Table 3.
The coverage of the 95% confidence interval (CI) and prediction interval (PI) obtained by fitting the model (1) using restricted maximum likelihood (N) and the coverage of the adjusted CI and PI using a variety of methods. The results are based on a random effects meta‐analysis with k studies and ν = 1. The table also includes the average I 2 across each of the 10 000 simulations.
| Method | Balanced studies | One small study | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| k = 3 | k = 5 | k = 7 | k = 10 | k = 100 | k = 3 | k = 5 | k = 7 | k = 10 | k = 100 | ||||
| CI | N | 89.6 | 91.0 | 92.2 | 92.9 | 94.7 | 88.4 | 90.9 | 91.9 | 92.6 | 94.8 | ||
| HK | 94.6 | 94.8 | 94.9 | 94.7 | 94.8 | 93.4 | 94.1 | 94.7 | 94.9 | 94.9 | |||
| HK2 | 99.8 | 97.7 | 96.7 | 95.9 | 95.0 | 99.7 | 97.6 | 96.6 | 95.9 | 95.1 | |||
| KR | 100 | 98.4 | 97.2 | 96.1 | 95.0 | 99.9 | 99.3 | 97.5 | 96.3 | 95.1 | |||
| SJ | 92.1 | 92.8 | 93.4 | 93.9 | 94.8 | 87.5 | 91.5 | 92.9 | 93.7 | 95.0 | |||
| SJ2 | 94.3 | 94.6 | 94.7 | 94.7 | 94.9 | 89.4 | 92.6 | 93.7 | 94.3 | 95.0 | |||
| PI | N | 100 | 92.8 | 89.0 | 88.3 | 94.9 | 100 | 93.4 | 89.5 | 89.1 | 95.3 | ||
| HK | 98.6 | 89.6 | 87.5 | 87.5 | 94.9 | 98.4 | 89.5 | 87.8 | 88.5 | 95.3 | |||
| HK2 | 100 | 92.9 | 89.1 | 88.3 | 94.9 | 100 | 93.5 | 89.8 | 89.3 | 95.3 | |||
| KR | 100 | 96.0 | 90.5 | 88.7 | 94.9 | 100 | 98.9 | 92.5 | 90.3 | 95.3 | |||
| SJ | 97.8 | 87.9 | 86.4 | 86.9 | 94.9 | 96.0 | 87.3 | 86.5 | 88.0 | 95.3 | |||
| SJ2 | 98.5 | 89.3 | 87.2 | 87.4 | 94.9 | 96.8 | 88.4 | 87.2 | 88.3 | 95.3 | |||
| I 2(%) | 33.2 | 38.7 | 40.9 | 43.1 | 52.5 | 33.7 | 39.3 | 42.0 | 44.6 | 52.8 | |||
| Method | One large study | Mixture of study sizes | |||||||||||
| k = 3 | k = 5 | k = 7 | k = 10 | k = 100 | k = 3 | k = 5 | k = 7 | k = 10 | k = 100 | ||||
| CI | N | 78.9 | 85.0 | 88.2 | 89.9 | 94.6 | 77.1 | 84.0 | 87.8 | 90.8 | 94.4 | ||
| HK | 89.1 | 90.7 | 92.2 | 92.9 | 94.7 | 85.8 | 89.9 | 92.0 | 93.9 | 95.5 | |||
| HK2 | 96.5 | 93.6 | 94.1 | 93.8 | 94.9 | 94.0 | 92.7 | 93.6 | 95.1 | 95.6 | |||
| KR | 100 | 100 | 99.5 | 98.4 | 94.9 | 97.5 | 97.4 | 97.4 | 96.9 | 95.0 | |||
| SJ | 79.1 | 85.0 | 88.5 | 90.6 | 94.8 | 73.9 | 85.7 | 89.6 | 92.1 | 94.6 | |||
| SJ2 | 78.5 | 82.9 | 86.6 | 89.4 | 94.7 | 65.5 | 66.6 | 69.3 | 72.0 | 86.9 | |||
| PI | N | 100 | 87.2 | 87.0 | 88.1 | 94.5 | 99.6 | 89.8 | 91.6 | 94.1 | 98.8 | ||
| HK | 95.8 | 85.5 | 86.4 | 87.8 | 94.5 | 94.3 | 89.2 | 91.6 | 94.1 | 98.9 | |||
| HK2 | 100 | 87.5 | 87.3 | 88.3 | 94.5 | 99.7 | 90.3 | 92.0 | 94.3 | 98.9 | |||
| KR | 100 | 100 | 99.8 | 98.3 | 94.5 | 99.7 | 99.9 | 98.4 | 97.0 | 98.9 | |||
| SJ | 88.3 | 81.9 | 84.3 | 86.7 | 94.5 | 81.2 | 86.7 | 90.8 | 93.8 | 98.8 | |||
| SJ2 | 88.3 | 81.3 | 83.8 | 86.6 | 94.5 | 81.3 | 85.9 | 90.0 | 93.0 | 98.8 | |||
| I 2(%) | 41.6 | 47.3 | 49.8 | 51.6 | 54.0 | 48.8 | 66.7 | 74.1 | 79.6 | 87.9 | |||