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Table 6 The mean and standard deviation (in parenthesis) of type I error and power.

From: A simulation study for comparing testing statistics in response-adaptive randomization

   Type I error of test statistics  
Target Method T MW T RISK T MO T MC T ML Row Mean
  SMLE 4.4(1.1) 4.6(4.1) 2.0(1.4) 5.0(0.6) 6.8(0.9) 4.6(2.4)
  DBCD 4.3(1.4) 5.1(5.1) 1.7(1.7) 4.8(1.2) 7.2(0.8) 4.6(2.9)
R Wald SEU 4.0(0.9) 3.4(2.4) 2.3(1.2) 4.8(0.2) 5.6(0.6) 4.0(1.7)
  GDL 4.4(0.8) 3.7(3.1) 2.1(1.6) 5.2(0.4) 6.6(1.0) 4.4(2.2)
  Mean 4.3(1.0) 4.2(3.6) 2.0(1.4) 5.0(0.7) 6.5(1.0) 4.4(2.3)
  SMLE 4.4(1.4) 8.6(3.5) 2.4(1.8) 5.5(1.4) 6.0(1.0) 5.4(2.8)
  DBCD 4.6(2.0) 10.2(4.4) 2.6(2.3) 5.7(2.2) 6.5(1.4) 5.9(3.5)
R Risk SEU 3.7(0.8) 7.6(2.3) 2.1(0.8) 5.4(1.3) 5.1(0.4) 4.8(2.2)
  GDL 4.2(1.3) 7.9(2.4) 2.4(1.9) 5.4(1.6) 5.8(1.4) 5.1(2.5)
  Mean 4.2(1.3) 8.6(3.1) 2.4(1.7) 5.5(1.5) 5.9(1.2) 5.3(2.8)
  SMLE 3.7(0.6) 2.4(0.5) 2.9(0.5) 4.8(0.4) 4.5(0.4) 3.7(1.0)
  DBCD 3.6(0.7) 2.1(0.8) 3.1(0.7) 4.7(0.3) 4.1(0.2) 3.5(1.1)
R Odds SEU 3.6(0.5) 3.6(0.8) 2.3(0.7) 4.7(0.3) 4.9(0.7) 3.8(1.1)
  GDL 3.7(0.8) 3.4(0.8) 3.0(1.1) 5.1(0.4) 4.5(0.4) 3.9(1.0)
  Mean 3.7(0.6) 2.9(0.9) 2.8(0.8) 4.9(0.4) 4.5(0.5) 3.7(1.1)
  SMLE 4.0(0.6) 2.7(1.2) 2.7(1.0) 5.0(0.2) 5.2(0.6) 3.9(1.3)
  DBCD 4.2(0.8) 3.3(2.6) 2.4(1.5) 5.0(0.4) 6.1(0.8) 4.2(1.9)
R LLR SEU 4.0(0.6) 2.8(1.6) 2.4(1.0) 4.9(0.2) 5.4(0.8) 3.9(1.5)
  GDL 3.7(0.5) 2.5(1.3) 2.7(1.2) 4.9(0.4) 5.4(0.9) 3.8(1.5)
  Mean 3.9(0.6) 2.8(1.6) 2.5(1.1) 5.0(0.3) 5.6(0.8) 4.0(1.5)
  SMLE 4.2(1.1) 6.2(4.0) 2.3(1.5) 5.2(0.8) 6.1(0.7) 4.8(2.4)
  DBCD 4.3(1.5) 6.9(5.2) 2.0(1.6) 5.2(1.3) 6.5(1.1) 5.0(3.0)
R RSIHR SEU 3.9(0.8) 4.8(3.4) 2.3(1.0) 4.8(0.4) 5.5(0.5) 4.3(1.9)
  GDL 4.3(0.9) 4.7(3.0) 2.2(1.6) 5.1(0.6) 6.1(0.9) 4.5(2.0)
  Mean 4.2(1.0) 5.7(3.8) 2.2(1.3) 5.1(0.8) 6.1(0.8) 4.6(2.3)
  RPW 4.2(0.8) 6.2(0.5) 2.5(1.6) 5.5(1.4) 5.4(0.8) 4.8(1.7)
  DL 4.3(0.8) 4.8(1.0) 2.6(1.7) 5.3(0.9) 5.3(0.4) 4.5(1.4)
  SMLE 4.2(0.9) 6.5(0.6) 2.8(1.8) 5.4(1.6) 5.1(0.8) 4.8(1.7)
R RPW DBCD 4.3(0.9) 6.7(1.0) 2.9(2.1) 5.7(1.8) 4.8(1.0) 4.9(1.9)
  SEU 3.8(0.6) 5.7(1.3) 2.2(0.6) 5.4(0.8) 5.1(0.6) 4.5(1.5)
  GDL 4.0(0.8) 5.1(0.6) 2.7(1.6) 5.2(0.7) 5.0(0.8) 4.4(1.3)
  Mean 4.1(0.8) 5.8(1.1) 2.6(1.5) 5.4(1.2) 5.1(0.7) 4.6(1.6)
Equal Allocation 4.0(0.5) 2.9(1.7) 2.4(1.0) 5.0(0.2) 5.6(0.8) 4.0(1.5)
   Power of test statistics
Target Method T MW T RISK T MO T MC T ML Row Mean
  SMLE 56.6(34.1) 48.6(35.2) 48.5(36.8) 57.6(33.4) 59.4(31.9) 54.2(33.2)
  DBCD 56.9(34.4) 49.5(35.9) 48.0(37.6) 57.7(33.9) 60.2(31.8) 54.5(33.7)
R Wald SEU 56.0(34.0) 47.7(34.8) 49.6(36.1) 57.5(33.0) 58.4(32.3) 53.8(32.9)
  GDL 57.3(34.0) 50.0(36.2) 50.6(36.9) 58.4(33.2) 60.0(32.0) 55.3(33.3)
  Mean 56.7(32.8) 49.0(34.2) 49.2(35.4) 57.8(32.1) 59.5(30.7) 54.4(33.0)
  SMLE 53.4(33.2) 57.9(31.5) 45.4(35.2) 56.2(32.7) 55.1(31.1) 53.6(31.7)
  DBCD 53.3(33.4) 60.0(30.5) 43.7(36.0) 56.5(32.9) 55.0(31.1) 53.7(31.9)
R Risk SEU 52.5(32.8) 55.3(32.2) 45.9(34.1) 55.2(32.1) 54.2(31.2) 52.6(31.3)
  GDL 53.2(33.3) 58.1(31.6) 45.8(35.8) 56.5(32.6) 55.2(31.7) 53.8(31.9)
  Mean 53.1(31.9) 57.8(30.3) 45.2(33.9) 56.1(31.3) 54.9(30.1) 53.4(31.5)
  SMLE 54.6(33.9) 47.1(34.3) 52.1(34.9) 57.6(32.6) 56.4(32.9) 53.6(32.5)
  DBCD 54.8(34.2) 47.3(35.2) 53.4(34.5) 57.8(32.7) 56.5(33.4) 53.9(32.8)
R Odds SEU 54.8(33.5) 50.8(33.8) 50.4(34.8) 57.5(32.5) 56.6(32.2) 54.0(32.1)
  GDL 54.6(34.2) 53.0(34.6) 52.5(35.0) 58.1(32.7) 56.8(33.0) 55.0(32.5)
  Mean 54.7(32.6) 49.5(33.2) 52.1(33.4) 57.8(31.4) 56.6(31.6) 54.1(32.3)
  SMLE 55.9(33.9) 48.4(35.0) 51.6(35.6) 58.0(32.8) 58.0(32.6) 54.4(32.8)
  DBCD 57.2(34.0) 49.9(35.9) 51.4(36.6) 58.6(33.1) 60.0(32.2) 55.4(33.2)
R LLR SEU 56.1(33.9) 48.5(34.8) 51.2(35.7) 58.1(32.8) 58.2(32.5) 54.4(32.8)
  GDL 56.4(34.1) 50.4(35.8) 53.1(35.9) 58.9(33.1) 59.5(32.5) 55.7(33.1)
  Mean 56.4(32.6) 49.3(34.0) 51.8(34.6) 58.4(31.7) 58.9(31.2) 55.0(32.7)
  SMLE 56.0(33.9) 54.8(33.7) 48.7(36.4) 57.5(33.2) 58.4(32.0) 55.1(32.6)
  DBCD 56.8(34.0) 56.3(33.4) 48.2(37.0) 58.2(33.2) 59.4(31.8) 55.7(32.8)
R RSIHR SEU 54.5(33.8) 50.5(34.5) 48.6(35.8) 56.4(33.0) 56.6(32.4) 53.3(32.7)
  GDL 57.4(33.7) 54.4(34.5) 50.6(36.6) 58.7(33.0) 59.7(32.1) 56.2(32.8)
  Mean 56.2(32.6) 54.0(32.8) 49.0(35.0) 57.7(31.8) 58.5(30.8) 55.1(32.5)
  RPW 52.4(32.3) 55.9(32.1) 46.3(34.1) 55.8(32.1) 52.9(30.1) 52.7(31.0)
  DL 56.0(33.5) 55.9(33.4) 50.0(36.1) 58.2(32.6) 57.4(32.5) 55.5(32.4)
  SMLE 51.7(32.3) 56.2(31.8) 46.7(33.7) 55.7(31.9) 51.7(30.2) 52.4(30.9)
R RPW DBCD 51.2(31.8) 57.3(31.2) 47.0(34.1) 56.0(31.5) 48.3(29.2) 52.0(30.6)
  SEU 54.0(33.1) 54.0(32.7) 48.3(34.4) 56.7(32.1) 55.9(31.7) 53.8(31.6)
  GDL 54.6(33.5) 56.0(33.0) 50.2(35.3) 57.8(32.4) 56.4(32.3) 55.0(32.0)
  Mean 53.3(31.4) 55.9(31.0) 48.1(33.2) 56.7(30.7) 53.8(29.8) 53.5(31.2)
Equal Allocation 56.2(33.9) 48.5(35.0) 50.9(35.9) 58.1(32.9) 58.4(32.4) 54.4(32.9)
  1. Mean values are calculated by averaging simulation results over the five null cases and the ten alternative cases of simulation scenarios listed in Tables 7-12. All results have been multiplied by 100% (alpha = 0.05, n = 30).