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 3 Statistical power of the SCIM self-care subscore model M3 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 M3	Permutated ePolr test based on model M3	t-test M3	Wilcoxon rank sum test M3	ANCOVA M3
80	40	40	1.00	.071 [.067,.075]	.050 [.046,.053]	.050 [.046,.053]	.049 [.046,.053]	.050 [.046,.053]
120	60	60	1.00	.071 [.067,.075]	.052 [.049,.056]	.052 [.049,.056]	.054 [.051,.058]	.052 [.049,.056]
160	80	80	1.00	.068 [.064,.072]	.050 [.046,.053]	.051 [.047,.055]	.049 [.046,.053]	.050 [.047,.054]
200	100	100	1.00	.069 [.065,.073]	.051 [.048,.055]	.051 [.047,.055]	.051 [.048,.055]	.050 [.047,.054]
240	120	120	1.00	.067 [.064,.072]	.049 [.045,.052]	.050 [.047,.054]	.049 [.046,.053]	.050 [.047,.054]
80	40	40	1.25	.113 [.108,.119]	.087 [.083,.092]	.080 [.076,.084]	.079 [.075,.084]	.080 [.076,.085]
120	60	60	1.25	.136 [.131,.142]	.108 [.103,.113]	.096 [.092,.101]	.099 [.094,.104]	.098 [.093,.102]
160	80	80	1.25	.152 [.147,.158]	.122 [.116,.127]	.109 [.104,.114]	.113 [.108,.118]	.108 [.103,.113]
200	100	100	1.25	.178 [.172,.184]	.142 [.136,.147]	.124 [.118,.129]	.128 [.123,.134]	.125 [.120,.131]
240	120	120	1.25	.205 [.199,.212]	.168 [.162,.174]	.149 [.144,.155]	.151 [.145,.156]	.150 [.144,.155]
80	40	40	1.50	.212 [.206,.219]	.172 [.166,.178]	.151 [.146,.157]	.155 [.149,.161]	.152 [.146,.158]
120	60	60	1.50	.285 [.278,.292]	.237 [.230,.244]	.205 [.199,.212]	.211 [.205,.218]	.207 [.200,.213]
160	80	80	1.50	.357 [.349,.364]	.306 [.299,.314]	.263 [.256,.270]	.270 [.263,.277]	.263 [.256,.270]
200	100	100	1.50	.422 [.414,.430]	.369 [.361,.376]	.313 [.306,.321]	.325 [.317,.332]	.314 [.306,.321]
240	120	120	1.50	.482 [.474,.490]	.429 [.421,.436]	.366 [.358,.373]	.375 [.367,.383]	.368 [.361,.376]
80	40	40	1.75	.330 [.322,.338]	.282 [.275,.289]	.245 [.238,.252]	.246 [.239,.253]	.247 [.240,.254]
120	60	60	1.75	.463 [.455,.471]	.408 [.401,.416]	.353 [.346,.361]	.360 [.353,.368]	.355 [.347,.362]
160	80	80	1.75	.575 [.567,.583]	.522 [.514,.530]	.455 [.447,.463]	.464 [.456,.472]	.457 [.449,.465]
200	100	100	1.75	.655 [.648,.663]	.606 [.598,.614]	.533 [.525,.541]	.549 [.541,.557]	.533 [.525,.541]
240	120	120	1.75	.728 [.721,.735]	.686 [.679,.693]	.609 [.601,.617]	.623 [.615,.631]	.609 [.601,.617]
80	40	40	2.00	.466 [.458,.474]	.414 [.406,.422]	.362 [.354,.370]	.368 [.360,.376]	.366 [.358,.374]
120	60	60	2.00	.622 [.614,.630]	.569 [.561,.577]	.504 [.496,.512]	.515 [.507,.523]	.505 [.497,.513]
160	80	80	2.00	.739 [.732,.746]	.695 [.687,.702]	.626 [.618,.634]	.639 [.632,.647]	.628 [.621,.636]
200	100	100	2.00	.828 [.822,.834]	.794 [.787,.800]	.721 [.714,.728]	.732 [.725,.739]	.721 [.713,.728]
240	120	120	2.00	.886 [.881,.891]	.860 [.855,.866]	.793 [.787,.800]	.806 [.799,.812]	.796 [.789,.802]
80	40	40	2.25	.585 [.577,.592]	.534 [.526,.542]	.470 [.462,.478]	.473 [.465,.481]	.474 [.466,.482]
120	60	60	2.25	.749 [.742,.756]	.700 [.693,.708]	.634 [.626,.642]	.644 [.636,.652]	.637 [.629,.644]
160	80	80	2.25	.856 [.851,.862]	.825 [.819,.831]	.760 [.753,.767]	.767 [.760,.774]	.761 [.754,.768]
200	100	100	2.25	.924 [.920,.928]	.903 [.898,.908]	.854 [.848,.859]	.861 [.855,.866]	.855 [.849,.861]
240	120	120	2.25	.960 [.956,.963]	.946 [.942,.950]	.910 [.905,.914]	.916 [.911,.920]	.912 [.907,.917]
80	40	40	2.50	.677 [.669,.684]	.629 [.621,.637]	.561 [.553,.569]	.563 [.555,.571]	.563 [.555,.571]
120	60	60	2.50	.841 [.835,.846]	.805 [.799,.812]	.740 [.733,.747]	.751 [.744,.758]	.743 [.736,.750]
160	80	80	2.50	.924 [.919,.928]	.903 [.898,.907]	.855 [.849,.861]	.863 [.858,.869]	.857 [.851,.862]
200	100	100	2.50	.965 [.962,.968]	.954 [.950,.957]	.924 [.920,.928]	.929 [.925,.933]	.925 [.921,.929]
240	120	120	2.50	.987 [.985,.989]	.982 [.979,.984]	.961 [.958,.964]	.965 [.962,.968]	.962 [.959,.965]
80	40	40	2.75	.760 [.753,.767]	.715 [.707,.722]	.654 [.647,.662]	.655 [.647,.663]	.655 [.648,.663]
120	60	60	2.75	.900 [.896,.905]	.877 [.872,.882]	.826 [.820,.832]	.830 [.824,.836]	.827 [.821,.833]
160	80	80	2.75	.962 [.959,.965]	.950 [.947,.954]	.915 [.910,.919]	.921 [.916,.925]	.916 [.911,.920]
200	100	100	2.75	.985 [.983,.987]	.980 [.978,.982]	.962 [.958,.965]	.965 [.962,.968]	.962 [.959,.965]
240	120	120	2.75	.995 [.994,.996]	.993 [.992,.995]	.982 [.980,.984]	.984 [.982,.986]	.983 [.981,.985]
80	40	40	3.00	.816 [.810,.822]	.777 [.770,.784]	.726 [.719,.734]	.726 [.718,.733]	.727 [.720,.734]
120	60	60	3.00	.939 [.935,.943]	.921 [.916,.925]	.882 [.877,.887]	.886 [.881,.891]	.883 [.878,.888]
160	80	80	3.00	.980 [.978,.982]	.974 [.971,.976]	.954 [.950,.957]	.957 [.954,.960]	.955 [.951,.958]
200	100	100	3.00	.995 [.994,.996]	.993 [.992,.994]	.983 [.980,.985]	.984 [.982,.986]	.983 [.980,.985]
240	120	120	3.00	.999 [.998,.999]	.998 [.997,.999]	.994 [.993,.995]	.995 [.994,.996]	.994 [.993,.995]

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

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