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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.