## Introduction

The use of the functions introduced in vignette 3, but this time using the OR method to estimate the variance components, is illustrated here. The reader should confirm that these give the same results as the corresponding ones obtained using the DBMH method. When the figure of merit is the empirical AUC, the two methods can be shown to be identical.

## Illustration of SsPowerGivenJK() using method = "OR"

power <- SsPowerGivenJK(dataset02, FOM = "Wilcoxon", J = 6, K = 251, method = "OR", analysisOption = "RRRC")

The returned value is a list containing the expected power, the non-centrality parameter, the denominator degrees of freedom and the F-statistic (the numerator degrees of freedom is always one less than the number of treatments, i.e., unity in this example).

str(power)
#> 'data.frame':    1 obs. of  4 variables:
#>  $powerRRRC: num 0.801 #>$ ncpRRRC  : num 8.91
#>  $df2RRRC : num 16.1 #>$ fRRRC    : num 4.49

Expected power is 0.80054026.

## Illustration of SsPowerTable() using method = "OR"

powTab <- SsPowerTable(dataset02, FOM = "Wilcoxon", analysisOption = "RRRC")

Now show the power table powTab.

powTab
#> $powerTableRRRC #> numReaders numCases power #> 1 3 >2000 <NA> #> 2 3 >2000 <NA> #> 3 4 1089 0.8 #> 4 4 1089 0.8 #> 5 5 344 0.801 #> 6 5 344 0.801 #> 7 6 251 0.801 #> 8 6 251 0.801 #> 9 7 211 0.801 #> 10 7 211 0.801 #> 11 8 188 0.801 #> 12 8 188 0.801 #> 13 9 173 0.801 #> 14 9 173 0.801 #> 15 10 163 0.802 #> 16 10 163 0.802 #> 17 11 155 0.801 #> 18 11 155 0.801 #> 19 12 149 0.802 #> 20 12 149 0.802 #> 21 13 144 0.801 #> 22 13 144 0.801 #> 23 14 140 0.802 #> 24 14 140 0.802 #> 25 15 137 0.802 #> 26 15 137 0.802 #> 27 16 134 0.802 #> 28 16 134 0.802 #> 29 17 131 0.801 #> 30 17 131 0.801 #> 31 18 129 0.801 #> 32 18 129 0.801 #> 33 19 127 0.801 #> 34 19 127 0.801 #> 35 20 126 0.802 #> 36 20 126 0.802 #> 37 21 124 0.801 #> 38 21 124 0.801 #> 39 22 123 0.802 #> 40 22 123 0.802 #> 41 23 122 0.802 #> 42 23 122 0.802 #> 43 24 121 0.803 #> 44 24 121 0.803 #> 45 25 120 0.802 #> 46 25 120 0.802 #> 47 26 119 0.802 #> 48 26 119 0.802 #> 49 27 118 0.802 #> 50 27 118 0.802 #> 51 28 117 0.801 #> 52 28 117 0.801 #> 53 29 117 0.803 #> 54 29 117 0.803 #> 55 30 116 0.802 #> 56 30 116 0.802 #> 57 31 115 0.801 #> 58 31 115 0.801 #> 59 32 115 0.803 #> 60 32 115 0.803 #> 61 33 114 0.801 #> 62 33 114 0.801 #> 63 34 114 0.803 #> 64 34 114 0.803 #> 65 35 113 0.801 #> 66 35 113 0.801 #> 67 36 113 0.802 #> 68 36 113 0.802 #> 69 37 112 0.8 #> 70 37 112 0.8 #> 71 38 112 0.802 #> 72 38 112 0.802 #> 73 39 112 0.803 #> 74 39 112 0.803 #> 75 40 111 0.801 #> 76 40 111 0.801 #> 77 41 111 0.802 #> 78 41 111 0.802 #> 79 42 111 0.803 #> 80 42 111 0.803 #> 81 43 110 0.801 #> 82 43 110 0.801 #> 83 44 110 0.802 #> 84 44 110 0.802 #> 85 45 110 0.802 #> 86 45 110 0.802 #> 87 46 110 0.803 #> 88 46 110 0.803 #> 89 47 109 0.801 #> 90 47 109 0.801 #> 91 48 109 0.802 #> 92 48 109 0.802 #> 93 49 109 0.802 #> 94 49 109 0.802 #> 95 50 109 0.803 #> 96 50 109 0.803 #> 97 51 108 0.8 #> 98 51 108 0.8 #> 99 52 108 0.801 #> 100 52 108 0.801 #> 101 53 108 0.802 #> 102 53 108 0.802 #> 103 54 108 0.802 #> 104 54 108 0.802 #> 105 55 108 0.803 #> 106 55 108 0.803 #> 107 56 107 0.8 #> 108 56 107 0.8 #> 109 57 107 0.801 #> 110 57 107 0.801 #> 111 58 107 0.801 #> 112 58 107 0.801 #> 113 59 107 0.802 #> 114 59 107 0.802 #> 115 60 107 0.802 #> 116 60 107 0.802 #> 117 61 107 0.803 #> 118 61 107 0.803 #> 119 62 107 0.803 #> 120 62 107 0.803 #> 121 63 106 0.8 #> 122 63 106 0.8 #> 123 64 106 0.801 #> 124 64 106 0.801 #> 125 65 106 0.801 #> 126 65 106 0.801 #> 127 66 106 0.802 #> 128 66 106 0.802 #> 129 67 106 0.802 #> 130 67 106 0.802 #> 131 68 106 0.802 #> 132 68 106 0.802 #> 133 69 106 0.803 #> 134 69 106 0.803 #> 135 70 106 0.803 #> 136 70 106 0.803 #> 137 71 106 0.804 #> 138 71 106 0.804 #> 139 72 105 0.8 #> 140 72 105 0.8 #> 141 73 105 0.801 #> 142 73 105 0.801 #> 143 74 105 0.801 #> 144 74 105 0.801 #> 145 75 105 0.801 #> 146 75 105 0.801 #> 147 76 105 0.802 #> 148 76 105 0.802 #> 149 77 105 0.802 #> 150 77 105 0.802 #> 151 78 105 0.802 #> 152 78 105 0.802 #> 153 79 105 0.803 #> 154 79 105 0.803 #> 155 80 105 0.803 #> 156 80 105 0.803 #> 157 81 105 0.803 #> 158 81 105 0.803 #> 159 82 105 0.803 #> 160 82 105 0.803 #> 161 83 104 0.8 #> 162 83 104 0.8 #> 163 84 104 0.8 #> 164 84 104 0.8 #> 165 85 104 0.801 #> 166 85 104 0.801 #> 167 86 104 0.801 #> 168 86 104 0.801 #> 169 87 104 0.801 #> 170 87 104 0.801 #> 171 88 104 0.801 #> 172 88 104 0.801 #> 173 89 104 0.802 #> 174 89 104 0.802 #> 175 90 104 0.802 #> 176 90 104 0.802 #> 177 91 104 0.802 #> 178 91 104 0.802 #> 179 92 104 0.802 #> 180 92 104 0.802 #> 181 93 104 0.802 #> 182 93 104 0.802 #> 183 94 104 0.803 #> 184 94 104 0.803 #> 185 95 104 0.803 #> 186 95 104 0.803 #> 187 96 104 0.803 #> 188 96 104 0.803 #> 189 97 104 0.803 #> 190 97 104 0.803 #> 191 98 104 0.804 #> 192 98 104 0.804 #> 193 99 104 0.804 #> 194 99 104 0.804 #> 195 100 103 0.8 #> 196 100 103 0.8 Since the default FOM = "Wilcoxon", the table is identical to that generated in vignette 3, which used method = "DBM". ## Illustrations of SsSampleSizeKGivenJ() using method = "OR" ### For RRRC generalization ncases <- SsSampleSizeKGivenJ(dataset02, FOM = "Wilcoxon", J = 10, method = "OR", analysisOption = "RRRC") ncases is a list containing the number of cases ncases$KRRRC and expected power ncases$powerRRRC. str(ncases) #> 'data.frame': 1 obs. of 2 variables: #>$ KRRRC    : num 163
#>  \$ powerRRRC: num 0.802

The required number of cases is 163 and expected power is 0.80156249.

### For FRRC generalization

ncases <- SsSampleSizeKGivenJ(dataset02, FOM = "Wilcoxon", J = 10, method = "OR", analysisOption = "FRRC")

The required number of cases is 131 and expected power is 0.80091813.

### For RRFC generalization

ncases <- SsSampleSizeKGivenJ(dataset02, FOM = "Wilcoxon", J = 10, method = "OR", analysisOption = "RRFC")

The required number of cases is 53 and expected power is 0.80496663.