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
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) |