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Table 7 Standard error of the interaction effect between treatment effect and covariate (age) in each of the models in the presence of high but plausible heterogeneity in the interaction effect

From: A comparison of the statistical performance of different meta-analysis models for the synthesis of subgroup effects from randomized clinical trials

No. of trials Performance measure Model 1 Model 2 Model 3 Model 4 Model 5 Model 6 Model 7
6 Empirical SE 0.09147 (0.00145) 0.09595 (0.00152) 0.10311 (0.00163) 0.09148 (0.00145) 0.09621 (0.00152) 0.10311 (0.00163) 1.87636 (0.02968)
Model SE 0.09125 (0.01059) 0.09486 (0.01456) 0.09568 (0.01640) 0.09125 (0.01059) 0.09528 (0.01454) 0.09568 (0.01640) 1.81917 (177.01665)
Relative error in model SE −0.24168 (1.72411) −1.13917 (1.77644) −7.20306 (1.70537) − 0.24417 (1.72406) − 0.97397 (1.77358) −7.20303 (1.70537) −3.04755 (2.09350)
10 Empirical SE 0.07081 (0.00112) 0.07410 (0.00117) 0.08183 (0.00129) 0.07081 (0.00112) 0.07410 (0.00117) 0.08183 (0.00129) 1.22368 (0.01935)
Model SE 0.07072 (0.00378) 0.07411 (0.00540) 0.07776 (0.00676) 0.07072 (0.00378) 0.07412 (0.00534) 0.07776 (0.00676) 1.23611 (36.09575)
Relative error in model SE −0.13873 (1.66686) 0.00346 (1.71505) −4.96244 (1.65106) −0.13683 (1.66689) 0.03390 (1.71257) −4.96244 (1.65106) 1.01558 (1.86656)
16 Empirical SE 0.05543 (0.00088) 0.05794 (0.00092) 0.06588 (0.00104) 0.05543 (0.00088) 0.05800 (0.00092) 0.06588 (0.00104) 0.93050 (0.01472)
Model SE 0.05606 (0.00144) 0.05883 (0.00200) 0.06377 (0.00321) 0.05606 (0.00144) 0.05867 (0.00196) 0.06377 (0.00321) 0.92118 (10.53523)
Relative error in model SE 1.13187 (1.65210) 1.53029 (1.68156) −3.21023 (1.64405) 1.13079 (1.65209) 1.15699 (1.67359) −3.21024 (1.64405) −1.00201 (1.70189)
20 Empirical SE 0.05012 (0.00079) 0.05259 (0.00083) 0.05887 (0.00093) 0.05012 (0.00079) 0.05253 (0.00083) 0.05887 (0.00093) 0.81872 (0.01295)
Model SE 0.05005 (0.00089) 0.05253 (0.00128) 0.05719 (0.00207) 0.05005 (0.00089) 0.05253 (0.00130) 0.05719 (0.00207) 0.80839 (6.13561)
Relative error in model SE −0.14153 (1.61861) −0.10115 (1.64049) −2.86836 (1.62743) −0.14211 (1.61860) 0.00514 (1.64349) −2.86838 (1.62743) −1.26192 (1.66352)
26 Empirical SE 0.04289 (0.00068) 0.04523 (0.00072) 0.05107 (0.00081) 0.04289 (0.00068) 0.04517 (0.00071) 0.05107 (0.00081) 0.67892 (0.01074)
Model SE 0.04404 (0.00054) 0.04615 (0.00074) 0.05064 (0.00127) 0.04404 (0.00054) 0.04612 (0.00074) 0.05064 (0.00127) 0.69302 (3.18236)
Relative error in model SE 2.69132 (1.65593) 2.02827 (1.65925) −0.83126 (1.64152) 2.69167 (1.65594) 2.10172 (1.65950) −0.83126 (1.64152) 2.07716 (1.68652)
30 Empirical SE 0.04099 (0.00065) 0.04331 (0.00068) 0.04889 (0.00077) 0.04099 (0.00065) 0.04323 (0.00068) 0.04889 (0.00077) 0.62743 (0.00992)
Model SE 0.04073 (0.00040) 0.04282 (0.00058) 0.04681 (0.00092) 0.04073 (0.00040) 0.04278 (0.00058) 0.04681 (0.00092) 0.63396 (2.30260)
Relative error in model SE −0.63932 (1.59872) −1.13154 (1.60574) −4.27073 (1.57354) −0.64006 (1.59871) −1.03999 (1.60736) −4.27072 (1.57354) 1.03939 (1.66192)
40 Empirical SE 0.03480 (0.00055) 0.03687 (0.00058) 0.04180 (0.00066) 0.03480 (0.00055) 0.03685 (0.00058) 0.04180 (0.00066) 0.55085 (0.00871)
Model SE 0.03545 (0.00022) 0.03722 (0.00034) 0.04099 (0.00053) 0.03545 (0.00022) 0.03719 (0.00034) 0.04099 (0.00053) 0.54445 (1.23398)
Relative error in model SE 1.87182 (1.63128) 0.94769 (1.63044) −1.92503 (1.59642) 1.87298 (1.63130) 0.93484 (1.62997) −1.92503 (1.59642) −1.16099 (1.60819)
50 Empirical SE 0.03198 (0.00051) 0.03364 (0.00053) 0.03806 (0.00060) 0.03198 (0.00051) 0.03368 (0.00053) 0.03806 (0.00060) 0.48328 (0.00764)
Model SE 0.03165 (0.00014) 0.03338 (0.00021) 0.03673 (0.00034) 0.03165 (0.00014) 0.03337 (0.00021) 0.03673 (0.00034) 0.48219 (0.75386)
Relative error in model SE −1.03205 (1.58095) −0.79436 (1.59442) −3.48739 (1.56226) −1.03213 (1.58094) −0.91692 (1.59272) −3.48739 (1.56226) − 0.22640 (1.61322)
  1. Values in brackets are Monte Carlo standard errors