Examkin

Question

Difficulty: Very hardMeasures of Association and Impact

During a weekly journal club, an attending physician presents a recently published multicenter, double-blind trial evaluating a novel monoclonal antibody for the prevention of severe asthma exacerbations. The trial enrolled 2,000 patients, who were assigned in a 1:1 ratio to receive either the new drug or a placebo.

Over a 1-year follow-up period, 150 patients in the placebo group experienced a severe exacerbation, compared to 107 patients in the treatment group. The 95%95\% confidence interval for the absolute risk reduction was reported as 0.0150.015 to 0.0710.071.

The attending states: "This drug is highly effective. It reduces the risk of exacerbations by roughly 29%29\%. Therefore, we only need to treat 4 patients to prevent one severe exacerbation. Furthermore, the results are statistically significant because the confidence interval for the risk difference is entirely above zero."

Which of the following statements accurately identifies the true Number Needed to Treat (NNT) and the primary conceptual error made by the attending?

  1. The true NNT is 24; the attending incorrectly calculated the NNT by taking the reciprocal of the relative risk reduction instead of the absolute risk reduction.Answer
  2. B
    The true NNT is 23; the attending incorrectly calculated the NNT by taking the reciprocal of the relative risk reduction instead of the absolute risk reduction.
  3. C
    The true NNT is 4; the attending correctly calculated the NNT but incorrectly claimed statistical significance, as the confidence interval for an absolute difference must not cross 1.
  4. D
    The true NNT is 8; the attending incorrectly calculated the overall study incidence rather than comparing the individual group event rates.
  5. E
    The true NNT is 10; the attending incorrectly calculated the NNT by taking the reciprocal of the experimental event rate instead of the absolute risk reduction.

Answer

The true NNT is 24; the attending incorrectly calculated the NNT by taking the reciprocal of the relative risk reduction instead of the absolute risk reduction.
The correct statement identifies that the true Number Needed to Treat (NNT) is 24 and that the attending mistakenly derived the NNT from the Relative Risk Reduction (RRR) instead of the Absolute Risk Reduction (ARR). The ARR is calculated by subtracting the experimental event rate (10.7%10.7\%) from the control event rate (15.0%15.0\%), yielding 4.3%4.3\% (0.0430.043). The NNT is the reciprocal of the ARR (1/0.043=23.251 / 0.043 = 23.25). Crucially, clinical biostatistics rules dictate that NNT must always be rounded UP to the next whole number (2424) to provide a conservative estimate of benefit. The attending calculated 1/0.2871 / 0.287 (the RRR), leading to a falsely low and exaggerated NNT of 4.

Step-by-Step Solution

1
Calculate the Control Event Rate (CER) and Experimental Event Rate (EER).
CER=1501000=0.150CER = \frac{150}{1000} = 0.150 (15%15\%). EER=1071000=0.107EER = \frac{107}{1000} = 0.107 (10.7%10.7\%).
Baseline incidence rates in both the placebo and treatment groups are required to determine the absolute impact of the intervention.
2
Calculate the Absolute Risk Reduction (ARR).
ARR=CER−EER=0.150−0.107=0.043ARR = CER - EER = 0.150 - 0.107 = 0.043 (4.3%4.3\%).
ARR represents the actual difference in risk between the two groups.
3
Calculate the Number Needed to Treat (NNT).
NNT=1ARR=10.043≈23.25NNT = \frac{1}{ARR} = \frac{1}{0.043} \approx 23.25.
NNT is defined mathematically as the reciprocal of the absolute risk reduction.
4
Apply clinical rounding rules for NNT.
23.2523.25 rounds UP to 2424.
Because a fraction of a patient cannot be treated, and to prevent overstating clinical efficacy, standard evidence-based medicine principles dictate that NNT is always rounded UP to the next whole number.
5
Identify the attending's calculative error.
The attending calculated 1/0.287=3.48→41 / 0.287 = 3.48 \rightarrow 4.
The attending used the Relative Risk Reduction (RRR=0.0430.150=0.287RRR = \frac{0.043}{0.150} = 0.287 or 28.7%28.7\%) instead of the ARR to calculate the NNT, a common clinical error that severely exaggerates benefit.

Key Concept

Number Needed to Treat (NNT) calculation and interpretation rules
Estimated Time:2m 0s
Rate this question

Topics

Measures of Association and Impact

More questions from this topic