Figures (0)  Tables (11)
    • No. of cured or affected organs Group Total
      1 2 … g
      0 m01 m02 … m0g m0+
      1 m11 m12 … m1g m1+
      2 m21 m22 … m2g m2+
      Total m+1 m+2 … m+g m++
      0 n01 n02 … n0g n0+
      1 n11 n12 … n1g n1+
      Total n+1 n+2 … n+g n++

      Table 1. 

      Frequency table for the number of cured or affected organs for subjects in g groups.

    • Sub_id Response Group Count Replicate
      1 0 1 m01 1
      1 0 1 m01 1
      2 1 1 m11 1
      2 0 1 m11 1
      3 1 1 m21 1
      3 1 1 m21 1
      4 0 2 m02 1
      4 0 2 m02 1
      5 1 2 m12 1
      5 0 2 m12 1
      6 1 2 m22 1
      6 1 2 m22 1
      7 0 1 n01 1
      8 1 1 n11 1
      9 0 2 n02 1
      10 1 2 n12 1

      Table 2. 

      The structure of stacked data (g = 2) in the first simulation (replicate = 1).

    • * stacked data (g = 2) file w/ name <data_g2_stacked>;
      * var names same with those in the above table (Table 2);
      proc genmod data = data_g2_stacked descending;
      freq count;
      class group sub_id;
      model response = group/link = identity dist = bin;
      repeated subject = sub_id/type = un corrw;
      by replicate;
      contrast 'group' group 1 -1;
      run;

      Table 3. 

      Pseudo SAS code using PROC GENMOD.

    • (m, n) π0 ρ g = 2 g = 4 g = 8
      QLR QW QS QGS QLR QW QS QGS QLR QW QS QGS
      E1 0.2 0.1 4.41 4.46 4.03 5.15 3.71 4.52 3.43 5.43 2.92 4.63 2.83 5.92
      0.5 5.35 4.44 4.04 5.07 4.67 5.67 3.62 5.68 4.31 8.25 3.42 6.70
      0.7 5.58 3.35 3.88 5.05 4.03 4.15 3.96 5.86 3.39 5.47 3.15 6.78
      0.5 0.1 5.79 6.50 5.09 5.10 5.70 7.48 4.89 4.90 5.75 8.34 4.90 4.91
      0.5 6.19 5.79 5.17 5.18 6.13 7.74 4.91 4.96 6.33 11.34 4.80 4.90
      0.7 5.18 3.58 5.40 5.03 4.94 4.86 4.30 4.99 4.80 6.81 4.02 4.88
      E2 0.2 0.1 4.98 5.18 4.66 5.08 4.62 5.37 4.29 5.24 4.47 5.75 4.21 5.54
      0.5 6.10 5.47 5.04 4.96 6.19 7.22 4.82 5.43 6.32 10.08 4.75 5.81
      0.7 6.01 4.12 5.01 5.03 6.15 6.04 4.70 5.46 6.46 9.74 4.70 5.91
      0.5 0.1 5.37 5.80 5.02 4.97 5.42 6.20 5.03 5.02 5.39 6.50 4.99 4.84
      0.5 5.63 5.38 5.17 5.03 5.64 6.36 5.03 4.98 5.66 7.87 4.82 4.92
      0.7 5.72 4.64 5.04 5.02 5.91 6.68 4.94 4.97 6.08 10.34 4.89 4.98
      Ug 0.2 0.1 4.46 4.79 4.13 5.22 4.10 5.08 3.86 5.56 4.00 5.63 3.84 5.90
      0.5 5.49 5.18 4.41 5.29 5.16 6.83 4.16 5.85 5.63 10.54 4.40 6.33
      0.7 5.21 3.83 5.04 5.34 4.88 5.05 4.18 5.91 5.18 8.19 4.18 6.48
      0.5 0.1 5.58 6.33 5.07 5.10 5.57 6.94 5.01 5.01 5.28 6.83 4.79 4.75
      0.5 5.79 6.13 5.12 4.99 5.88 7.94 4.94 4.94 5.99 9.87 5.01 5.00
      0.7 5.27 4.77 4.66 5.10 5.17 6.26 4.57 4.96 5.36 10.40 4.56 5.01

      Table 4. 

      The empirical type I error rates (in %) under Rosner's model for different test procedures, under H0 : π1 = … = πg = π0 at the nominal level of α = 0.05.

    • (m, n) π0 ρ g = 2 g = 4 g = 8
      QLR QW QS QGS QLR QW QS QGS QLR QW QS QGS
      E1 0.2 0.1 9.53 4.20 4.24 5.12 4.49 4.70 3.65 5.43 3.48 5.29 3.24 5.91
      0.5 5.12 4.96 4.63 5.05 4.46 5.84 4.16 5.66 4.40 7.26 4.09 6.75
      0.7 5.00 5.01 4.61 5.01 4.79 6.10 4.36 5.86 4.30 7.23 3.90 6.71
      0.5 0.1 5.43 5.96 5.22 5.21 5.41 6.68 5.03 4.99 5.32 7.39 4.75 4.75
      0.5 5.35 5.87 5.18 5.17 5.38 6.73 5.04 5.00 5.44 7.78 4.96 4.90
      0.7 5.36 5.82 5.18 5.17 5.37 6.75 5.03 5.01 5.37 7.74 4.90 4.91
      E2 0.2 0.1 5.27 4.85 4.61 4.98 4.70 5.30 4.48 5.17 4.65 5.91 4.41 5.51
      0.5 5.13 5.24 5.00 5.05 5.19 6.03 4.94 5.41 5.14 6.82 4.80 5.69
      0.7 5.00 5.10 4.87 4.88 5.20 5.98 4.98 5.30 5.19 7.05 4.81 5.85
      0.5 0.1 5.10 5.38 4.98 4.99 5.17 5.76 4.98 4.96 5.14 6.11 4.86 4.84
      0.5 5.03 5.29 4.95 4.96 5.27 5.92 5.12 5.09 5.16 6.26 4.91 4.92
      0.7 5.17 5.39 5.11 5.10 5.19 5.88 5.06 5.07 5.17 6.33 4.93 4.92
      Ug 0.2 0.1 6.04 4.69 4.44 5.24 4.22 4.98 4.04 5.38 4.18 5.83 4.07 5.83
      0.5 5.00 5.38 4.76 5.29 4.88 6.24 4.62 5.88 4.96 7.21 4.60 6.35
      0.7 4.98 5.33 4.73 5.34 4.78 6.20 4.44 5.76 4.95 7.36 4.70 6.57
      0.5 0.1 5.22 5.66 5.04 5.04 5.14 6.11 4.89 4.83 5.27 6.51 4.95 4.91
      0.5 5.16 5.66 5.02 5.00 5.24 6.31 4.96 4.98 5.25 6.73 4.93 4.92
      0.7 5.15 5.64 5.04 5.03 5.11 6.25 4.88 4.85 5.30 6.83 5.01 4.99

      Table 5. 

      The empirical type I error rates (in %) under Donner's model for different test procedures, under H0 : π1 = … = πg = π0 at the nominal level α = 0.05.

    • (m, n) R g = 2 g = 4 g = 8
      QLR QW QS QGS QLR QW QS QGS QLR QW QS QGS
      Under H1A E1 1.2 40.08 41.85 37.77 39.69 28.79 32.45 26.55 28.68 39.23 45.40 36.65 39.53
      1.5 39.38 40.72 36.03 36.96 28.98 32.62 25.86 26.61 39.36 46.20 35.67 36.40
      1.8 42.22 41.79 37.90 34.83 31.91 34.64 27.64 25.12 44.06 51.39 38.91 34.40
      E2 1.2 68.10 69.03 66.88 67.45 56.03 58.12 54.52 54.80 75.50 77.90 74.19 74.20
      1.5 66.54 67.36 64.68 63.67 55.00 57.17 52.92 51.08 74.78 77.23 72.82 70.45
      1.8 69.73 69.61 67.39 60.69 58.20 59.80 55.36 47.87 78.27 80.48 75.89 66.73
      Ug 1.2 49.68 53.22 46.03 51.75 37.79 43.17 34.37 40.34 66.70 70.98 64.24 67.36
      1.5 49.10 52.34 43.75 49.02 37.68 43.31 32.50 37.94 65.72 70.48 62.12 63.07
      1.8 52.49 53.55 45.70 46.96 41.39 45.53 35.05 35.65 70.62 74.58 66.03 60.01
      Under H1B E1 1.2 63.68 65.29 60.93 64.20 78.76 81.12 76.60 79.45 94.25 95.48 93.42 94.84
      1.5 62.59 63.97 58.40 61.04 77.57 79.78 74.02 75.93 93.66 95.03 92.14 92.79
      1.8 64.50 64.54 58.94 58.38 79.66 80.83 74.82 72.72 94.86 95.79 92.84 90.90
      E2 1.2 91.25 91.70 90.63 91.04 98.64 98.75 98.47 98.50 99.98 99.99 99.98 99.98
      1.5 90.31 90.73 89.18 69.47 98.27 98.45 97.95 97.75 99.96 99.97 99.94 99.93
      1.8 91.09 91.29 89.44 86.91 98.50 98.58 98.06 96.73 99.99 99.99 99.98 99.90
      Ug 1.2 76.34 79.25 72.91 78.61 90.10 92.53 87.61 91.94 99.85 99.90 99.82 99.87
      1.5 75.08 78.18 68.95 76.05 89.23 91.98 84.67 89.96 99.82 99.88 99.71 99.77
      1.8 76.68 78.55 68.12 73.58 90.33 92.20 83.85 87.93 99.87 99.91 99.73 99.64

      Table 6. 

      The powers (in %) under Rosner's model at the nominal level of α = 0.05.

    • (m, n) ρ g = 2 g = 4 g = 8
      QLR QW QS QGS QLR QW QS QGS QLR QW QS QGS
      Under H1A E1 0.1 39.38 40.53 38.55 39.65 28.46 31.70 27.45 28.93 39.27 44.79 37.68 39.85
      0.5 34.98 36.19 34.41 34.25 25.33 28.74 24.30 24.71 34.47 40.73 32.78 33.37
      0.7 33.13 34.26 32.51 32.48 23.87 27.27 22.89 23.41 32.10 38.64 30.53 31.45
      E2 0.1 67.81 68.55 67.36 67.41 55.48 57.43 54.69 54.84 75.26 77.48 74.41 74.48
      0.5 60.20 60.90 59.91 59.50 47.65 49.65 47.02 46.73 65.83 68.64 64.98 64.69
      0.7 57.29 57.97 57.00 56.66 44.95 46.93 44.25 44.15 62.33 65.35 61.41 61.41
      Ug 0.1 49.44 52.49 47.99 51.55 37.92 42.85 35.98 40.43 66.66 70.72 65.05 67.43
      0.5 43.89 47.12 42.42 45.12 33.36 38.73 31.38 34.75 58.11 63.13 56.45 58.31
      0.7 41.47 44.73 39.95 42.87 30.82 36.20 28.83 32.48 54.20 59.60 52.47 54.61
      Under H1B E1 0.1 64.00 64.84 63.19 64.59 78.84 80.71 78.09 79.53 94.30 95.45 93.94 94.69
      0.5 57.48 58.69 56.83 56.76 72.05 74.73 71.05 71.08 90.23 92.21 89.48 89.52
      0.7 54.77 55.82 54.00 53.91 68.75 71.52 67.58 67.69 87.84 90.22 86.97 87.27
      E2 0.1 91.43 91.72 91.25 91.31 98.53 98.67 98.46 98.50 99.98 99.98 99.98 99.98
      0.5 86.11 86.49 85.91 85.50 96.28 96.56 96.16 95.97 99.85 99.87 99.84 99.83
      0.7 83.63 83.95 83.42 83.08 95.06 95.44 94.90 94.77 99.68 99.73 99.66 99.64
      Ug 0.1 76.36 78.83 75.10 78.32 90.02 92.30 88.97 91.55 99.88 99.91 99.85 99.89
      0.5 69.42 72.58 68.03 70.66 84.68 88.06 83.14 85.82 99.45 99.61 99.37 99.44
      0.7 66.47 69.60 64.85 67.86 81.80 85.58 79.97 83.27 99.04 99.33 98.92 99.07

      Table 7. 

      The powers (in %) under Donner's model at the nominal level of α = 0.05.

    • No. of cured ears Treatment Total
      Cefaclor Amoxicillin
      0 9 7 16
      1 7 5 12
      2 23 13 36
      Total 39 25 64
      0 20 19 39
      1 34 36 70
      Total 54 55 109

      Table 8. 

      Number of cured ears at 42 d in children treated with cefaclor and amoxicillin.

    • Constrained MLEs Unconstrained MLEs
      Cefaclor Amoxicillin Cefaclor Amoxicillin
      $ \hat{{\text{π}}}_i $ $ \hat{{\text{π}}}_0 $ = 0.6482 $ \hat{{\text{π}}}_1$ = 0.6528 $ \hat{{\text{π}}}_2 $ = 0.6425
      $ \hat{R} $ $ \hat{R}_0 $ = 1.3182 $ \hat{R} $ = 1.3172
      $ \hat{\rho} $ $ \hat{\rho}_0 $ = 0.5862 $ \hat{\rho}_1 $ = 0.5964 $ \hat{\rho}_2 $ = 0.5699
      QLR QW QS QGS
      Statistic 0.0394 0.0391 0.0395 0.0265
      p-value 0.8426 0.8432 0.8424 0.8706

      Table 9. 

      Constrained and unconstrained MLEs along with statistics and p-values under Rosner's model for the OME dataset.

    • No. of affected eyes Genetic type Total
      DOM AR SL ISO
      0 15 7 3 67 92
      1 6 5 2 24 37
      2 7 9 14 57 87
      Total 28 21 19 148 216

      Table 10. 

      Number of affected eyes for patients in four genetic groups.

    • DOM AR SL ISO
      Constrained
      MLEs      		 $ \hat{{\text{π}}}_i $ $ \hat{{\text{π}}}_0 $ = 0.4884
      $ \hat{\rho} $ $ \hat{\rho}_0 $ = 0.6572
      Unconstrained MLEs $ \hat{{\text{π}}}_i $ $ \hat{{\text{π}}}_1 $ = 0.3625 $ \hat{{\text{π}}}_2 $ = 0.5455 $ \hat{{\text{π}}}_3 $ = 0.7926 $ \hat{{\text{π}}}_4 $ = 0.4658
      $ \hat{\rho} $ $ \hat{\rho} $ = 0.6416
      QLR QW QS QGS
      Statistic 12.0385 16.3267 11.3158 10.6890
      p-value 0.0073 0.0010 0.0101 0.0135

      Table 11. 

      Constrained and unconstrained MLEs along with statistics and p-values under Donner's model for the retinitis pigmentosa dataset.