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The number needed to treat (NNT) or number needed to treat for an additional beneficial outcome (NNTB) is an
epidemiological Epidemiology is the study and analysis of the distribution (who, when, and where), patterns and determinants of health and disease conditions in a defined population. It is a cornerstone of public health, and shapes policy decisions and evid ...
measure used in communicating the effectiveness of a health-care intervention, typically a treatment with
medication A medication (also called medicament, medicine, pharmaceutical drug, medicinal drug or simply drug) is a drug used to diagnose, cure, treat, or prevent disease. Drug therapy ( pharmacotherapy) is an important part of the medical field and ...
. The NNT is the average number of patients who need to be treated to prevent one additional bad outcome (e.g. the number of patients that need to be treated for one of them to benefit compared with a control in a clinical trial). It is defined as the inverse of the
absolute risk reduction The risk difference (RD), excess risk, or attributable risk is the difference between the risk of an outcome in the exposed group and the unexposed group. It is computed as I_e - I_u, where I_eis the incidence in the exposed group, and I_u is th ...
, and computed as 1/(I_u - I_e), where I_e is the incidence in the treated (exposed) group, and I_u is the incidence in the control (unexposed) group. counterfactual conditionals Counterfactual conditionals (also ''subjunctive'' or ''X-marked'') are conditional sentences which discuss what would have been true under different circumstances, e.g. "If Peter believed in ghosts, he would be afraid to be here." Counterfactual ...
, relaxes this assumption and yields bounds on NNT. A type of
effect size In statistics, an effect size is a value measuring the strength of the relationship between two variables in a population, or a sample-based estimate of that quantity. It can refer to the value of a statistic calculated from a sample of data, the ...
, the NNT was described in 1988 by
McMaster University McMaster University (McMaster or Mac) is a public research university in Hamilton, Ontario, Canada. The main McMaster campus is on of land near the residential neighbourhoods of Ainslie Wood and Westdale, adjacent to the Royal Botanical Ga ...
's Laupacis, Sackett and Roberts. The ideal NNT is 1, where everyone improves with treatment and no one improves with control. A higher NNT indicates that treatment is less effective. NNT is similar to number needed to harm (NNH), where NNT usually refers to a therapeutic intervention and NNH to a detrimental effect or risk factor. A combined measure, the number needed to treat for an additional beneficial or harmful outcome (NNTB/H), is also used.


Relevance

The NNT is an important measure in
pharmacoeconomics Pharmacoeconomics refers to the scientific discipline that compares the value of one pharmaceutical drug or drug therapy to another. It is a sub-discipline of health economics. A pharmacoeconomic study evaluates the cost (expressed in monetary te ...
. If a clinical endpoint is devastating enough (''e.g.''
death Death is the irreversible cessation of all biological functions that sustain an organism. For organisms with a brain, death can also be defined as the irreversible cessation of functioning of the whole brain, including brainstem, and brain ...
,
heart attack A myocardial infarction (MI), commonly known as a heart attack, occurs when blood flow decreases or stops to the coronary artery of the heart, causing damage to the heart muscle. The most common symptom is chest pain or discomfort which ma ...
), drugs with a high NNT may still be indicated in particular situations. If the endpoint is minor, health insurers may decline to reimburse drugs with a high NNT. NNT is significant to consider when comparing possible side effects of a medication against its benefits. For medications with a high NNT, even a small incidence of adverse effects may outweigh the benefits. Even though NNT is an important measure in a clinical trial, it is infrequently included in medical journal articles reporting the results of clinical trials. There are several important problems with the NNT, involving bias and lack of reliable confidence intervals, as well as difficulties in excluding the possibility of no difference between two treatments or groups. NNT may vary substantially over time, and hence convey different information as a function of the specific time-point of its calculation. Snapinn and Jiang showed examples where the information conveyed by the NNT may be incomplete or even contradictory compared to the traditional statistics of interest in survival analysis. A comprehensive research on adjustment of the NNT for explanatory variables and accommodation to time-dependent outcomes was conducted by Bender and Blettner, Austin, and Vancak et al.


Explanation of NNT in practice

There are a number of factors that can affect the meaning of the NNT depending on the situation. The treatment may be a drug in the form of a pill or injection, a surgical procedure, or many other possibilities. The following examples demonstrate how NNT is determined and what it means. In this example, it is important to understand that every participant has the condition being treated, so there are only "diseased" patients who received the treatment or did not. This is typically a type of study that would occur only if both the control and the tested treatment carried significant risks of serious harm, or if the treatment was unethical for a healthy participant (for example, chemotherapy drugs or a new method of appendectomy - surgical removal of the appendix). Most drug trials test both the control and the treatment on both healthy and "diseased" participants. Or, if the treatment's purpose is to prevent a condition that is fairly common (an anticoagulant to prevent heart attack for example), a prospective study may be used. A study which starts with all healthy participants is termed a prospective study, and is in contrast to a retrospective study, in which some participants already have the condition in question. Prospective studies produce much higher quality evidence, but are much more difficult and time-consuming to perform. In the table below: *I_e is the probability of seeing no improvement after receiving the treatment (this is 1 minus the probability of seeing improvement with the treatment). This measure applies only to the treated group. *I_u is the probability of seeing no improvement after receiving the control (this is 1 minus the probability of seeing improvement with only the control). This measure applies only to the control (unexposed) group. The control group may receive a
placebo A placebo ( ) is a substance or treatment which is designed to have no therapeutic value. Common placebos include inert tablets (like sugar pills), inert injections (like Saline (medicine), saline), sham surgery, and other procedures. In general ...
treatment, or in cases where the goal is to find evidence that a new treatment is more effective than an existing treatment, the control group will receive the existing treatment. The meaning of the NNT is dependent on whether the control group received a placebo treatment or an existing treatment, and, in cases where a placebo treatment is given, the NNT is also affected to the quality of the placebo (i.e. for participants, is the placebo completely indistinguishable from the tested treatment.


Real-life example

ASCOT-LLA manufacturer-sponsored study addressed the benefit of
atorvastatin Atorvastatin is a statin medication used to prevent cardiovascular disease in those at high risk and to treat abnormal lipid levels. For the prevention of cardiovascular disease, statins are a first-line treatment. It is taken by mouth. Common ...
10 mg (a
cholesterol Cholesterol is any of a class of certain organic molecules called lipids. It is a sterol (or modified steroid), a type of lipid. Cholesterol is biosynthesized by all animal cells and is an essential structural component of animal cell memb ...
-lowering drug) in patients with
hypertension Hypertension (HTN or HT), also known as high blood pressure (HBP), is a long-term medical condition in which the blood pressure in the arteries is persistently elevated. High blood pressure usually does not cause symptoms. Long-term high b ...
(high blood pressure) but no previous cardiovascular disease (
primary prevention Preventive healthcare, or prophylaxis, consists of measures taken for the purposes of disease prevention.Hugh R. Leavell and E. Gurney Clark as "the science and art of preventing disease, prolonging life, and promoting physical and mental hea ...
). The trial ran for 3.3 years, and during this period the
relative risk The relative risk (RR) or risk ratio is the ratio of the probability of an outcome in an exposed group to the probability of an outcome in an unexposed group. Together with risk difference and odds ratio, relative risk measures the association be ...
of a "primary event" (heart attack) was reduced by 36% (relative risk reduction, RRR). The ''absolute'' risk reduction (ARR), however, was much smaller, because the study group did not have a very high rate of cardiovascular events over the study period: 2.67% in the control group, compared to 1.65% in the treatment group. Taking atorvastatin for 3.3 years, therefore, would lead to an ARR of only 1.02% (2.67% minus 1.65%). The number needed to treat to prevent one cardiovascular event would then be 98.04 for 3.3 years.


Numerical example


Modern Approach to NNT

The above calculations for NNT are valid under monotonicity, where treatment can't have a negative effect on any individual. However, in the case where the treatment may benefit some individuals and harm others, the NNT as defined above cannot be estimated from a Randomized Controlled Trial (RCT) alone. The inverse of the absolute risk reduction only provides an upper bound, i.e., \text \leqslant 1/(I_u - I_e). The modern approach defines NNT literally, as the number of patients one needs to treat (on the average) before saving one. However, since "saving" is a counterfactual notion (a patient must recover if treated and not recover if not treated) the logic of counterfactuals must be invoked to estimate this quantity from experimental or observational studies. The probability of "saving" is captured by the Probability of Necessity and Sufficiency (PNS), where \text = P(\text). Once PNS is estimated, NNT is give as \text = \text^. However, due to the counterfactual nature of PNS, only bounds can be computed from an RCT, rather than a precise estimate. Tian and Pearl have derived tight bounds on PNS, based on multiple data sources, and Pearl showed that a combination of observational and experimental data may sometimes make the bounds collapse to a point estimate. Mueller and Pearl provide a conceptual interpretation for this phenomenon and illustrate its impact on both individual and policy-makers decisions.


See also

*
Population Impact Measures Population impact measures (PIMs) are biostatistical measures of risk and benefit used in epidemiological and public health research. They are used to describe the impact of health risks and benefits in a population, to inform health policy. Freq ...
*
Number needed to vaccinate Number needed to vaccinate (NNV) is a metric used in the evaluation of vaccines, and in the determination of vaccination policy. It is defined as the average number of patients that must be vaccinated to prevent one case of disease. It is a specif ...
* Number needed to harm


References


External links


Number Needed to Treat (NNT) Calculator
{{Clinical research studies Drug discovery Epidemiology Medical statistics