Table 1.
Minimum and maximum error rates of DerSimonian-Laird and Hartung-Knapp-Sidik-Jonkman methods for mixtures of trial sizes
|
Outcome |
|
No of |
Equally sized |
One small trial |
50–50 |
One large trial |
||||
|---|---|---|---|---|---|---|---|---|---|---|
| I 2 | 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 | ||
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.