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