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Home , Number needed to harm, Number needed to treat

Confidence Interval for NNT • As with other estimates, it is important that the uncertainty in the estimated number needed to treat is accompanied by a confidence interval.

• A common method is that proposed by Cook and Sacket (1995) and based on calculating first the confidence interval NUMBER NEEDED TO TREAT for the difference between the two proportions. • The result of this calculation is 'inverted' (ie: 1/CI) to give a (CONTINUATION) confidence interval for the NNT. Hamisu Salihu, MD, PhD

Confidence Interval for NNT Confidence Interval for NNT

• This computation assumes that ARR estimates from a sample of similar trials are normally distributed, so we can use the 95th percentile point from the standard normal distribution,

z0.95 = 1.96, to identify the upper and lower boundaries of the 95% CI.

Solution Class Exercise

• In a parallel to test the benefit of additional anti‐ hyperlipidemic agent to standard , patients with acute (MI) were randomly assigned to the standard therapy or the new treatment that contains standard therapy and simvastatin (an HMG‐CoA reductase inhibitor). At the end of the study, of the 2223 patients in the control group 622 died as compared to 431 of 2221 patients in the Simvastatin group. – Calculate the NNT and the 95% CI for Simvastatin – Is Simvastatin beneficial as additional therapy in acute cases of MI?

1 Confidence Interval Number Needed to for NNT Treat

• The NNT to prevent one additional death is 12 (95% • A negative NNT indicates that the treatment has a CI, 9‐16). harmful effect

• Accordingly, the results are significant if the NNT 95% • E.g., an NNT of ‐20 indicates that if 20 patients are CI does not include infinity. treated with the new treatment, one fewer would have a good outcome than if they all received • The 95% CI for the NNT associated with a non‐ standard treatment significant treatment effect is difficult to interpret • A negative NNT is called the and thus is frequently omitted from articles. (NNTH)

Number needed to Number needed to harm (NNH) harm (NNH)

• The number needed to harm is an analogous concept • The NNTH is defined as the number of patients to express the probability of additional adverse needed to be treated for one additional patient to be events occurring in randomized controlled trials harmed. because of treatment. • In other words, NNTH represents the number of • In both NNT and NNH, the concept of people exposed to a given treatment such that on is converted into a number of individuals, a more average and over a given follow up period, one intuitively understandable quantity. additional person experiences the adverse effect of interest

Number needed to Deriving NNT and harm (NNH) NNTH given the OR

• The NNTH is an estimator of risk that focuses only on • Let’s now derive a relationship between the relative the additional risk conferred by a treatment; risk (oftentimes given as the OR) and the NNT as well as the NNTH • It does not express the total risk attributable to the combination of the background risk and the risk due • Assuming in a clinical trial, we offer a new treatment to exposure. to a randomized group (A) and a to a randomized control group (B) • This should be taken into consideration when using the NNTH as an adjunct to clinical decision making • Assuming the treatment is supposed to be beneficial and will lead to a lowered frequency of the outcome (e.g., death)

2 Deriving NNT and NNTH given the OR Deriving NNT and NNTH given the OR

Attributable risk (AR)Ŧ (AR)

• This is a measure of association based on an absolute difference between two risk estimates. Population APopulation B • In computational terms, Attributable risk (AR) or risk difference is the difference between the rates in exposed and non‐exposed groups (could be cumulative incidence or incidence density rate)

Ie ‐I0 = AR • In a , AR is calculated as the difference in cumulative incidences (risk difference) or incidence densities (rate difference). Ie E Ē E • AR reflects the absolute risk of the exposure or the excess risk of the Ē outcome (e.g. ) in the exposed group compared with the non‐ I0 exposed group.

• AR is sometimes referred to as attributable risk in the exposed because it is used to quantify risk in the exposed group that is attributable to the exposure.

Attributable risk (AR) Attributable risk (AR) percentŦ

• The attributable risk is actually the incidence of the disease in • While the AR gives the absolute excess risk, interest may the exposed that would be eliminated if exposure were sometimes lie in knowing what % of the entire risk in the eliminated, assuming causal relationship. exposed group this represents.

• Because of this some utilize the expression “etiologic fraction” • AR% measures that attribute. It is defined as the percent of to describe the AR. the incidence of the disease in the exposed that is due to the exposure.Ŧ • This should be used with caution when there is some reasonable certainty regarding a causal‐relationship between • In other words, it is the percent of the incidence of the exposure and outcome disease in the exposed that would be eliminated if exposure were eliminated, assuming causality. • Otherwise, a better and non‐comital expression is the “excess fraction” which does not denote causality

3 Attributable risk (AR) percent Class QUIZ

• Suppose the risk of developing CHD in obese individuals is 60/1000 and in non‐obese = 20/1000. Assuming that 90 million people in the US are obese. How many cases of obesity‐ related CHD could be potentially prevented from occurring in the US through an obesity intervention program that is 100%, 75%, 25% and 10% effective respectively?

Solution

• Calculate the absolute excess risk due to obesity. This is given by 60‐20 per 103 = 40/1000

• 90 million adults are exposed (obese) and the excess cases due to their being obese will be 40/1000 × 90 million = 3.6 million. This is potentially the maximum number preventable through the obesity intervention program

• Assuming 100% effectiveness, the intervention should prevent 3.6 million new cases of CHD; 75%, 25% and 10% effectiveness will potentially prevent 2.7 million, 0.9 million and 360,000 cases respectively.

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