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