NNT/NNH Calculator & Log-rank to Hazard Ratio

Overview

Systematic reviews frequently encounter trials that report incomplete survival data – a log-rank p-value but no Hazard Ratio, or probabilities without a directly computed NNT. ParCC bridges these gaps with two tools in the HR Converter module.

Tutorial A: Extracting a Hazard Ratio from a Log-rank Test

The Scenario – Adjuvant Chemotherapy in Colon Cancer

An older trial (published 2005) reports:

The paper does not report a Hazard Ratio, which you need for your meta-analysis.

The Peto Approximation

When only summary log-rank statistics are available, the Peto method estimates:

\[\ln(HR) = \pm \frac{\sqrt{\chi^2}}{\sqrt{E/4}}\]

with a 95% confidence interval:

\[\ln(HR) \pm \frac{1.96}{\sqrt{E/4}}\]

where \(E\) is the total number of events.

In ParCC

  1. Navigate to Convert > HR -> Probability & NNT > Log-rank -> HR tab.
  2. Select input type: Chi-squared statistic.
  3. Enter chi-squared = 6.8, Total events = 142.
  4. Select direction: Treatment is better (HR < 1).
  5. Result: HR = 0.68 (95% CI: 0.51 - 0.91).

Alternative: From a p-value

If the paper reports only “log-rank p = 0.009”:

  1. Select input type: p-value.
  2. Enter p = 0.009, Total events = 142.
  3. ParCC converts the p-value to a z-statistic via \(z = \Phi^{-1}(1 - p/2)\), then applies the same Peto formula.

Tutorial B: Computing NNT for a Formulary Decision

The Scenario – Hospital P&T Committee

A Pharmacy & Therapeutics committee asks: “How many patients must we treat with Drug X to prevent one additional death?” The trial reports:

The Formula

\[NNT = \left\lceil \frac{1}{ARR} \right\rceil = \left\lceil \frac{1}{p_{control} - p_{intervention}} \right\rceil\]

In ParCC

  1. Navigate to Convert > HR -> Probability & NNT > NNT/NNH tab.
  2. Select input mode: Two Probabilities.
  3. Enter Control = 0.18, Intervention = 0.12.
  4. Result: ARR = 6.0%, NNT = 17.

Interpretation: For every 17 patients treated with Drug X for 12 months, one additional death is prevented.

Other Input Modes

ParCC supports four ways to compute NNT:

Input Mode You provide ParCC calculates
Direct ARR Absolute risk reduction NNT = ceil(1/ARR)
Two Probabilities Control & intervention probabilities ARR, then NNT
RR + Baseline Relative Risk + control probability ARR = p0 x (1 - RR), then NNT
OR + Baseline Odds Ratio + control probability Converts to probabilities via Zhang & Yu, then NNT

NNT vs NNH

When the intervention increases risk (ARR < 0), the result is reported as NNH (Number Needed to Harm) with an orange warning. This happens when testing safety endpoints rather than efficacy.

When to Use These Tools

References

  1. Tierney JF, Stewart LA, Ghersi D, Burdett S, Sydes MR. Practical methods for incorporating summary time-to-event data into meta-analysis. Trials. 2007;8:16.
  2. Parmar MKB, Torri V, Stewart L. Extracting summary statistics to perform meta-analyses of the published literature for survival endpoints. Statistics in Medicine. 1998;17(24):2815-2834.
  3. Altman DG, Andersen PK. Calculating the number needed to treat for trials where the outcome is time to an event. BMJ. 1999;319(7223):1492-1495.