Network Meta-Analysis (NMA) requires all treatment effects on a common scale. However, trials report results as Odds Ratios, Relative Risks, or Standardised Mean Differences depending on the outcome type. ParCC provides bidirectional conversions to unify these metrics before pooling.
You are conducting an NMA comparing three antidepressants. Your systematic review found:
To pool these in a single NMA, you need all three on the same scale.
The Zhang & Yu (1998) formula accounts for baseline risk:
\[RR = \frac{OR}{1 - p_0 + p_0 \times OR}\]
where \(p_0\) is the baseline risk in the control group.
In ParCC:
If the outcome were rare (<10%), OR ~ RR and conversion wouldn’t matter. But with a 30% baseline risk, the OR of 1.85 overstates the effect compared to the RR of 1.42. Failing to convert would bias the NMA.
The Chinn (2000) approximation uses the logistic distribution:
\[\ln(OR) = SMD \times \frac{\pi}{\sqrt{3}} \approx SMD \times 1.8138\]
In ParCC:
To bring Trial C onto the RR scale (matching Trials A and B):
\[\ln(RR) = \ln\left(\frac{e^{\ln(OR)}}{1 - p_0 + p_0 \times e^{\ln(OR)}}\right)\]
ParCC chains the Chinn and Zhang & Yu methods automatically.
| Scenario | Conversion | Method |
|---|---|---|
| NMA mixing binary effect measures | OR -> RR or RR -> OR | Zhang & Yu (1998) |
| NMA mixing binary + continuous outcomes | SMD -> log(OR) | Chinn (2000) |
| Clinical interpretation of OR | OR -> RR | Zhang & Yu – RR is more intuitive |
| Checking the rare-disease approximation | Compare OR and RR at your baseline risk | If they diverge >10%, convert explicitly |
When the baseline risk is very low (\(p_0 < 0.10\)), OR ~ RR mathematically. ParCC displays a note when this approximation holds. For common outcomes (>10%), always convert explicitly.