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Difficulty: Very hardMeasures of Disease Frequency and Association

A randomized, double-blind trial is conducted to evaluate a new monoclonal antibody targeting interleukin-5 (IL-5) in patients with severe eosinophilic asthma. The study follows participants for exactly 12 months to monitor for acute asthma exacerbations requiring hospital admission. According to the published results, patients receiving the new biologic agent experienced an exacerbation rate of 3% during the study period. Furthermore, the authors report that this treatment yielded a 40% relative risk reduction in hospital-requiring exacerbations when compared to standard therapy. Based on the provided data, how many patients must receive the new monoclonal antibody for one year to prevent a single acute asthma exacerbation?

  1. A
    2
  2. B
    20
  3. C
    33
  4. 50Answer
  5. E
    83

Answer

50
The correct answer is 50 because finding the Number Needed to Treat requires the Absolute Risk Reduction (ARR), which is the difference between the Control Event Rate (CER) and the Treatment Event Rate (TER). Given RRR=40%RRR = 40\% and TER=3%TER = 3\%, one must first derive the CER: 0.40=(CER−0.03)/CER0.40 = (CER - 0.03) / CER, which solves to CER=0.05CER = 0.05. The ARR=0.05−0.03=0.02ARR = 0.05 - 0.03 = 0.02. The NNT is the inverse of the ARR (1/0.02=501 / 0.02 = 50).

Step-by-Step Solution

1
Extract the given variables from the clinical scenario.
Treatment Event Rate (TER) = 3%3\% (0.030.03), Relative Risk Reduction (RRR) = 40%40\% (0.400.40).
Identifying the known parameters is the prerequisite for calculating missing association and frequency metrics.
2
Use the Relative Risk Reduction formula to solve algebraically for the unstated Control Event Rate (CER).
RRR=CER−TERCER⇒0.40=CER−0.03CER⇒0.40×CER=CER−0.03⇒0.60×CER=0.03⇒CER=0.05RRR = \frac{CER - TER}{CER} \Rightarrow 0.40 = \frac{CER - 0.03}{CER} \Rightarrow 0.40 \times CER = CER - 0.03 \Rightarrow 0.60 \times CER = 0.03 \Rightarrow CER = 0.05 (5%5\%).
The Absolute Risk Reduction (ARR) requires both the CER and TER. Since only RRR and TER are provided, the CER must be derived mathematically first.
3
Calculate the Absolute Risk Reduction (ARR).
ARR=CER−TER⇒ARR=0.05−0.03=0.02ARR = CER - TER \Rightarrow ARR = 0.05 - 0.03 = 0.02 (2%2\%).
The ARR represents the absolute difference in risk between the control and treatment groups, which is the necessary denominator for calculating the Number Needed to Treat.
4
Calculate the Number Needed to Treat (NNT).
NNT=1ARR⇒NNT=10.02=50NNT = \frac{1}{ARR} \Rightarrow NNT = \frac{1}{0.02} = 50.
The NNT yields the final number of patients who must receive the therapy over the study period to prevent one additional adverse event.

Key Concept

Calculating the Number Needed to Treat (NNT) through the algebraic derivation of the Control Event Rate (CER) when only the Treatment Event Rate (TER) and Relative Risk Reduction (RRR) are provided.
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Topics

Measures of Disease Frequency and Association

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