표제지

초록

Abstract

목차

기호 설명 23

1장 서론 24

2장 연구 방법 26

2.1. 고정된 무작위 설계(FR) 26

2.2. 반응-적응 설계(Response-Adaptive design) 26

2.2.1. 무작위 승자 플레이 설계(RPW) 27

2.3. 밴딧-기반 설계(Bandit-Based design) 33

2.3.1. 가속화된 톰슨 샘플링 설계(ATS) 34

2.3.2. 제약 조건을 갖는 무작위 동적 프로그래밍을 사용한 최적 설계(CRDP) 36

3장 모의실험 46

3.1. 모의실험 목적 46

3.2. 모의실험 설계 47

1) 2-arm 실험 설계 48

2) Sample size calculation 48

3) 3-arm 실험 설계 49

3.3. 모의실험 결과 평가 기준 50

3.4. 모의실험 결과 51

3.4.1. 2-arm 51

3.4.2. Sample size calculation 80

3.4.3. 3-arm 81

4장 고찰 123

5장 결론 125

참고문헌 127

Table 3.1. In the RPW design, these results correspond to the scenario in which α＝0, β＝1, n＝75, θA＝0.5, θB ∈ (0.1, 0.9).[이미지참조] 53

Table 3.2. In the RPW design, these results correspond to the scenario in which α＝0, β＝5, n＝75, θA＝0.5, θB ∈ (0.1, 0.9).[이미지참조] 53

Table 3.3. In the ATS design, these results correspond to the scenario in which ρ＝0.5, n＝75, θA＝0.5, θB ∈ (0.1, 0.9).[이미지참조] 59

Table 3.4. In the ATS design, these results correspond to the scenario in which ρ＝3, n＝75, θA＝0.5, θB ∈ (0.1, 0.9).[이미지참조] 59

Table 3.5. In the CRDP design, these results correspond to the scenario in which p＝0.9, ℓ＝0.15n, n＝75, θA＝0.5, θB ∈ (0.1, 0.9).[이미지참조] 67

Table 3.6. Comparison of different two-arm trial designs when θA＝0.3, θB＝0.5. The table presents the performance for four methods: FR, RPW, ATS, and CRDP,...[이미지참조] 76

Table 3.7. Minimum sample size corresponding to 80% power for each design based on effect size (α＝0.1). 80

Table 3.8. In the RPW design, these results correspond to the scenario in which n＝75, θA＝0.5, θB ∈ (0.1, 0.9), θC＝0.5.[이미지참조] 82

Table 3.9. In the ATS design for Batch＝1, 2, these results correspond to the scenario in which ρ＝0.5, n＝75, θA＝0.5, θB ∈ (0.1, 0.9), θC＝0.5[이미지참조] 89

Table 3.10. In the ATS design for Batch＝4, 8, these results correspond to the scenario in which ρ＝0.5, n＝75, θA＝0.5, θB ∈ (0.1, 0.9), θC＝0.5[이미지참조] 89

Table 3.11. In the ATS design for Batch＝1, 2, these results correspond to the scenario in which ρ＝3, n＝75, θA＝0.5, θB ∈ (0.1, 0.9), θC＝0.5[이미지참조] 90

Table 3.12. In the ATS design for Batch＝4, 8, these results correspond to the scenario in which ρ＝3, n＝75, θA＝0.5, θB ∈ (0.1, 0.9), θC＝0.5[이미지참조] 90

Table 3.13. The effect of changing the degree of randomisation, p, on the performance measures when n＝25 and θA＝θB＝θC＝0.2 for the RDP design in...[이미지참조] 103

Table 3.14. The effect of changing the degree of randomisation, p, on the performance measures when n＝25 and θA＝θB＝θC＝0.2 for the RDP design in...[이미지참조] 103

Table 3.15. In the CRDP design for action3, these results correspond to the scenario in which p＝0.9, ℓ＝0.24n, n＝25, θA＝0.5, θB ∈ (0.1, 0.9), θC＝0.5[이미지참조] 104

Table 3.16. In the CRDP design for action6, these results correspond to the scenarioin which p1＝0.8, p2＝0.15, p3＝0.05, ℓ＝0.24n, n＝25, θA＝0.5, θB ∈...[이미지참조] 106

Table 3.17. Comparison of different three-arm trial designs when θA＝0.3, θB＝0.4, θC＝0.7. The table presents the performance for four methods: FR, RPW,...[이미지참조] 115

Table 3.18. Comparison of different three-arm trial designs when θA＝0.1, θB＝0.5, θC＝0.9. The table presents the performance for four methods: FR, RPW,...[이미지참조] 119

Figure 3.1. The changes in power and type I error for each RPW design when n＝25, 50, 75, 100, θA＝0.5 and θB ∈ (0.1, 0.9). The upper dashed line at 0.8...[이미지참조] 54

Figure 3.2. The changes in percentage of patients on the superior treatment arm for each RPW design when n＝25, 50, 75, 100, θA＝0.5 and θB ∈ (0.1, 0.9).[이미지참조] 55

Figure 3.3. The changes in average bias of the treatment effect estimator for each RPW design when n＝25, 50, 75, 100, θA＝0.5 and θB ∈ (0.1, 0.9).[이미지참조] 56

Figure 3.4. The changes in power and type I error for each ATS design when ρ＝0.5, n＝25, 50, 75, 100, θA＝0.5 and θB ∈ (0.1, 0.9). The upper dashed...[이미지참조] 60

Figure 3.5. The changes in power and type I error for each ATS design when ρ＝3, n＝25, 50, 75, 100, θA＝0.5 and θB ∈ (0.1, 0.9). The upper dashed line at 0.8...[이미지참조] 61

Figure 3.6. The changes in percentage of patients on the superior treatment arm for each ATS design when ρ＝0.5, n＝25, 50, 75, 100, θA＝0.5 and θB ∈...[이미지참조] 62

Figure 3.7. The changes in percentage of patients on the superior treatment arm for each ATS design when ρ＝3, n＝25, 50, 75, 100, θA＝0.5 and θB ∈ (0.1, 0.9).[이미지참조] 63

Figure 3.8. The changes in average bias of the treatment effect estimator for each ATS design when ρ＝0.5, n＝25, 50, 75, 100, θA＝0.5 and θB ∈ (0.1, 0.9).[이미지참조] 64

Figure 3.9. The changes in average bias of the treatment effect estimator for each ATS design when ρ＝3, n＝25, 50, 75, 100, θA＝0.5 and θB ∈ (0.1, 0.9).[이미지참조] 65

Figure 3.10. The changes in power and type I error for CRDP design when p＝0.9, ℓ＝0.15n, n＝25, 50, 75, 100, θA＝0.5 and θB ∈ (0.1, 0.9). The upper dashed...[이미지참조] 68

Figure 3.11. The changes in percentage of patients on the superior treatment arm for CRDP design when p＝0.9, ℓ＝0.15n, n＝25, 50, 75, 100, θA＝0.5 and...[이미지참조] 69

Figure 3.12. The changes in average bias of the treatment effect estimator for CRDP design when p＝0.9, ℓ＝0.15n, n＝25, 50, 75, 100, θA＝0.5 and...[이미지참조] 70

Figure 3.13. The changes in power and type I error for each design when n＝25, 50, 75, 100, θA＝0.5 and θB ∈ (0.1, 0.9).[이미지참조] 73

Figure 3.14. The changes in percentage of patients on the superior treatment arm for each design when n＝25, 50, 75, 100, θA＝0.5 and θB ∈ (0.1, 0.9).[이미지참조] 74

Figure 3.15. The changes in average bias of the treatment effect estimator for each design when n＝25, 50, 75, 100, θA＝0.5 and θB ∈ (0.1, 0.9).[이미지참조] 75

Figure 3.16. The power for each design when n＝25, 50, 75, 100, θA＝0.3 and θB＝0.5.[이미지참조] 77

Figure 3.17. The percentage of patients on the superior treatment arm for each design when n＝25, 50, 75, 100, θA＝0.3 and θB＝0.5.[이미지참조] 78

Figure 3.18. The average bias of the treatment effect estimator for each design when n＝25, 50, 75, 100, θA＝0.3 and θB＝0.5.[이미지참조] 79

Figure 3.19. The changes in power and type I error for each RPW design when n＝25, 50, 75, 100, θA＝0.5, θB ∈ (0.1, 0.9), θC＝0.5. The upper dashed line at...[이미지참조] 83

Figure 3.20. The changes in percentage of patients on the superior treatment arm for each RPW design when n＝25, 50, 75, 100, θA＝0.5, θB ∈ (0.1, 0.9),...[이미지참조] 84

Figure 3.21. The changes in average bias for θA and θB of the treatment effect estimator for each RPW design when n＝25, 50, 75, 100, θA＝0.5, θB ∈...[이미지참조] 85

Figure 3.22. The changes in average bias for θB and θC of the treatment effect estimator for each RPW design when n＝25, 50, 75, 100, θA＝0.5, θB ∈...[이미지참조] 86

Figure 3.23. The changes in average bias for θA and θC of the treatment effect estimator for each RPW design when n＝25, 50, 75, 100, θA＝0.5, θB ∈...[이미지참조] 87

Figure 3.24. The changes in power and type I error for each ATS design when ρ＝0.5, n＝25, 50, 75, 100, θA＝0.5, θB ∈ (0.1, 0.9), θC＝0.5. The upper...[이미지참조] 91

Figure 3.25. The changes in power and type I error for each ATS design when ρ＝3, n＝25, 50, 75, 100, θA＝0.5, θB ∈ (0.1, 0.9), θC＝0.5. The upper dashed...[이미지참조] 92

Figure 3.26. The changes in percentage of patients on the superior treatment arm for each ATS design when ρ＝0.5, n＝25, 50, 75, 100, θA＝0.5, θB ∈ (0.1, 0.9),...[이미지참조] 93

Figure 3.27. The changes in percentage of patients on the superior treatment arm for each ATS design when ρ＝3, n＝25, 50, 75, 100, θA＝0.5, θB ∈ (0.1, 0.9),...[이미지참조] 94

Figure 3.28. The changes in average bias for θA and θB of the treatment effect estimator for each ATS design when ρ＝0.5, n＝25, 50, 75, 100, θA＝0.5,...[이미지참조] 95

Figure 3.29. The changes in average bias for θA and θB of the treatment effect estimator for each ATS design when ρ＝3, n＝25, 50, 75, 100, θA＝0.5,...[이미지참조] 96

Figure 3.30. The changes in average bias for θB and θC of the treatment effect estimator for each ATS design when ρ＝0.5, n＝25, 50, 75, 100, θA＝0.5,...[이미지참조] 97

Figure 3.31. The changes in average bias for θB and θC of the treatment effect estimator for each ATS design when ρ＝3, n＝25, 50, 75, 100, θA＝0.5,...[이미지참조] 98

Figure 3.32. The changes in average bias for θA and θC of the treatment effect estimator for each ATS design when ρ＝0.5, n＝25, 50, 75, 100, θA＝0.5,...[이미지참조] 99

Figure 3.33. The changes in average bias for θA and θC of the treatment effect estimator for each ATS design when ρ＝3, n＝25, 50, 75, 100, θA＝0.5,...[이미지참조] 100

Figure 3.34. The effect of changing the degree of constraining, ℓ, on the power and percentage of patients on the superior treatment when θA＝0.2, θB＝0.8,...[이미지참조] 101

Figure 3.35. The changes in performance measures for CRDP design in action3 when ℓ＝0.24n, n＝25, θA＝0.5, θB ∈ (0.1, 0.9), θC＝0.5.[이미지참조] 105

Figure 3.36. The changes in performance measures for CRDP design in action6 when ℓ＝0.24n, n＝25, θA＝0.5, θB ∈ (0.1, 0.9), θC＝0.5.[이미지참조] 107

Figure 3.37. The changes in power and type I error for each design when n＝25, 50, 75, 100, θA＝0.5, θB ∈ (0.1, 0.9), θC＝0.5. The upper dashed line at 0.8...[이미지참조] 110

Figure 3.38. The changes in percentage of patients on the superior treatment arm for each design when n＝25, 50, 75, 100, θA＝0.5, θB ∈ (0.1, 0.9), θC＝0.5.[이미지참조] 111

Figure 3.39. The changes in average bias for θA and θB of the treatment effect estimator for each design when n＝25, 50, 75, 100, θA＝0.5, θB ∈ (0.1, 0.9),...[이미지참조] 112

Figure 3.40. The changes in average bias for θB and θC of the treatment effect estimator for each design when n＝25, 50, 75, 100, θA＝0.5, θB ∈ (0.1, 0.9),...[이미지참조] 113

Figure 3.41. The changes in average bias for θA and θC of the treatment effect estimator for each design when n＝25, 50, 75, 100, θA＝0.5, θB ∈ (0.1, 0.9),...[이미지참조] 114

Figure 3.42. The power for each design when n＝25, 50, 75, 100, θA＝0.3, θB＝0.4, θC＝0.7.[이미지참조] 116

Figure 3.43. The percentage of patients on the superior treatment arm for each design when n＝25, 50, 75, 100, θA＝0.3, θB＝0.4, θC＝0.7.[이미지참조] 117

Figure 3.44. The average bias for θA&θB, θB&θC, θA&θC of the treatment effect estimator for each design when n＝25, 50, 75, 100, θA＝0.3, θB＝0.4, θC＝0.7.[이미지참조] 118

Figure 3.45. The power for each design when n＝25, 50, 75, 100, θA＝0.1, θB＝0.5, θC＝0.9.[이미지참조] 120

Figure 3.46. The percentage of patients on the superior treatment arm for each design when n＝25, 50, 75, 100, θA＝0.1, θB＝0.5, θC＝0.9.[이미지참조] 121

Figure 3.47. The average bias for θA&θB, θB&θC, θA&θC of the treatment effect estimator for each design when n＝25, 50, 75, 100, θA＝0.1, θB＝0.5, θC＝0.9.[이미지참조] 122