Confidence intervals for NNT/NNH

Confidence intervals for NNT/NNH - Precision & Significance

• The 95% Confidence Interval (CI) for an NNT or NNH indicates the precision of the point estimate. A narrow CI implies a precise estimate; a wide CI suggests more uncertainty.

• Calculation: The CI for NNT/NNH is the reciprocal of the CI for the Absolute Risk Reduction (ARR) or Absolute Risk Increase (ARI).

  • Formula: $CI_{NNT} = [1/CI_{upper}(ARR), 1/CI_{lower}(ARR)]$.
  • Note the endpoints are inverted, which can be counter-intuitive.

• Interpretation of Significance:

  • The key is whether the CI for the ARR/ARI crosses 0.
  • If the CI for ARR/ARI contains 0, the corresponding CI for NNT/NNH will span to infinity (∞).
  • An NNT/NNH confidence interval that contains ∞ is not statistically significant.

⭐ If a single 95% CI for an outcome measure contains values for both benefit (NNT) and harm (NNH), it means the underlying CI for ARR/ARI crossed zero. The result is therefore not statistically significant, and we cannot be confident if the intervention is helpful, harmful, or has no effect.

Interpretation Algorithm - Decoding the Data

• Step 1: Start with the CI for Risk Difference.

  • The CI for NNT/NNH is the reciprocal of the CI for the Absolute Risk Reduction (ARR) or Absolute Risk Increase (ARI).
  • First, calculate the CI for the risk difference (e.g., 95% CI for ARR is 0.05 to 0.15).
  • Then, invert the bounds to find the CI for NNT:
    • $CI_{NNT} = [1/ARR_{upper}, 1/ARR_{lower}]$

• Step 2: Check for Statistical Significance.

  • The key question: Does the CI for ARR/ARI cross 0?
    • No (Significant): The effect is real. The CI for NNT/NNH will be a simple range of positive numbers (e.g., NNT of 7 to 20).
    • Yes (Not Significant): The effect is not statistically significant. The CI for NNT/NNH becomes discontinuous.

• Step 3: Interpret the NNT/NNH CI.

⭐ When a 95% CI for an effect includes values for both benefit and harm (e.g., NNT of 10 to NNH of 15), it means the CI for the underlying risk difference crossed zero. This renders the result statistically non-significant, and we cannot be confident if the intervention helps or hurts.

High‑Yield Points - ⚡ Biggest Takeaways

• The 95% CI for NNT/NNH is the reciprocal of the 95% CI for the ARR/ARI.
• If the CI for the risk difference (ARR/ARI) crosses zero, the NNT/NNH's CI will include infinity.
• An NNT/NNH CI that includes infinity is not statistically significant.
• This implies the true effect could range from benefit to harm.
• A wide CI indicates poor precision of the NNT/NNH point estimate.