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Table 1 Minimum and maximum error rates of DerSimonian-Laird and Hartung-Knapp-Sidik-Jonkman methods for mixtures of trial sizes

From: The Hartung-Knapp-Sidik-Jonkman method for random effects meta-analysis is straightforward and considerably outperforms the standard DerSimonian-Laird method

Outcome   No of Equally sized One small trial 50–50 One large trial
  I2 trials DL HKSJ DL HKSJ DL HKSJ DL HKSJ
Continuous 0 2-20 3.4–4.6 4.5–6 3.4–4.5 4.7–5.4 3.3–4.1 4.6–5.4 3.2–4.4 4.5–5.7
0.25–0.9 2 6–25 4.7–5.4 13.8–30.9 6.5–9.2 13.8–30.9 6.5–9.2 13.8–30.9 6.5–9.2
3 5.9–17.5 4.7–5.6 10.8–21.7 6–8 10.2–20.8 5.9–7.7 13.7–22.1 7.1–10.7
4 5.6–14.2 4.5–5.5 9–16.8 5.6–7 11.9–18.4 6.6–9.6 12.6–17.3 5.9–10.5
5 5.7–12.7 4.7–5.5 8.2–13.6 5.5–6.7 9.9–14.7 5.6–7.9 11.6–14.5 5.3–9.9
10 5.6–8.8 4.8–5.6 6.4–8.8 5–5.6 9–10.3 5.4–7.2 8.5–10 5.3–8.8
20 5.6–6.6 4.6–5.3 5.8–7.1 4.8–5.5 7.1–7.8 5–6.4 6.9–7.8 4.9–7.2
Risk ratio 0 2-20 0.9–4.2 2.1–6.9 2.8–4.1 2.7–6.5 3.0–4.1 2.7–6.8 2.7–4.3 2.7–5.5
0.25–0.9 2 2.5–26.3 2.8–6.7 14.3–33.7 6–10.2 14.3–33.7 6–10.2 14.3–33.7 6–10.2
5 2.5–12.9 3.9–5.7 7.9–15 5.5–7.2 9.8–15.7 5.2–7.9 11.4–14.2 5.2–10.6
10 2.6–8.9 2.7–5.4 6–9.7 3.8–5.7 8.6–11 4.8–9.1 7.3–10.1 3.6–8.7
Odds ratio 0 2-20 1.3–4.3 2.7–6.1 3–4 3–6.7 3–4 3–6.7 2.9–4.1 3–5.4
0.25–0.9 2 2.9–25.3 3.2–5.9 13.7–33.5 6.1–9.6 13.7–33.5 6.1–9.6 13.7–33.5 6.1–9.6
5 3–12.7 3.9–5.3 7.9–14.4 5.4–6.9 9.9–15.8 5.3–8.1 11.6–14.2 5.2–10.5
10 2.9–8.8 3.2–5.3 5.7–9.6 3.9–5.7 8.4–11.7 4.8–9.3 7.4–10.1 3.8–8.8
  1. Error rates for the following scenarios: equally sized trials; one small trial, 1/10th of other trials; 50–50% small and large trials (ratio 1:10); one large trial (10 times larger than other trials). No of trials: number of trials. DL: DerSimonian & Laird meta-analysis method. HKSJ: Hartung-Knapp-Sidik-Jonkman meta-analysis method.