Baseline-adjusted proportional odds models for the quantification of treatment effects in trials with ordinal sum score outcomes

Buri, Muriel; Curt, Armin; Steeves, John; Hothorn, Torsten

doi:10.1186/s12874-020-00984-2

Table 2 Statistical power of the SCIM total sum score model M2 for all simulation settings (1:1 allocation) compared with that of conventional approaches

From: Baseline-adjusted proportional odds models for the quantification of treatment effects in trials with ordinal sum score outcomes

Experimental conditions (1:1 allocation)				Novel model-based methods		Conventional approaches
N total	N trtmt	N ctrl	Odds ratio	Asymptotic ePolr test based on model M2	Permutated ePolr test based on model M2	t-test M2	Wilcoxon rank sum test M2	ANCOVA M2
80	40	40	1.00	.060 [.056,.063]	.048 [.044,.051]	.049 [.046,.053]	.047 [.044,.051]	.049 [.045,.052]
120	60	60	1.00	.064 [.060,.068]	.053 [.050,.057]	.055 [.051,.059]	.053 [.050,.057]	.052 [.049,.056]
160	80	80	1.00	.059 [.055,.063]	.051 [.047,.054]	.051 [.048,.055]	.050 [.046,.053]	.050 [.047,.054]
200	100	100	1.00	.058 [.055,.062]	.050 [.047,.054]	.049 [.045,.052]	.051 [.047,.054]	.050 [.046,.053]
240	120	120	1.00	.055 [.052,.059]	.048 [.045,.052]	.050 [.046,.053]	.050 [.047,.054]	.049 [.045,.052]
80	40	40	1.25	.099 [.094,.104]	.084 [.079,.088]	.078 [.074,.082]	.076 [.072,.080]	.080 [.075,.084]
120	60	60	1.25	.123 [.118,.129]	.108 [.103,.113]	.095 [.091,.100]	.099 [.094,.104]	.094 [.089,.099]
160	80	80	1.25	.140 [.134,.145]	.125 [.120,.130]	.105 [.101,.110]	.110 [.105,.115]	.106 [.101,.111]
200	100	100	1.25	.161 [.155,.167]	.144 [.138,.150]	.120 [.115,.126]	.126 [.121,.131]	.123 [.118,.129]
240	120	120	1.25	.187 [.181,.193]	.172 [.166,.178]	.139 [.133,.144]	.149 [.143,.154]	.141 [.135,.147]
80	40	40	1.50	.196 [.189,.202]	.170 [.164,.177]	.148 [.142,.154]	.151 [.146,.157]	.149 [.143,.155]
120	60	60	1.50	.265 [.258,.273]	.238 [.232,.245]	.196 [.190,.202]	.205 [.198,.211]	.201 [.195,.208]
160	80	80	1.50	.338 [.330,.346]	.315 [.307,.322]	.253 [.246,.260]	.268 [.261,.275]	.261 [.254,.268]
200	100	100	1.50	.403 [.395,.410]	.377 [.369,.384]	.308 [.301,.315]	.323 [.315,.330]	.310 [.303,.318]
240	120	120	1.50	.465 [.457,.473]	.439 [.431,.447]	.355 [.347,.363]	.377 [.369,.385]	.368 [.360,.375]
80	40	40	1.75	.317 [.310,.325]	.286 [.278,.293]	.241 [.234,.248]	.248 [.241,.255]	.247 [.240,.254]
120	60	60	1.75	.444 [.436,.452]	.410 [.402,.418]	.342 [.334,.350]	.355 [.348,.363]	.345 [.337,.352]
160	80	80	1.75	.542 [.534,.550]	.510 [.502,.518]	.428 [.420,.436]	.448 [.440,.456]	.437 [.429,.445]
200	100	100	1.75	.640 [.633,.648]	.617 [.609,.624]	.517 [.509,.525]	.541 [.533,.549]	.527 [.519,.535]
240	120	120	1.75	.718 [.711,.726]	.696 [.689,.704]	.590 [.582,.597]	.620 [.612,.628]	.605 [.597,.613]
80	40	40	2.00	.446 [.438,.454]	.404 [.396,.412]	.344 [.336,.351]	.355 [.348,.363]	.356 [.348,.364]
120	60	60	2.00	.605 [.597,.613]	.572 [.564,.580]	.487 [.479,.495]	.507 [.499,.515]	.495 [.487,.503]
160	80	80	2.00	.722 [.715,.729]	.697 [.689,.704]	.598 [.590,.605]	.618 [.610,.626]	.610 [.602,.617]
200	100	100	2.00	.817 [.811,.824]	.799 [.793,.805]	.703 [.695,.710]	.729 [.722,.736]	.714 [.707,.722]
240	120	120	2.00	.873 [.867,.878]	.859 [.853,.864]	.772 [.765,.778]	.796 [.789,.802]	.780 [.773,.786]
80	40	40	2.25	.566 [.558,.574]	.526 [.518,.534]	.449 [.441,.457]	.462 [.454,.470]	.461 [.453,.469]
120	60	60	2.25	.728 [.721,.736]	.700 [.693,.708]	.606 [.598,.614]	.624 [.616,.632]	.619 [.611,.627]
160	80	80	2.25	.847 [.841,.853]	.827 [.821,.833]	.736 [.729,.743]	.755 [.748,.762]	.749 [.742,.756]
200	100	100	2.25	.916 [.911,.920]	.904 [.899,.909]	.829 [.823,.835]	.849 [.843,.854]	.841 [.835,.846]
240	120	120	2.25	.951 [.947,.954]	.943 [.940,.947]	.885 [.879,.890]	.899 [.894,.904]	.893 [.888,.898]
80	40	40	2.50	.660 [.653,.668]	.624 [.616,.631]	.538 [.530,.546]	.554 [.546,.562]	.554 [.546,.562]
120	60	60	2.50	.828 [.822,.834]	.806 [.800,.813]	.713 [.706,.721]	.735 [.728,.742]	.728 [.720,.735]
160	80	80	2.50	.915 [.911,.920]	.903 [.898,.908]	.834 [.828,.840]	.852 [.846,.857]	.843 [.837,.849]
200	100	100	2.50	.959 [.956,.962]	.953 [.949,.956]	.903 [.898,.908]	.918 [.913,.922]	.912 [.907,.917]
240	120	120	2.50	.983 [.981,.985]	.980 [.978,.982]	.950 [.946,.953]	.958 [.954,.961]	.955 [.952,.959]
80	40	40	2.75	.747 [.739,.753]	.710 [.703,.717]	.626 [.618,.634]	.636 [.628,.643]	.641 [.633,.648]
120	60	60	2.75	.891 [.886,.896]	.872 [.866,.877]	.799 [.793,.806]	.817 [.810,.823]	.809 [.803,.816]
160	80	80	2.75	.958 [.954,.961]	.949 [.945,.952]	.896 [.891,.901]	.905 [.901,.910]	.904 [.899,.909]
200	100	100	2.75	.985 [.983,.987]	.982 [.979,.984]	.950 [.947,.954]	.959 [.955,.962]	.955 [.951,.958]
240	120	120	2.75	.995 [.994,.996]	.994 [.992,.995]	.977 [.974,.979]	.981 [.979,.984]	.980 [.978,.982]
80	40	40	3.00	.805 [.798,.811]	.776 [.769,.783]	.700 [.693,.708]	.707 [.700,.715]	.710 [.702,.717]
120	60	60	3.00	.934 [.930,.938]	.923 [.919,.928]	.867 [.861,.872]	.879 [.874,.885]	.873 [.868,.879]
160	80	80	3.00	.979 [.977,.982]	.975 [.973,.978]	.945 [.941,.949]	.951 [.947,.954]	.949 [.946,.953]
200	100	100	3.00	.993 [.991,.994]	.992 [.990,.993]	.978 [.976,.981]	.981 [.979,.983]	.981 [.978,.983]
240	120	120	3.00	.998 [.997,.999]	.998 [.997,.999]	.991 [.989,.992]	.994 [.992,.995]	.993 [.991,.994]

Point estimates of the statistical power and 95% Wilson confidence intervals are reported

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