(Circulation. 1999;99:377-383.)
© 1999 American Heart Association, Inc.
Clinical Investigation and Reports |
Reporting Risks and Benefits of Therapy by Use of the Concepts of Unqualified Success and Unmitigated Failure
Applications to Highly Cited Trials in Cardiovascular Medicine
From the Departments of Medicine (G.B.J.M., M.S.) and Statistics (M.S.), University of British Columbia, and the Vancouver Hospital and Health Sciences Centre, Vancouver, British Columbia, Canada.
Correspondence and reprint requests to Dr G.B. John Mancini, Vancouver Hospital and Health Sciences Centre, Laurel Street Pavilion–Suite 3300, 950 West 10th Avenue, Vancouver, British Columbia V5E 4Z3.
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Abstract |
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Background—The NNT (number needed to treat) and NNH (number needed to harm) are useful in conveying the results of clinical trials because they emphasize the effort that must be expended to accomplish a single, tangible outcome. But NNT conveys the effort required to achieve a positive outcome without distinguishing between the presence or absence of treatment-related adverse events. Similarly, NNH conveys harm without accounting for the achievement or lack of achievement of the benefit of therapy. Consequently, a mathematical model was developed to extend the NNT and NNH to represent the effort required to achieve "unqualified success" (NNTUS, treatment success without treatment-induced side effects) and "unmitigated failure" (NNHUF, lack of treatment success with treatment-induced side effects).
Methods and Results—NNTUS was calculated by adjusting the absolute risk reduction to allow for the probability of not incurring a treatment-related adverse event. NNHUF was similarly calculated by adjusting the absolute risk of incurring a treatment-related adverse event by the probability of not incurring any treatment-related benefit. The impact of conveying clinical trial data by the use of NNT, NNTUS, NNH, and NNHUF is illustrated by means of 11 highly cited trials identified systematically from the cardiovascular literature. The treatment effort measured by the NNTUS and the NNHUF was consistently higher than that given by the traditional NNT and NNH. These increments ranged from 1% to several hundred percent.
Conclusions—The NNTUS and the NNHUF represent the treatment effort required on average to achieve 1 unqualified success and 1 unmitigated failure. NNTUS and NNHUF balance benefit and harm in an objective way and are relevant for making service delivery decisions.
Key Words: number needed to treat • number needed to harm • clinical trials • unqualified success • unmitigated failure • cardiovascular diseases
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Introduction |
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The concept of "number needed to treat" (NNT)1 2 has been defined as the reciprocal of the absolute risk reduction due to a given therapy and conveys the effort that must be expended on average to accomplish a single, tangible, and positive treatment outcome in a patient. This expression of service delivery effort is easily understood and is relevant to the context within which care is delivered. However, it is implicit in the NNT that the clinical effort expended to achieve 1 beneficial outcome is accompanied by a finite risk of simultaneously inducing a treatment-related adverse event. For example, there is an obvious difference in impact in saving the life of a patient suffering an acute myocardial infarction depending on whether thrombolytic therapy does or does not induce a nonfatal but serious hemorrhagic complication. The conventional NNT does not distinguish between these 2 strikingly different clinical outcomes. Both outcomes are positive with respect to mortality but quite different with respect to impact on the patient, the patient's family, the health care providers, and the cost to the health care system.
We have recently developed a mathematical model that refines the concept of NNT to assist in the process of weighing the benefits of therapies against the harm that they may induce.3 We have proposed an adjusted NNT that gives a clinically meaningful measure of what we term "unqualified success" (NNTUS). In the example given, the NNTUS is a measure of the effort that must be expended to prevent death from acute myocardial infarction by administering thrombolytic therapy without incurring a treatment-related hemorrhagic complication in the same patient. The effort needed to achieve this unqualified success is obviously greater than that estimated by the conventional NNT. This ideal, unqualified success, is the outcome that more clearly depicts what clinicians strive to achieve and what patients expect.
The concept of NNT can also be used to assess adverse outcomes of therapy (number needed to harm, NNH).4 This estimate conveys the treatment effort expended before 1 patient experiences an adverse treatment-related outcome. In a fashion analogous to the discussion above, there is a great difference between suffering a side effect and surviving as a result of therapy compared with suffering a side effect and dying. The latter circumstance can be considered to represent an "unmitigated failure" and an adjustment can be made to the NNH calculation to represent this dismal situation (NNHUF). Again, the conventional NNH does not distinguish between failure and unmitigated failure.
The purpose of this article is to illustrate the usefulness of these concepts through an analysis of frequently cited trials in cardiovascular medicine.
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Methods |
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Mathematical Model
We review the basic concepts developed more fully in another study.3 If p1 is the proportion of the untreated population suffering from a certain condition (primary event or primary endpoint) and p2 is the corresponding proportion in the treated population (commonly, p2<p1), then the absolute risk reduction due to the treatment is given by: p1-p2. The NNT is then defined as 1/(p1-p2) (ie, the reciprocal of the absolute risk reduction).
We considered an adjusted NNT representing the number of patients who must be observed on average to encounter 1 successfully treated patient who, in addition, did not suffer adverse events due to the treatment.3 We termed this the NNT for unqualified success (NNTUS). If we assume that in any treated individual the prevention of the primary event is independent of the induction of the adverse event, the chance of such an unqualified success in the treated population is calculated as the absolute risk reduction multiplied by the chance of not experiencing an adverse event due to the treatment: (p1-p2)[1-(q1-q2)], where q1 is the frequency of the adverse events in the treated group and q2 is the frequency of this event in a control or untreated group (typically q2<q1). The corresponding NNTUS is then calculated as the reciprocal: 1/{(p1-p2)[1-(q1-q2)]}.
However, it is conceivable that in certain situations there may be an association between the prevention of the primary event and the induction of the adverse event. In this case, although the value of the general NNT remains unchanged, the chance of an unqualified success is now given by (p1-p2)d, where d is the chance of not inducing an adverse event in individuals in whom the primary event has been successfully prevented. When a positive association exists between primary prevention and adverse event induction, d is clearly <1-(q1-q2), and thus, NNTUS, the reciprocal of (p1-p2)d, is increased, representing a larger treatment effort. This situation is illustrated in Results, with details given in the Appendix.
The mathematical definition of NNH and of its extension, NNHUF, are also fully developed in another study.3 These new estimates assume implicitly that the primary event and the induced adverse event are, in some sense, comparable. Utility theory provides methods by which decisions contingent on events of unequal consequence may be made.5 A common method is cost–benefit analysis, whereby decisions can be carried out based on the dollar cost of events of varying significance. We have previously illustrated the use of our NNT estimates in the context of cost–benefit analysis.3
Method of Selection of Clinical Trials From the Literature
The Institute for Scientific Information (Philadelphia, Pa) was
employed to identify high-impact articles in
cardiovascular science. Databases beginning in January
1990 and ending in June 1996 were searched. The searches were
undertaken from the Science Citation Index
Cardiovascular System category and also from a database
consisting of articles published in Lancet and the New
England Journal of Medicine. A threshold of 50 or more citations
was set, which yielded 1141 articles. The 120 most cited articles were
reviewed to identify clinical trials and to exclude basic science
articles. The strategy successfully identified 11 suitable articles
reflecting a diversity of therapies, trial designs, and both positive
and negative outcomes. The precision of the estimates increases (and
the SE decreases) as the sample size or magnitude of the difference in
the event rates between the study groups increase. Because most studies
are planned with sufficient power to identify efficacy, but not
necessarily adverse events, some of the estimates of NNH and
NNHUF have large SEs (Table
). However, our
emphasis is primarily on the impact conveyed by the point
estimates.
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Results |
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The first 6 studies pertain to the field of electrophysiology and arrhythmia management. The first of these studies by Connelly et al6 represents 1 of the early trials that used Coumadin to prevent strokes in patients with atrial fibrillation. The desired outcome in this study was prevention of an event cluster that included nonlacunar stroke, noncentral nervous system embolism, and fatal or intracranial hemorrhage. This article provided data on bleeding complications in the categories of fatal/major and minor bleeding. NNT-related parameters are calculated for either or both of these categories of bleeding. To attain prevention of the embolic event cluster in 1 patient, about 59 patients must be treated. However, to achieve this without also inducing a fatal/major or a minor bleed, 65 patients need to be treated. This is obtained under the assumption that there is no association between stroke prevention and the induction of a bleed, and represents a 10% increase in treatment effort. Conversely, only 11 patients need to be treated before being faced with some form of bleeding complication. However, the NNHUF suggests that 1 patient that has not benefited from prevention of the embolic cluster of events will have experienced either some type of bleeding, minor bleeding, or fatal/major bleeding after treating 317 408 or 1429 patients, respectively.
Suppose, however, that the conservative assumption of independence between successful stroke prevention and the induction of a bleed is relaxed and that a direct dependence between these events is assumed to exist. For example, assume a 50% increase in bleeds in individuals in whom embolic events were successfully prevented, relative to those in whom prevention was unsuccessful. In that case, the NNTUS rises further to 68, and now represents a 15% increase in treatment effort when compared with the simple NNT (details in Appendix).
Similar extensions of the calculations of NNT values under varying assumptions of dependence can be applied to the results of any of the trials reviewed. However, for simplicity, the results we present here are based on the conservative assumption of independence between the primary and the adverse events.
NNT estimates can also be calculated in the context of cost–benefit
analysis.6 For example, in a previous
study,3 we showed that, by the use of annual cost
estimates derived from Swedish data,7 8 59 individuals
need to be treated to prevent 1 stroke, which means the total cost of
treatment exceeds the cost of a stroke by $7120 per year per stroke
prevented. However, because 65 individuals need to be treated to
produce an unqualified success (see Table
), the treatment will be
cost-effective provided that the cost of a bleed exceeds $10 522 per
year. Similar utility analyses may be applied to the
NNTUS and NNHUF
calculations in any of the other trials discussed below.
The article by Coplen et al9 is a meta-analysis of the use of quinidine after cardioversion for the maintenance of sinus rhythm. We selected the maintenance of sinus rhythm at 12 months as the desired outcome. The NNT and NNTUS, calculated on the basis of the reported pooled rate difference, are close (4.10 and 4.19, respectively), indicating only a 2% increase in treatment effort to achieve 1 unqualified success. However, with respect to harm, only 47 patients needed to be treated with quinidine after cardioversion before 1 death was induced. The NNHUF suggests that after treating only 94 patients this way, 1 patient will not maintain sinus rhythm at 12 months and will die within that time.
The article by Lee et al10 outlines the role of catheter ablation for the abolition of atrioventricular nodal re-entrant tachycardia (AVNRT). Although it does not describe a randomized trial, it is nevertheless amenable to the calculations we propose. It is not unusual to have available only this type of information at the outset of application of new technologies. Many hospitals and clinics need quantitative ways of assessing these new therapies if they wish to get involved early in delivering innovative therapy and need to predict its impact on resource utilization. Because there is no control arm, calculations can be made only by making an assumption about what would happen to patients denied this therapy. This theoretical control arm of patients would have no abolition of AVNRT and would be subjected to none of the treatment-related side effects (AV block in this case). The calculations show that scarcely >1 patient needs to be treated to obtain a good outcome and that an 8% greater treatment effort (1.22 versus 1.32, NNT versus NNTUS, respectively) will ensure an unqualified success. On the other hand, after 13 cases, at least 1 pacemaker will have to be inserted for AV block and after 72 cases, a pacemaker may have to be inserted in a patient whose ablation did not abolish AVNRT. The latter circumstance is not likely to occur because creation of AV block would necessarily abolish the specific AVNRT. Even so, the impact on service delivery is conveyed in very concrete terms by the use of this methodology and the results can be readily used for planning services.
The studies by Calkins et al11 and Jackman et al12 deal with ablation of Wolff-Parkinson-White bypass tracts. As with the study by Lee et al,10 these studies are not randomized trials and, therefore, the assumption of a theoretical comparative arm is invoked as above. Both of these articles suggest that barely >1 patient needs to be treated to ensure a successful outcome and that the treatment effort to obtain an unqualified success is only 1 to 2% higher than suggested by the NNT. However, in contrast to the article by Lee et al, in these articles the treatment-related adverse events that are reported may occur in the absence of the desired outcome. These include coronary occlusion and cardiac tamponade. Thus, the comparison between NNH and NNHUF is more meaningful and it shows that there is a marked increase in the NNHUF compared with the standard NNH. This suggests that many hundreds of patients would have to be treated by this method before a single patient would be expected to sustain an untoward effect without curing the bypass-dependent arrhythmia. Conveying the results in this way more clearly helps to juxtapose the benefits against the dire, but infrequent, occurrences of coronary occlusion and cardiac tamponade.
The CAST study13 is representative of an unexpected, adverse trial result. The use of encainide or flecainide in patients with ventricular ectopy postmyocardial infarction was associated with an increased risk of mortality from arrhythmia and shock. Patients receiving placebo incurred no direct benefit but also no harm from the drugs. Thus, the values of NNH and NNHUF are the same (ie, about 21 patients). To calculate NNT in this case, one would have to consider the placebo as the active drug. The values of NNT and NNTUS are identical here and are also mathematically equivalent to NNH: about 21 patients need to be treated by placebo (ie, quinidine is withheld) to prevent 1 drug-related death.
The studies by Pfeffer et al14 and Cohn et al15 evaluate therapy in patients with left ventricular dysfunction. The first compares captopril with placebo in postacute myocardial infarction, whereas the second compares 2 effective therapies, enalapril and the combination of hydralazine and isosorbide dinitrate in patients with chronic heart failure. In these studies, the treatment-related adverse side effects (cough, taste abnormality, dizziness/hypotension) are much more trivial in nature than the desired outcome (ie, decreased mortality). Nevertheless, these complications can be factored into the impact on treatment effort by the use of the NNT and NNH calculations. Thus, the comparison of captopril with placebo14 shows that the NNTUS is only 2% to 3% greater than the NNT; ie, therapy is very effective and reduction in mortality can be achieved without side effects after treating on average only 24 patients. However, after treating 38 patients (NNH), a practitioner will encounter a side effect that requires a management decision. This number is put into a different perspective by the NNHUF calculation that shows that despite the occurrence of side effects, nearly 200 patients must be treated before encountering 1 case in which side effects occur without improving mortality.
The interpretation of the study by Cohn et al15 is
different because 2 effective therapies are being compared. The NNT
suggests that after treating 18 or 19 people, 1 more life would be
saved by the use of enalapril as compared with vasodilator and
diuretic therapy. The NNTUS is 4%
higher. That is, the treatment effort to prevent a death while not
incurring an adverse effect by enalapril that would not have been
induced by the alternative therapy is slightly increased. This is
largely because the side effect profile is not too different, except
with respect to cough. The NNH shows that, after 
26 patients have
been treated, a side effect will be encountered in the enalapril group
that would not have been seen if the alternative therapy had been used.
However, the NNHUF shows that 79 patients must
be treated in this way before encountering 1 patient with no benefit
from enalapril and with an adverse effect that would not have been seen
with the vasodilator approach.
The GISSI-2 study16 evaluated the efficacy of tissue-plasminogen activator (t-PA) and streptokinase (SK) with or without heparin therapy for the prevention of death plus severe left ventricular damage. A comparison of t-PA with SK, irrespective of heparin use, can be carried out and counterbalanced with major bleeding as the adverse outcome. Because SK did slightly better than t-PA in the prevention of death plus severe left ventricular dysfunction, we believe that SK is the treatment arm and t-PA is the control or alternative therapy arm. The NNT and NNTUS are almost identical and suggest that after treatment of about 165 patients, 1 prevention of death plus severe left ventricular dysfunction will be noted that would not have been seen with the use of t-PA. The NNH suggests that >230 patients would need to be treated with SK before seeing a major bleeding episode that would not have occurred with t-PA. Even more important, >1000 patients would need to be treated with SK instead of t-PA before seeing a major bleed and failure to prevent death or severe left ventricular damage.
Buchwald et al17 undertook an evaluation of partial ileal bypass to lower cholesterol as secondary prevention therapy in patients with coronary disease. Surgical deaths, kidney stones, and operations for gallstones or bowel obstruction were considered for this analysis. Thus, to prevent 1 cardiovascular death without incurring any adverse events, 44 patients must be treated. This represents an increased effort of 29% compared with the 34 patients predicted by the conventional NNT. Moreover, after treating only 58 patients, an unmitigated failure will occur.
Finally, Lichtlen and coworkers18 evaluated the role of
nifedipine in preventing progression of
atherosclerosis. The provocative finding
was that new lesions could be prevented but critical cardiac events
occurred with slightly greater frequency in the nifedipine
group. A single new lesion can be prevented after treating about 12 or
13 patients. The NNTUS is minimally increased
compared with the conventional NNT. However, after treating <51
patients, a critical cardiac event can be expected. After treating
125 patients, a critical cardiac event will occur in a patient in
whom a new lesion will not have been prevented.
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Discussion |
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Numerical and statistical results of clinical trials are often difficult to translate into terms relevant to clinical practice. The NNT has been proposed as a method to overcome this problem. However, the conventional NNT does not distinguish between successful outcomes that are associated with or not associated with treatment-related adverse events. We have chosen the term unqualified success to refer to a successful outcome unaccompanied by treatment-related adverse events, explicitly measured by a new parameter, the NNTUS. Similarly, we have extended the concept of NNH by creating a new index, NNHUF, which is a measure of the treatment effort expended on average before a patient will suffer an adverse, treatment-related effect without benefiting from the therapy. We describe this outcome as an unmitigated failure. We systematically identified and analyzed commonly cited trials from the cardiovascular field to illustrate the use of these new parameters. Studies of diverse designs and outcomes provided a broad framework for the applications.
The use of frequencies, probabilities, and relative or absolute risk reduction indexes to convey clinical impact is hampered because these parameters are dimensionless and abstract. The NNT approach, in contrast, provides a direct connection with the clinical context of health care delivery because it is expressed in patient numbers. It is a direct reflection of the effort required to achieve the desired outcome. The qualities and strengths of this approach have been recently reviewed.4 These properties are retained by the new concepts of NNTUS and NNHUF. Thus, the traditional approaches and the 2 new parameters are directly applicable to clinical practice because they show the effort required to achieve a particular therapeutic outcome or to produce an adverse event. They can be applied to any outcome for which a comparison group is available consisting of either placebo or alternate choice of therapy. They are treatment-specific: the indexes are determined by the specific treatment and comparison arms of trials, the therapeutic outcome of interest (usually the primary end point), the treatment-related adverse effects, and the duration of treatment required to achieve the outcome. Finally, if costs of achieving the desired and untoward effects are known, our estimates can be used to calculate the economic impact of various therapies.3
NNTUS and NNHUF also share the same limitations as the traditional NNT. The numbers generated by these measures can only be used to compare different disease conditions when the outcomes and the duration of therapy are similar. Furthermore, the estimates are valid only when applied to populations having a baseline risk similar to the patients studied in the original clinical trials. Moreover, the calculations represent point estimates for which measures of precision need to be considered. The SE of these estimates are smallest, and the point estimates are therefore most precise, when they are derived from large trials or properly executed systematic reviews and meta-analyses, and when treatment-induced event rates are considerably different between the groups. Despite this limitation, even approximate point estimates are valuable if used as interim benchmarks, pending accumulation of further experience or new studies.
The advantage of the NNTUS and NNHUF is that these new measures provide single, clinically relevant numbers that objectify the process of balancing benefit against harm. This process takes place intuitively, imprecisely, and qualitatively in day-to-day practice. The new approach provides a mathematically valid way of doing this and it is particularly helpful when applied to therapies that are associated with severe treatment-related adverse events (eg, significant bleeding with anticoagulant or thrombolytic therapy or the significant morbidity associated with surgical or interventional procedures). We have shown that it is also useful when more minor, treatment-related adverse events are significant enough to have an impact on service delivery or patient preferences. Despite physician education and patient counseling regarding the frequency with which adverse treatment-related events may occur with a given therapy, individuals intuitively hope for unqualified successes and often perceive the occurrence of any major, adverse event as an unmitigated failure. Thus, the NNTUS and the NNHUF depict these circumstances more precisely and they represent the outcomes that are sought or are of real concern in clinical practice. These calculations may be especially helpful in weighing evidence for or against preventive therapy when even low rates of adverse events can have a great impact on whether prophylactic therapy is considered acceptable or not (eg, use of nifedipine to prevent the formation of new lesions18 ). Finally, because the NNTUS is invariably larger than the NNT, it provides a more realistic index of the average effort required to achieve a single, purely beneficial outcome. In some cases, an NNTUS significantly larger than the NNT or a very small NNHUF might prevent the premature acceptance of certain therapies, or at least abate the initial enthusiasm regarding their clinical utility.
Our measures are developed under the simplifying assumption that the occurrence of treatment-related adverse effects is independent of the occurrence of the desired benefits. This is a reasonable assumption as a first approximation for most clinical purposes. Trials are usually undertaken with methods or interventions for which there is some a priori information regarding the type and frequency of possible adverse outcomes and their interdependence through dose–response investigations. Should the events be dependent (eg, higher efficacy associated with greater adverse effects), then the NNTUS and NNHUF can be adjusted accordingly as demonstrated in Results and in the Appendix and also in our previous work.3 We have shown that such adjustments generally increase the disparity between NNT and NNTUS and between NNH and NNHUF. Thus, the calculations we have presented based on independence provide merely conservative estimates of the difference between the traditional approach based on NNT or NNH and the new concepts of NNTUS and NNHUF we are proposing.
In conclusion, we have developed a modification of the traditional NNT that helps to integrate the desired and the adverse effects of any therapy into single, clinically relevant parameters that reflect the treatment effort required to attain unqualified success and unmitigated failure. The approach retains all the positive attributes of the traditional NNT and NNH while reflecting more accurately the workload required to achieve both desired and untoward outcomes. More regular reporting of these calculations in clinical trials, especially meta-analyses and systematic analyses, will help convey results in a clinically compelling and understandable fashion that can facilitate decision making at the bedside, in the clinic, in the boardroom, and in the offices of public health administrators.19 20 21 22
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Appendix 1 |
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Calculation of NNTUS When a Positive Association Exists Between Prevention of the Primary Event and Induction of an Adverse Event
Using the study by Connelly et al,6 we recall that p1=5.2%, p2=3.5%, q1 (all bleeds)=18.5%, q2=9.5%.
Suppose that success of treatment is accompanied by an increased likelihood of inducing the adverse event. More specifically, assume that 50% more bleeds occur when strokes are successfully prevented than when they are not. If we let y denote the chance that a bleed is induced when a stroke has not been successfully prevented, then 1.5y denotes the chance of a bleed when a stroke has been successfully prevented. The chance of successful prevention of a stroke is given by p1-p2=1.7%; the total chance of inducing a bleed is given by q1-q2=9%. Now, the total chance of inducing a bleed is made up of 2 parts: inducing a bleed while preventing a stroke (with corresponding chance of 1.5yx1.7%) or inducing a bleed without preventing a stroke (with chance yx(100%-1.7%)=yx98.3%). This yields the equation: 9%=1.5yx1.7%+yx98.3%; with the solution: y=8.92%. It follows that the chance of inducing a bleed when a stroke has been successfully prevented is 1.5y=13.39%.
Now, to calculate NNTUS under these assumptions, we use the formula NNTUS=1/{(p1-p2)d}, given in Methods, where d represents the chance that no bleeds are induced in individuals in whom a stroke was successfully prevented. Thus d=100%-13.39%=86.61%, and hence NNTUS=68.03, compared with the value of 65 obtained under the assumption of independence.
Received July 13, 1998; revision received September 23, 1998; accepted October 9, 1998.
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