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Difficulty: HardMeasures of Association and Impact

A pragmatic, open-label, multicenter clinical trial investigates a novel PCSK9 inhibitor added to high-intensity statin therapy versus statin therapy alone for the secondary prevention of myocardial infarction (MI). The study enrolls patients with severe familial hypercholesterolemia who have a history of a prior MI.

Patients are followed for a period of 5 years. The researchers present the following primary outcome data regarding the incidence of recurrent MI:

Treatment GroupTotal Patients (nn)Recurrent MI Events
Novel Therapy + Statin4,000280
Statin Alone (Control)4,000400

The 95% confidence interval for the absolute risk difference between the two groups is reported as [0.015,0.045][0.015, 0.045].

Based on the trial data provided, which of the following is the most accurate statistical interpretation regarding the primary endpoint?

  1. The relative risk reduction is 30%, and 34 patients must be treated to prevent one recurrent MI.Answer
  2. B
    The absolute risk reduction is 30%, and 4 patients must be treated to prevent one recurrent MI.
  3. C
    The relative risk reduction is 30%, and 33 patients must be treated to prevent one recurrent MI.
  4. D
    The number needed to treat to prevent one recurrent MI would remain 34 even if the drug were prescribed to a lower-risk population.
  5. E
    The absolute risk reduction is 3%, but this finding is not statistically significant because the 95% confidence interval for the risk difference does not include 1.0.

Answer

The relative risk reduction is 30%, and 34 patients must be treated to prevent one recurrent MI.
Based on the trial data, the Control Event Rate (CER) is 400/4000=0.10400/4000 = 0.10 and the Experimental Event Rate (EER) is 280/4000=0.07280/4000 = 0.07. The Relative Risk Reduction (RRR) is calculated as CER−EERCER\frac{\text{CER} - \text{EER}}{\text{CER}}, which equals 0.10−0.070.10=30%\frac{0.10 - 0.07}{0.10} = 30\%. The Absolute Risk Reduction (ARR) is CER−EER=0.03\text{CER} - \text{EER} = 0.03. The Number Needed to Treat (NNT) is the inverse of the ARR (10.03=33.33\frac{1}{0.03} = 33.33). Standard epidemiological convention dictates that NNT must always be rounded up to the next whole number (ceiling function) to ensure at least one event is statistically prevented. Therefore, the NNT is 34.

Step-by-Step Solution

1
Calculate the incidence (risk) in both groups.
Control Event Rate (CER) = 400/4,000=0.10400 / 4,000 = 0.10 (10%). Experimental Event Rate (EER) = 280/4,000=0.07280 / 4,000 = 0.07 (7%).
Baseline incidence rates are required to calculate all subsequent measures of association and impact.
2
Calculate the Relative Risk Reduction (RRR).
RRR=CER−EERCER=0.10−0.070.10=0.30\text{RRR} = \frac{\text{CER} - \text{EER}}{\text{CER}} = \frac{0.10 - 0.07}{0.10} = 0.30 (30%).
RRR represents the proportion of baseline risk that is removed by the intervention.
3
Calculate the Absolute Risk Reduction (ARR).
ARR=CER−EER=0.10−0.07=0.03\text{ARR} = \text{CER} - \text{EER} = 0.10 - 0.07 = 0.03 (3%).
ARR is the direct difference in risk between the two groups, necessary for calculating the Number Needed to Treat.
4
Calculate the Number Needed to Treat (NNT).
NNT=1ARR=10.03=33.33\text{NNT} = \frac{1}{\text{ARR}} = \frac{1}{0.03} = 33.33. Rounded up = 34.
By strict statistical convention, NNT is always rounded UP to the next whole number (ceiling function) to ensure that at least one full event is prevented.
5
Evaluate statistical significance using the provided confidence interval.
The 95% CI is [0.015,0.045][0.015, 0.045]. Because it does not cross 0 (the null value for a difference), the ARR is statistically significant.
Understanding the correct null value is critical; differences use 0, whereas ratios use 1.0.

Key Concept

Calculation of Absolute Risk Reduction (ARR), Relative Risk Reduction (RRR), Number Needed to Treat (NNT) with proper rounding conventions, and interpretation of risk difference confidence intervals.
Estimated Time:2m 0s
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Topics

Measures of Association and Impact

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