather than placebo], 3 patients its anti-fracture use [also by the US (or a percentage) of the number of [5 minus 2] would be spared the FDA]for the management of post- patients who developed fractures adverse outcome [fractures in this menopausal osteoporosis with a with either treatment. case]. Thus, if 1 patient were to be NNT of 14 for new morphometric Thus, Absolute Risk [AR1] for spared the adverse outcome, how vertebral fractures and a NNT of getting fractures with placebo many patients would be needed to 91 for hip fractures. A very low would be be treated with Zolendronic acid? NNT thus may not always be possible or necessary to allow for 28/574 = 0.0487 or 4.87% This would be marketing approval and would 100 x 1 And the Absolute Risk [AR2] for depend upon the disease, outcome getting fractures with zolendronic 3 and intervention being evaluated. acid would be Or 33 patients. Number Needed to Treat- 9/553 = 0.0168 or 1.68% You will realize that we have For the sake of simplicity, we already arrived at this number harm [NNT-H] round off these values to 5% and using the formula 1/ARR The number needed to treat 2% respectively in the subsequent Thus, NNT- B is that single that we have discussed above calculations. number which tells the practicing is for benefit. A similar metric is Step 2 clinician about the number of the number needed to treat to It is obvious from the data that patients he would need to treat harm or NNT-H or NNH as it is the Zolendronic acid group has a with one intervention rather than frequently referred to in literature significant protective effect as it has another, to prevent one adverse is defined as the number of patients fewer fractures relative to placebo. outcome [for a defined period who need to be treated with one Thus, there is a risk difference under defined conditions]. It can intervention [rather than another] [RD] between the two groups and also be defined as the number of for one patient to be harmed or we calculate this next. The risk patients that would need to treated for one patient to have an adverse difference is simply the difference with one intervention rather than outcome. Let us understand this between the two absolute risks another, to prevent one additional as well with a published example. or AR1- AR2, and is also called adverse outcome. Montelescot G and colleagues9 Absolute Risk Reduction [ARR] In our example, we can interpret evaluated n=4033 patients Thus, the ARR would be 5% - 2% the NNT- B as follows – A total with non-ST segment elevation or 3% (i.e. 3/100 = 0.03) of 33 patients need to be treated [NSTEMI] acute coronary Step 3 with Zolendronic acid [rather than syndromes to assess the effect of placebo] to prevent one patient from The final step is the actual the timing of administration of getting afracture [or additional calculation of NNT-B, which is Prasugrel (a P2Y12 antagonist) vis fracture]over a 24-month period. given by the formula à vis the angiography, on major A perfect NNT-B would really be ischaemic events within 30 days NNT-B = 1/ARR 1! This means that every time one (Table 2). The patients were divided NNT-B = 1/0.03 =33 patients. patient is treated, one patient is in a 1:1 ratio into two groups- one How did we arrive at this formula and prevented from getting an adverse that received 30mg of Prasugrel thus the number? outcome. It is intuitive that as pre-angiography followed by 30 If Zolendronic acid were to the NNT-B increases, fewer and mg Prasugrel post angiography be completely ineffective [which fewer patients would be helped. in the event that percutaneous would be our null hypothesis], the As a general rule of thumb, lower intervention [PCI] was undertaken fracture risk with both Zolendronic the NNT-B, the better is the and the second group that received acid and placebo would be identical treatment. For example, Quetiapine placebo initially followed by 60mg at 5%. The ARR would then be monotherapy has an NNT - B of 6 of Prasugrel in the event that zero [5%-5%]. Zolendronic acid and the combination of olanzapine percutaneous intervention [PCI] is however effective and only and fluoxetine an NNT - B of 4, was needed. Safety was assessed 2% patients treated with it get both single digit NNTs relative according to the Thrombolysis fractures relative to the 5% treated to their placebo comparators7 for in Myocardial Infarction [TIMI] with placebo. If we were to see the the management of acute bipolar criteria of major and minor bleeding impact on 100 patients, 2/100 would depression [approved by the US episodes regardless of whether or get fractures with Zolendronic FDA]. not they were related to the PCI. acid and 5/100 with placebo.Thus, On the other hand, Zolendronic The safety data of the two groups every time that n = 100 patients acid [relative to placebo; the Pivotal is described in Table 2. The group are treated with Zolendronic acid Fracture Trial,],8 was approved for that received Placebo pre-treatment 92 Journal of The Association of Physicians of India ■ Vol. 65 ■ August 2017

Table 2: The association major and minor bleeding episodes in patient with NSTE a NNT-H for sedation of 7 giving with differential timings of Prasugrel a LHH value of 0.58. Lamotrigine, Number of patients Number of patients Total a mood stabilizer had a NNT-B with major or minor without major or minor similar to olanzapine of 12, but a bleeding episodes bleeding episodes NNT-H for sedation of 42, giving Prasugrel 30 mg pre angiography 52 1985 2037 an efficacy: sedation LHH value of followed by 30 mg in the event of PCI [ n = 2037] 3.5. The LHH values thus indicate Placebo pre-angiography followed by 27 1969 1996 superiority of Lamotrigine over 60 mg Prasugrel in the event of PCI quetiapine and quetiapine over [n= 1996] olanzapine [in that order] in terms followed by 60 mg of Prasugrel the comparator. For example, the of risk vs. benefits, thus enabling had fewer bleeding episodes and NNT- H of Valbenazine, a newly the clinician to make an informed this difference was statistically approved drug for the management choice. significant [p = 0.003]. of Tardive Dyskinesia is 76 [for The Number Needed to Similar to the NNT -B, we discontinuation due to an adverse calculate the NNT –H or NNH in event] compared to a NNT - B of Screen [NNS] 4 [both NNT-B and NNT-H being 3 steps National strategies for disease Step 1 relative to placebo comparator] over a six-week period.10 screening to identify patients The absolute risk of bleeding at risk of developing disease with Prasugrel (30mg) pre- Likelihood to be Helped or or with yet undetected disease angiography [AR1] followed by 30 Harmed [LHH] – the Ratio [for example, use of the Prostate mg post intervention is 52/2037 or Specific Antigen (PSA) for the 2.6%. The absolute risk of bleeding of NNH to NNT diagnosis of prostate cancer or with Placebo pre-angiography mammography for the detection of Since interventions can produce followed by 60 mg Prasugrel post breast cancer] require evidence that both benefits and harm, any intervention is 27/1996 or 1.4%. measures the value addition that comparison of two interventions any screening test provides. The Step 2 will produce two NNTs – one for Number Needed to Screen [NNS] We next calculate the risk benefit [NNT-B] and one for harm is one such metric and was first difference [RD] or Absolute risk [NNT-H]. A lesser-used metric developed by Rembold in 199811 reduction [ARR] as called the “Likelihood to be helped / as a metric to define the number harmed” [LHH] is calculated as the AR1-AR2 or 2.6 – 1.4 = 1.2% (i.e. of people that are needed to be ratio of NNT-H to NNT-B since 1.2/100 = 0.012) screened to prevent one death or treatment decisions are almost Step 3 one adverse event or one life-year always a trade-off between harm The NNT –H or NNH is gained.While it is conceptually and benefit. Intuitively, the value of calculated as 1/ARR or 1/0.012 or similar to the metrics of NNT- B LHH should be greater than 1 and 83 patients. and NNT- H, its calculation differs the further away from 1 that the slightly. This is interpreted to mean value is, greater is the likelihood that everytime 83 patients are that the intervention produces We require the knowledge of treated with Prasugrel [30 mg] more benefit than harm. Let us two elements before beginning the pre angiography followed by 30 understand this with an example. calculation of NNS mg post intervention rather than Srivastava and Ketter7 i n • The background risk or placebo followed by Prasugrel their eloquent narrative review prevalenceof the disease in [60 mg], one additional patient evaluated RCTs that studied the population will experience a major or minor quetiapine, olanzapine and • Knowledge of mortality or an bleeding episode [harm]. The lamotrigine among other drugs adverse outcome in screened authors of the paper concluded for the management of acute and unscreened cases that pre – treatment with Prasugrel bipolar depression [all studies with increased the rate of bleeding Let us now understand the steps placebo comparators]; a difficult complications. The study was in the calculations of NNS with an to treat disorder. Quetiapine [a also stopped by the Data Safety example. second-generation anti-psychotic] Monitoring Committee for safety Step 1- Calculate the cumulative rate of had a NNT-B of 6 and a NNT-H concerns. deathsin the two groups of 6 for sedation giving a LHH for Unscreened group- The Cancer Unlike the NNT-B, the NNT-H or efficacy: sedation of 1. Olanzapine Intervention and Surveillance NNH should be high as this indicates [also a second-generation anti- ModelingNetwork (CISNET) USA, lesser likelihood of harm relative to psychotic] had a NNT-B of 12, and Journal of The Association of Physicians of India ■ Vol. 65 ■ August 2017 93 estimates that the mortality from dying of myocardial infarction Confidence Intervals for the Number breast cancer in the absence of any from 3% to 2%. The NNT would Needed screening mammography would be 100. Drug B reduces the risk of Similar to other measures we be 3% for a woman aged 40 years dying from rabies from 100% to estimate in statistics [for example or older.12 Thus, the death rate 99%. The NNT is again 100. These risk ratio, odds ratio] where we without screening would be 3% or NNTs simply cannot be compared! give confidence intervals to help 30 per 1000 women screened. The reason is that rabies is a disease the reader gauge the margin of Screening group- Let us assume with 100% mortality [baseline error or uncertainty that was seen that a screening technique X is risk] and even a 1% reduction with the study, the number needed developed that reduces mortality [giving a NNT of 100] will make to treat similarly needs to be by 90%. Now the deaths will be 3 a huge impact to the disease. In accompanied by a confidence per 1000 women screened. the MI example, while the NNT interval. Several methods exist for Step 2 –Calculate the number of of 100 is the same, given that the the calculation of CIs and the Wald deaths prevented [lives saved] due to baseline risk of death itself is low, method is a commonly used one.18 screening13 the 1% reduction may or may not Stating the direction of effect really be meaningful. Thus, any Because intervention X is 90% Although the NNT was comparison of NNTs [benefits or effective, 27 lives per 1000 women originally devised as a measure harm] must be made with a clear screened are saved [or deaths of benefit, as interventions can understanding of the baseline risks prevented] produce both harm and benefit, that are involved.14 Step 3- Calculate the number needed simply stating the NNT without When NNTs are needed to be to screen as the reciprocal of the giving the direction [benefit or calculated for “time to an event” absolute difference in cumulative harm] can become difficult for the 13 mortality When we carry out survival reader. Thus, the terms NNT-B 15 Since 27 deaths were prevented analysis [time to an event analysis], to indicate benefit and NNT-H for 1000 women screened, for one the calculation of the number are recommended for use while death to be prevented, 1000/27 or 37 needed to treat can become difficult presenting this metric.2 women would need to be screened as patients will have varying follow The importance of stating the [NNS = 37 for an intervention that up times and some of them may be comparator censored as well. The calculation reduces mortality by 90% from Since the NNT makes use of 13 is thus significantly dependent upon 30/1000 to 3/1000]. Absolute risks in both groups, time. In survival or time to an event If intervention Y were to produce it is logical that both groups are study, we use the term NNT[t] and only a 10% reduction in morality, alluded to when presenting the calculate more than one NNT[t] at 0.1 x 30 = 3 lives per 1000 women NNT. However, this does not several time points [which can be screened would be saved happen routinely in literature. For fixed in advance]. The calculation instance, simply stating that Drug Thus, to save 1 life, 1000/3 or at each time point is based on the X has a NNT of 25 makes no sense, 333 women need to be screened survival probability at that time unless the comparator Drug Y is [NNS = 333 for an intervention point which is estimated either by clearly stated. that produces a 10% reduction in the Kaplan-Meier method or Cox mortality] regression method. A time specific Stating the time frame of the study Logically therefore, the lower NNT(t) is defined as the average Randomized controlled trials the NNS, the more useful is the number of patients needed to be [RCTS] are often conducted over a screening test. treated to observe one event-free long period of time. Hence stating patient more in the intervention the time frame along with the Challenges Associated group relative to the control group presentation of the NNT becomes with the Use of NNTs at a given time point t.16 very important. Let us understand this with an example. Study 1 Interpret with caution and with an Presenting NNTs in compares two treatments X and Y understanding of the baseline risk Research Papers – Key over a two-year period and yields A risk is essentially the Points to be Remembered a NNT-B of 25. Study 2 compares probability that something will two treatments A and B over a happen. If we toss an unbiased Though NNTs are now widely 10-year period and gives a NNT-B coin once for instance, the “risk” of used, their reporting in literature is of 25. Though the NNT – B for both heads would be 50%. Similarly, we less than optimal.17 The following studies are identical, it is a very can define risks in medicine as well. need to be remembered while different matter to produce benefit Let us take a hypothetical example presenting NNTs in publications. in 1 patient for every 25 patients of a drug A reducing the risk of treated over 2 years versus over 10 94 Journal of The Association of Physicians of India ■ Vol. 65 ■ August 2017 years! Thus, mentioning the time clinicians make an informed choice ACCOAST Investigators. Pretreatment with frame for the study is a crucial when more than one intervention prasugrel in non-ST-segment elevation acute coronary syndromes. N Engl J Med component for presenting the NNT. is available. The explanation 2013; 369:999-1010. In the example of association of and elaboration document of the 10. Citrome L. Valbenazine for tardive fractures with Zolendronic acid, CONSORT guidelines suggest dyskinesia: A systematic review of the the NNT of 33 is over a 24-month that the NNT-B and NNT-H can efficacy and safety profile for this newly period. be presented as metrics for binary approved novel medication-What is the data from Randomized Controlled number needed to treat, number needed Criticisms of the NNT Trials.23 Clinicians should learn to harm and likelihood to be helped or harmed? Int J Clin Pract 2017; May 12. how to derive and use NNT from Katz N and colleagues19 in results of RCTs as the reciprocal 11. Rembold CM. Number needed to screen: their eloquent narrative review Development of a statistic for disease of the Absolute risk difference. have put together evidence on screening. BMJ 1998; 1:317:307. However, since benefits and risks and summarized the challenges 12. Mandelblatt JS, Cronin KA, Bailey S, et are two sides of the same coin, associated with the use of the al. Effects of mammography screening each intervention in a RCT would NNT. These range from the NNT under differentscreening schedules: model have both a NNT-B and a NNT-H estimates of potential benefits and harms. having an infinite value when the and both need to be considered Ann Intern Med 2009; 151:738–747. ARR is zero or close to zero [when in tandem so as to make careful, 13. Hendrick ER, Helvie MA. Mammography the interventions tested have very individualized, patient -centric as screening: a new estimate of number similar effects], to the NNT being also policy decisions. needed to screen to prevent one breast dependent upon the choice of the cancer death. AJR 2012; 198:723-28. Acknowledgment binary outcome or not translating 14. McCormack PJ. Number needed to treat into the same NNT value when the The authors are grateful to and baseline risks. CMAJ 2008; 179:1174. intervention is actually used in the Dr. Robin Ferner from the West 15. Gogtay NJ, Thatte UM. Survival analysis. J real-world setting. Midlands Centre for Adverse Assoc Phy Ind 2017; 65:80-84. Reactions Monitoring, Birmingham, 16. Altman DG, Andersen PK. Calculating NNT and the Cost and for his constructive inputs that the number needed to treat where the helped refine the manuscript. outcome is time to an event. BMJ 1999; Reimbursements of 319:1492-1495. Treatments References 17. Hildebrandt M, Vervölgyi E, Bender R. Calculation of NNTs in RCTs with time-to- 20 Graziano and colleagues 1. Cook RJ, Sackett DL. The number needed event outcomes: A literature review. BMC have suggested that the NNT to treat: a clinically useful measure of Medical Research Methodology 2009; 9:21. treatment effect. BMJ 1995; 310:452–454. can be used by policy makers 18. Bender R. Calculating confidence intervals for pricing negotiations with the 2. Altman DG. Confidence intervals for for the number needed to treat. Controlled pharmaceutical industry and the number needed to treat. BMJ 1998; Clinical Trials 2001; 22:101-110. 317:1309e12. have expounded on this using the 19. Katz N, Paillard CF, Inwegen VR. A review example of NNT for regorafenib 3. Laupacis A, Sackett DL, Roberts RS. An of the use of the Number needed to Treat assessment of clinically useful measures [salvage therapy for metastatic to Evaluate the efficacy of analgesics.The of the consequences of treatment. N Engl Journal of Pain 2015; 16:116-123. colorectal cancer, the CORRECT J Med 1988; 318:1728e33. 20. Graziano F, Rulli E, Biagioli E, et al. Number trial].21 4. Suissa S. The Number Needed to Treat: 25 needed to treat for pricing costly anti- Conclusions Years of Trials and Tribulations in Clinical cancer drugs. The example of regorafenib RCTs report results in a wide Research. Rambam Maimonides Medical in metastatc colorectal cancer. Annals of Journal 2015; 6:e0033. Oncology 2016; 27:247-48. variety of ways that include relative 5. Boonen S, Reginster JY, Kaufman JM, et al. risk, odds ratio, hazard ratio and the 21. Grothey A, Van Cutsem E, Sobrero A, et al. Fracture risk and zoledronic acid therapy in Regorafenib monotherapy for previously p value when two interventions are menwith osteoporosis. N Engl J Med 2012; treated metastatic colorectal cancer being compared. Many clinicians 1;367:1714-23. (CORRECT): an international, multi-centre, have difficulty in translating these 6. Gogtay NJ, Deshpande S, Thatte UM. randomised, placebo-controlled, phase 3 findings into actual patient care Measures of Association. J Assoc Phy Ind trial. Lancet 2013; 381:303–312. as the answer to the question 2016; 64:70-3. 22. Cordell HW. Number needed to treat [NNT]. “which therapy between the two 7. Srivastava S, Ketter AT. Clinical relevance Annals of Emergency Medicine 1999; 33:433- should I use in my patient?” is of treatments for acute bipolar disorder: 36. often not clear to them.22 The NNT balancing therapeutic and adverse effects. 23. Moher D, Hopewell S, Schulz FK, et Clinical Therapeutics 2011; 33:B40-B48. al. CONSORT 2010 Explanation and offers clinicians a “yardstick” Elaboration: updated guidelines for for measurements as it helps 8. Black ND, Delmas DP, Eastell R, et al. Once- yearly zolendronic acid for the treatment reporting parallel group randomised trials. compare benefits and harms of of post menopausal osteoporosis. N Engl J BMJ 2010; 340:c869. treatment by converting them into Med 2007; 356:1809-22. a single number. It helps practicing 9. Montalescot G, Bolognese L, Dudek D, et al.