Number needed to treat: A primer for neurointerventionalists (2025)

Abstract

Introduction

The advancement of care of emergent large-vessel occlusion patients through improvements in mechanical thrombectomy (MT) makes it increasingly important to understand the health-care value proposition of these treatments in contemporary neurointerventional (NI) practice.¹ As the evidence for treatment benefit of MT has mounted,^2,3 so have the number of patients undergoing therapy.^4,5 Since NI specialists critically review data and report on and apply relevant literature, there is a need to have a robust understanding of common statistical models and data-analysis methods. The number needed to treat (NNT) has become an important statistical tool in the stroke literature. Landmark trials such as DAWN, SWIFT-Prime, and EXTEND-IA have taken advantage of this intuitive number to bring the efficacy of their respective interventions into focus and greater perspective for patients, health-care providers, and all key stakeholders.^6–8 Here, we review the concepts underlying the NNT, given its application in recent stroke trials, and present calculations of this number for other commonly used stroke therapies.

History of the NNT

Fundamentally, the NNT represents the number of patients that need to be treated for one patient to have a positive outcome or achieve prevention of an adverse outcome. Initially described by Laupacis in 1988, it was an effort to simplify statistical reporting for physicians and other providers. Simultaneously, it had the benefit of yielding a more tangible piece of data that is readily understandable by patients and their families, facilitating informed decision making to undergo various therapies.⁹

Caveats and limitations

Initially, this unique statistical concept did not catch on, only becoming mainstream years later. Further, as this type of analysis began to make its way into the reporting of certain landmark trials, criticisms surrounded the statistic were raised. Specifically, these concerned the inability to provide confidence intervals and apply a time to event studies, and the lack of generalizability for meta-analysis. Some argue the simplification that the NNT provides is an oversimplification of benefits/harms, given it is not equal to response rate. For example, some patients will improve or decline independent of the intervention provided, a concept curtailed by an appropriate control arm. The context of use is also a key consideration when informing the public. The NNT provides the number needed to reach a pre-specified effect but is not in itself a measure of the clinical significance of said effect. This is important when relaying this to patients, as they may misinterpret the value provided.¹⁰ Clinicians must use clinical judgment to interpret the impact of findings in daily practice. A NNT of 3 for any improvement in muscle ache versus the same for prevention of myocardial infarction has dramatically different implications. Nevertheless, forged by its utility and the power of summary, the NNT has become a critical element in modern medical reporting.^11,12 For the fast-changing landscape of health-care economics, it has revolutionized return on investment analysis as costs of care continue to rise.

Importantly, given the increasing popularity of this statistical method, it is imperative to understand potential misinterpretation or misrepresentation of data. The NNT calculation can be precise to the decimal, and misrepresenting the results by rounding up or down is a common mistake. At least one decimal place should be represented when values are in the single- to double-digit range. Moreover, time of follow-up after a treatment or time of treatment is key in influencing the NNT, given that the longer a study in general, the smaller the NNT. For example, prevention trials that last three months may have NNTs in the 500 s, while the same population followed at three years may have NNTs in the 50 s, even though the drug may have the same effect in risk reduction and just requires time to show that potential. Thus, it is crucial to highlight the time period of the study along with the NNT. Perhaps most importantly, there needs to be explicit description of the comparison groups that led to the calculation. For example, comparing three different drug-dosing regimens would lead to radically different NNTs, depending on which regimen is chosen as the reference to make a comparison to if no placebo or control group is available. These simple rules should be intuitive and on hand when reviewing new trials with NNT results reported.

Theory and calculation of the NNT

The NNT is the reciprocal of absolute risk reduction (ARR; i.e. 1/ARR). ARR is the difference between the absolute risk of an event in the experimental treatment group compared to its control or ARx–ARy. In its most simple form then, the NNT is 1/treatment effect. This is directly applicable to studies of binary incidence of an unfavorable/favorable outcome. For example, take a hypothetical study measuring the effect of drug x in achieving reperfusion after stroke. This wonder drug x is able to achieve reperfusion in only 90% of patients receiving it compared to 50% in the placebo group. This means the ARR is 90%–50% = 40%. Therefore, the NNT to achieve one additional case of reperfusion with drug x compared to placebo is 1/0.40 = 2.5 patients.

$$\text{NNT}=\frac{1}{\text{TreatmentEffect}}=\frac{1}{\text{ARR}}=\frac{1}{\text{AR}x-\text{AR}y}$$

What if the NNT is not reported alongside a trial? One of the elegant elements of this method is that calculation is possible from almost any cohort. To make this point, we will utilize specific examples from the NI and stroke literature. The DEFUSE 3 cohort did not provide the NNT. For ease of calculation and comparison with aforementioned trials, we will use the secondary efficacy outcome of functional independence at 90 days. The endovascular arm achieved this in 45% of cases compared to 17% in the medical therapy arm. So, the ARR would be 45%–17% = 28%. Thus, the NNT for one person to achieve functional independence at 90 days is 1/0.28 = 3.6. This can now be readily compared to the other thrombectomy trials. Table 1 summarizes the NNT for recent stroke trials (reported and calculated).

Number needed to harm and other metrics

These calculations are also helpful when looking at safety outcomes where endpoints are negatives (injury or death) rather than positives (e.g. independent functional recovery). In that case, the terminology changes to the number needed to harm (NNH), while the calculation and overall statistical analysis remain the same. While this is different from the NNT, it should be noted that the NNT includes the harm done by the treatment in question. Other metrics of particular interest to acute stroke care have been suggested as useful measures such as the number needed to image (NNI) and the number needed to screen (NNS). The NNI was recently defined as the number of imaging examinations needed to have one positive test—an important concept for imaging modality selection and the economics of these tests.¹³ The NNS was developed to create better large-scale screening strategies, and is defined as the number of patients that need to be screened to prevent one adverse event.¹⁴ As stroke systems triage evolves, these metrics may gain traction in the literature.

Additional considerations of the NNT calculation

A particular concern with the NNT in the NI field is that we often deal with the issue of time-to-event study design (e.g. survival or event-free survival studies). The concept of the NNT can also be applied to these trials with minor modification proposed initially by Altman and further refined by Bowry.^11,15 This adjustment utilizes Kaplan–Meier analysis, a frequently used method to plot and analyze time-to-event data (such as stroke or survival) and provides a probability of the said event occurring at different time points. For example, one can graph survival in a placebo and treatment group to analyze how the mean survival time differs. By utilizing data from a Kaplan–Meier analysis, one can derive the ARR at a specified time point as the difference in survival rates (S(t)). Thus, the NNT is 1/[Sa(t)–Sb(t)] (treatment group “a” Sa(t) compared to control group “b” Sb(t)). For example, take the event-free survival in the NASCET trial estimated visually from Kaplan–Meier graphs, event-free rate of ipsilateral stroke at 24 months was 0.9 for the surgical arm versus 0.75 for the medical arm. Thus, NNT = 1/(0.9–0.75) or 6.7.¹⁶

$$\text{NNT}=\frac{1}{\mathit{Sa}(t)-\mathit{Sb}(t)}$$

When the hazards ratio (HR) is available (as it is frequently after Cox regression analysis), it can alternatively be used to derive the survival probability of the treatment group at a specified time point. The HR is a ratio of the rate of event in the treatment arm over the rate in the control arm over a time interval. The NNT would then be 1/[Sb(t)^HR–Sb(t)]. For example, the CHANCE trial of dual antiplatelet therapy compared to monotherapy for stroke/transient ischemic attack showed a survival free of stroke rate of 0.89 in the aspirin-only group at 90 days with a hazard ratio of 0.68. Thus, the NNT = 1/[0.89^0.68–0.89] or 29.6 patients.¹⁷

$$\text{NNT}=\frac{1}{\mathit{Sb}(t)\text{HR}-\mathit{Sb}(t)}$$

Intuitively, the length of follow-up or specified time point of analysis will shape the NNT in binary incidence and time-to-event studies, respectively. In other words, for binary studies, the NNT will fall as the time from start of treatment increases. An example of this is the binary incidence in The Stroke Prevention by Aggressive Reduction in Cholesterol Levels (SPARCL) trial where the NNT with high-intensity statins to prevent a stroke at one year was 258 compared to 45 at five years.¹⁸ Therefore, for time-to-event studies, there is not one NNT but rather a continuous value as a spectrum over various time points. Thus, specified clinically relevant time points are often chosen to present these data (e.g. 90 days, one year, five years), and should always be sought when interpreting NNT reporting for such trials. Moreover, it should be noted that disease risk in itself is not a constant either, as we know the risk of stroke is higher in the acute phase compared to a more constant chronic risk. In addition, patients differ from one another, and baseline risks will vary accordingly. Hence, the NNT should be interpreted as a general guide from a pooled and selective trial population undergoing care, just like any other statistical parameter from trials.

In the neuroendovascular literature, we frequently deal with the ordinal modified Rankin scale (mRS). While some use this to create a binary variable of functional independence (e.g. mRS 0–2 vs. 3–6), there is value in looking at shifts in this scale, given the clinical value it can represent for patients and providers. Using ordinal logistic regression, recent MT trials have been able to analyze the more subtle treatment effects of one-point improvements directly throughout the scale and provide so-called ordinal NNTs concurrently. While the interpretation of the NNT remains the same between the NNT and the ordinal NNT, the calculation differs. Some propose a simplified formula of 1/(proportion with better outcome)–(proportion with worse outcome).¹⁹ This tends to require a matching process where similar patients (e.g. of similar age, sex, and stroke severity) are compared one-to-one and the outcome is ruled in favor of the control or intervention arm to provide the proportion in the NNT equation. Other methods utilize an expert review of outcomes to create joint distribution tables that depict the shifts in mRS.²⁰ Thus, it is important to understand the uniqueness of this approach, but the calculation itself remains an in-depth expert statistician endeavor. Interestingly, the NNT is generally lower with this analysis than with binary pooled analysis, supporting lower n’s for parallel trials and fewer false-neutral results.

$$\begin{array}{c}\text{OrdinalNNT}\\ =\frac{1}{\{\begin{array}{c}(\text{proportionwithbetteroutcome})\\ -(\text{proportionwithworseoutcome})\end{array}\}}\end{array}$$

To understand the basics, consider the following example. Drug x versus placebo is being tested in 50 - to 70-year-olds, and you decide your outcome is a scale of improvement from 0 to 10, but any improvement is believed to be clinically significant. As such, you can organize this ordinal outcome into a good outcome (increase or no change in the number on scale) and bad outcome (a decrease in the number on the scale). Given all patients are not equal, you divide them up into like-individuals—in this case, those aged 50–60 and those aged 61–70. If 50/100 had a good outcome in the 50–60 group and 70/100 had a good outcome in the 61–70 group, then the NNT = 1/(120/200)–(80/200) = 5 people need to be treated with drug x for any improvement in the scale.

As with any statistical calculation, there needs to be validation of significance. In the NNT, the confidence intervals (CI) for the ARR are the corresponding analysis. This means that the NNT can be reported with CI being the NNT for the low and high number of the ARR confidence intervals. For example, if the ARR is 0.2 and the 95% CI is 0.1–0.3, the NNT would be five patients with a 95% CI of 3–10 patients. While this can be useful, it is rarely presented in this fashion, given statistical significance is derived for the pre-NNT calculations of ARR, HR, or Kaplan–Meier analysis. This is partly because nonsignificant studies potentially reach 0% or negative risk reduction, making the fraction mathematically undefined. Speculatively, this may also be a newer consideration for the NNT calculation that has not reached widespread acceptance, and it may be considered confusing to show ranges of patient numbers. While non-traditional, bringing forth these CI NNTs in statistically significant studies would provide more information and greater confidence in the data for the clinicians on the ground making treatment decisions.

NNT and stroke

Recent thrombectomy trials have published their NNT. The DAWN trial revealed a NNT of 2 for better score for disability at 90 days and 2.8 for functional independence.⁶ SWIFT Prime found a NNT of 2.6 for improved disability outcome and 4 for functional independence.⁸ EXTEND-IA reported a NNT of 2.8 to achieve at least a one-point improvement on the functional score, and a NNT of 3.2 to achieve functional independence at 90 days.⁷ A corollary to MT from a distinct field is primary angioplasty for STEMI compared to thrombolytics; this has shown short-term mortality benefit with a NNT of 50.²¹

For perspective, let us look at intravenous therapies in acute stroke. The NINDS trial reported that 90-day mRS of 0–1 was achieved in 39% of patients in the tissue plasminogen activator (tPA) group compared to 26% for placebo, giving a treatment effect of 13% and a corresponding NNT of 8; taking any improvement in mRS gives a NNT of 3.1.^20,22 ECASS-3 looking at alteplase in the 3 - to 4.5-hour time window showed a 90-day mRS of 0–1 in 52.4% of the experimental arm compared to 45.2%, for a NNT of 14.²³ It is important to note the profound time dependence of intravenous tPA where the NNT for benefit are 3.6 for 0–90 minutes, 4.3 for 91–180 minutes, 5.9 for 181–270 minutes, and 19.3 for 271–360 minutes.²⁴ In addition, there is a nontrivial risk calculated as a NNH of 126 for severe disability or death, and 29.7–40.1 for any decline in mRS.²⁵

What sort of NNT are seen in stroke-prevention interventions? For carotid diseases, carotid endarterectomy in symptomatic high-grade stenosis in the NASCET trial led to an ARR of 17% at two years or a NNT of 6.¹⁶ Treatment of atherosclerosis with statins in the SPARCL trial generated a NNT of 45 at five years of treatment, with the number likely much larger for shorter time frames such as 90 days.¹⁸ Despite pooling six primary prevention trials, aspirin does not seem to have a role in primary prevention of stroke and, if used, leads to a 0.03% increase in risk of major extracranial hemorrhage or a NNH of 3333.²⁶ Secondary prevention with aspirin remains the mainstay of treatment for stroke, with a NNT of 227 per year or almost 67 patients at five years of treatment.²⁶ Moreover, in the Chinese Acute Stroke Trial (CAST) and the International Stroke Trial (IST), the early administration of aspirin within the first 48 hours after stroke led to a reduction in recurrent stroke, with a NNT between 91 and 200.^27,28

It is important to highlight that the NNT can also be dramatically affected by the timing of interventions. This can be illustrated by the hemicraniectomy trials. For example, the Hemicraniectomy After Middle Cerebral Artery Infarction with Life-threatening Edema (HAMLET) trial, which looked at hemicraniectomy within four days of stroke found an ARR for improved outcomes of 0 compared to 51% in a pooled analysis of patients (from DECIMAL, DESTINY, and HAMLET) treated within 48 hours or a NNT of 2.^29,30

Conclusion

The NNT is a powerful statistical tool to help understand treatment effect. The closer the NNT is to 1, the more effective the treatment. With the advent of new stroke trials, the NNT can help the NI community to gauge the comparative treatment effect of various interventions at different time points and communicate this effectively with patients, health-care providers, and other key stakeholders.

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The authors received no financial support for the research, authorship, and/or publication of this article.

References