Table 8Comparison of coverage across random effects methods (selected scenarios with high heterogeneity)

ScenarioKProportionSample sizeExp countApproximate untransformedApproximate logitApproximate arcsineDiscrete (fraction converged)Discrete (random)Discrete (hybrid)
S150.001small<0.11.0000.0001.0000.1600.9310.989
M150.001medium0.11.0000.0000.9970.4970.9380.969
S250.005small0.21.0000.4171.0000.5830.9380.964
X150.001mixed0.20.9920.0000.6450.6480.9660.978
S350.01small0.30.9990.7660.7960.7970.9760.981
L150.001large0.61.0000.8330.8150.9540.9600.962
M250.005medium0.61.0000.8440.8060.9460.9630.965
X250.005mixed1.10.8140.7980.8260.9800.9410.922
M350.01medium1.30.9260.8960.8420.9970.9720.969
S450.05small1.70.7550.9230.8791.0000.9580.958
X350.01mixed2.20.7630.8240.7970.9980.8410.839
L250.005large3.20.7010.9230.8911.0000.9280.928
S550.1small3.40.7690.9380.9061.0000.9180.918
L350.01large6.40.7760.9110.8801.0000.8890.889
M450.05medium6.40.7680.9080.8700.9990.8820.881
X450.05mixed10.90.7170.7400.8281.0000.7020.702
M550.1medium12.80.8300.8780.8661.0000.8490.849
S650.4small13.70.8610.8800.8751.0000.8590.859
S750.5small17.10.8530.8600.8641.0000.8500.850
X550.1mixed21.90.7230.8190.8151.0000.7500.750
L450.05large31.80.8250.8660.8610.9990.8420.842
M650.4medium51.40.8350.8320.8411.0000.8150.815
L550.1large63.70.8400.8470.8611.0000.8290.829
M750.5medium64.20.8870.8640.8911.0000.8670.867
X650.4mixed87.50.8270.8540.8351.0000.8280.828
X750.5mixed109.40.8260.8370.8380.9990.8360.835
L650.4large254.60.8770.8520.8721.0000.8530.853
L750.5large318.30.8650.8290.8711.0000.8450.845
S1150.001small<0.10.0000.0001.0000.3350.8720.957
M1150.001medium0.10.2150.0000.5000.8150.9790.983
X1150.001mixed0.10.9640.0000.6530.8640.9560.962
S2150.005small0.10.8060.0000.5700.8470.9670.972
S3150.01small0.30.9960.0230.4790.9770.9880.965
M2150.005medium0.60.9990.4630.5511.0000.9750.975
L1150.001large0.61.0000.4680.5720.9990.9570.956
X2150.005mixed0.70.7880.2950.6361.0000.9530.953
M3150.01medium1.10.7810.6530.6901.0000.9740.974
X3150.01mixed1.30.6680.6230.7031.0000.9190.919
S4150.05small1.40.5270.7110.7391.0000.9460.946
S5150.1small2.70.5710.8470.8411.0000.9210.921
L2150.005large3.10.5060.8390.8280.9990.9280.928
M4150.05medium5.70.6840.9250.8781.0000.8850.885
L3150.01large6.30.6710.9140.8631.0000.8890.889
X4150.05mixed6.70.6950.8620.8411.0000.9000.900
S6150.4small10.80.9320.9220.9231.0000.9180.918
M5150.1medium11.50.8460.9280.8981.0000.8830.883
X5150.1mixed13.40.7740.9090.8601.0000.8730.873
S7150.5small13.50.9530.9230.9391.0000.9330.933
L4150.05large31.40.8600.8680.8741.0000.8440.844
M6150.4medium45.90.9340.8850.9121.0000.9040.904
X6150.4mixed53.50.9200.8960.9091.0000.9050.905
M7150.5medium57.40.9590.8770.9401.0000.9350.935
L5150.1large62.80.8900.8570.8971.0000.8600.860
X7150.5mixed66.90.9390.8920.9171.0000.9310.931
L6150.4large251.40.9390.8800.9311.0000.9200.920
L7150.5large314.20.9480.8570.9201.0000.9190.919
S1300.001small<0.10.0000.0001.0000.5460.9630.980
M1300.001medium0.10.0000.0000.2740.9560.9760.977
X1300.001mixed0.10.8260.0000.4050.9740.9720.947
S2300.005small0.10.0000.0000.2240.9780.9830.961
S3300.01small0.30.8570.0000.1971.0000.9770.977
M2300.005medium0.51.0000.1120.2841.0000.9740.974
L1300.001large0.50.9990.0740.2951.0000.9780.978
X2300.005mixed0.60.8140.0090.4201.0000.9630.963
M3300.01medium1.10.6660.3260.5011.0000.9650.965
X3300.01mixed1.30.4470.2440.5451.0000.9390.939
S4300.05small1.40.2660.4120.5801.0000.9360.936
S5300.1small2.70.4250.7550.7650.9990.9190.919
L2300.005large2.70.2450.6670.7071.0000.9160.916
M4300.05medium5.40.5530.9250.8311.0000.8620.862
L3300.01large5.50.5050.9200.8101.0000.8790.879
X4300.05mixed6.40.6660.8710.7521.0000.8610.861
M5300.1medium10.80.8000.9300.8521.0000.8230.823
S6300.4small10.90.9340.9200.9211.0000.9140.914
X5300.1mixed12.70.7890.9360.8471.0000.8690.869
S7300.5small13.60.9530.9090.9221.0000.9250.925
L4300.05large27.40.8770.8760.8921.0000.8000.800
M6300.4medium43.00.9600.9020.9301.0000.9160.916
X6300.4mixed50.80.9560.9120.9301.0000.9300.930
M7300.5medium53.80.9760.8840.9411.0000.9410.941
L5300.1large54.90.9110.8250.9011.0000.8130.813
X7300.5mixed63.50.9520.8800.9211.0000.9300.930
L6300.4large219.40.9530.8500.9271.0000.9060.906
L7300.5large274.30.9610.8470.9351.0000.9310.931

“Discrete” stands for discrete likelihood methods. Scenarios are ordered by number of studies (K), and then by expected count. Bold horizontal lines separate scenarios by number of studies. White and grey shading separates scenarios with expected counts ≤1, between 1 and 5, and ≥5. We code scenarios using two characters, a letter (indicating sample size scenarios; S=small, M=medium, L=large, X=mixed); and a number (indicating the true proportions; 1=0.001, 2=0.005, 3=0.01, 4=0.05, 5=0.1, 6=0.4, 7=0.5). The column “Discrete (fraction converged)” shows the proportion of simulations for which random effects methods converged successfully. Values of 1.000 mean that random effects methods converged successfully in all 1000 simulations in a scenario, and a value of e.g., 0.335 means that they converged in 335 out of 1000 simulations in a scenario. The columns “Discrete (random)” and “Discrete (hybrid)” are identical when the fraction converged is 1.000, because the random effects method was used in all simulations.

From: Results

Cover of Simulation-Based Comparison of Methods for Meta-Analysis of Proportions and Rates
Simulation-Based Comparison of Methods for Meta-Analysis of Proportions and Rates [Internet].
Trikalinos TA, Trow P, Schmid CH.

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