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Difficulty: HardMeasures of Association and Impact

An independent medical advisory board is reviewing a newly developed oral agent for the prevention of major adverse cardiovascular events (MACE) in patients with familial hypercholesterolemia. They are analyzing 55-year outcome data from a randomized, placebo-controlled trial to evaluate the drug's net clinical benefit.

The trial provides the following cumulative incidence data over the 55-year study period:
- Baseline risk (placebo group) of MACE: 25%25\%
- Relative risk (RR) of MACE with the new agent: 0.600.60
- Baseline risk (placebo group) of drug-induced hepatotoxicity: 2%2\%
- Relative risk (RR) of drug-induced hepatotoxicity with the new agent: 2.02.0

Based on these findings, what is the absolute difference between the Number Needed to Harm (NNH) for hepatotoxicity and the Number Needed to Treat (NNT) to prevent one MACE over the 55-year period?

(Enter the exact whole number.)

Answer: 40

Answer

The absolute difference between the NNH and NNT is 40.
To find the NNT and NNH, you must first convert the given Relative Risks (RR) and baseline risks (CER) into absolute risks for the treatment group (EER). For MACE, the CER is 0.250.25 and the RR is 0.600.60, yielding an EER of 0.150.15. The ARR is 0.25−0.15=0.100.25 - 0.15 = 0.10, meaning the NNT is 10.10=10\frac{1}{0.10} = 10. For hepatotoxicity, the CER is 0.020.02 and the RR is 2.02.0, yielding an EER of 0.040.04. The ARI is 0.04−0.02=0.020.04 - 0.02 = 0.02, meaning the NNH is 10.02=50\frac{1}{0.02} = 50. The absolute difference between the NNH (5050) and the NNT (1010) is 4040.

Step-by-Step Solution

1
Calculate the Experimental Event Rate (EER) and Absolute Risk Reduction (ARR) for MACE.
EER for MACE = 0.25×0.60=0.150.25 \times 0.60 = 0.15 (15%15\%). ARR = Control Event Rate (CER) - EER = 0.25−0.15=0.100.25 - 0.15 = 0.10 (10%10\%).
Relative Risk (RR) is the ratio of EER to CER. Therefore, EER=CER×RREER = CER \times RR. ARR is the absolute difference in risk between the control and experimental groups for a beneficial outcome.
2
Calculate the Number Needed to Treat (NNT) for MACE.
NNT=1ARR=10.10=10NNT = \frac{1}{ARR} = \frac{1}{0.10} = 10.
NNT represents the number of patients who need to receive the intervention to prevent one adverse event.
3
Calculate the Experimental Event Rate (EER) and Absolute Risk Increase (ARI) for hepatotoxicity.
EER for hepatotoxicity = 0.02×2.0=0.040.02 \times 2.0 = 0.04 (4%4\%). ARI = EER - CER = 0.04−0.02=0.020.04 - 0.02 = 0.02 (2%2\%).
Just like with beneficial outcomes, the EER for an adverse effect is calculated as CER×RRCER \times RR. ARI is the absolute increase in risk caused by the intervention.
4
Calculate the Number Needed to Harm (NNH) for hepatotoxicity and find the absolute difference.
NNH=1ARI=10.02=50NNH = \frac{1}{ARI} = \frac{1}{0.02} = 50. The absolute difference is ∣50−10∣=40|50 - 10| = 40.
NNH represents the number of patients who need to be exposed to the risk factor to cause one additional adverse event. The question specifically asks for the absolute difference between NNH and NNT.

Key Concept

Calculation of Absolute Risk Reduction (ARR), Absolute Risk Increase (ARI), Number Needed to Treat (NNT), and Number Needed to Harm (NNH) using Relative Risk (RR) and baseline incidence.
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Topics

Measures of Association and Impact

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