A Bayesian Adaptive Design in Cancer Phase I Trials Using Dose Combinations with Ordinal Toxicity Grades
Abstract
:1. Introduction
2. Method
2.1. Dose–Toxicity Model
2.2. Prior and Posterior Distributions
2.3. Trial Design
- Each patient in the first cohort of two patients receives the same dose combination .
- In the ith cohort of two patients:
- (a)
- If i is even, then patient receives dose and patient receives dose , where
- (b)
- If i is odd, then patient receives dose and patient receives dose , where
- Repeat Step 2 until n patients are enrolled to the trial subject to the following stopping rule.
3. Simulations
3.1. Set-Up and Scenarios
3.2. Operating Characteristics
3.2.1. Safety
3.2.2. Efficiency
3.3. Results
4. Discrete Approach
- (i)
- Let ,, and .
- (ii)
- Let .
4.1. Operating Characteristics
4.2. Illustration
5. Concluding Remarks
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Average % Grade 2 | Average % DLTs (Z = 3) | ||||
---|---|---|---|---|---|
Scenario | Design | (Z = 2) | (%Trials: DLT Rate (Z = 3) > 0.43) | ||
Binary | Ordinal | Binary | Ordinal | ||
1a | EWOC | 76.12 | 81.41 | 16.31 (0.0) | 10.86 (0.0) |
CRM | 76.03 | 81.32 | 16.47 (0.0) | 11.14 (0.0) | |
1b | EWOC | 78.47 | 83.33 | 16.35 (0.0) | 11.48 (0.0) |
CRM | 78.76 | 84.34 | 16.16 (0.0) | 10.48 (0.0) | |
2a | EWOC | 61.22 | 61.77 | 30.31 (0.0) | 29.37 (0.0) |
CRM | 59.36 | 60.39 | 32.33 (0.23) | 31.26 (0.47) | |
2b | EWOC | 64.34 | 65.23 | 30.44 (0.07) | 29.45 (0.40) |
CRM | 62.32 | 67.80 | 32.45 (0.43) | 31.67 (0.70) | |
3a | EWOC | 67.65 | 69.63 | 25.29 (0.0) | 22.96 (0.0) |
CRM | 65.29 | 67.46 | 27.36 (0.0) | 25.53 (0.0) | |
3b | EWOC | 69.67 | 71.48 | 25.25 (0.0) | 23.30 (0.0) |
CRM | 67.40 | 69.27 | 27.53 (0.0) | 25.64 (0.0) | |
4a | EWOC | 58.98 | 58.47 | 32.64 (0.07) | 33.06 (1.10) |
CRM | 57.74 | 57.79 | 33.95 (0.20) | 34.11 (1.57) | |
4b | EWOC | 61.90 | 61.51 | 32.90 (0.03) | 33.17 (0.97) |
CRM | 60.73 | 60.37 | 34.06 (0.20) | 34.45 (1.57) | |
5a | EWOC | 49.11 | 48.44 | 36.73 (2.63) | 37.66 (6.30) |
CRM | 48.38 | 47.73 | 37.00 (2.17) | 38.55 (10.20) | |
5b | EWOC | 57.39 | 55.96 | 36.71 (2.33) | 38.14 (8.97) |
CRM | 57.06 | 55.10 | 36.96 (2.13) | 38.98 (13.40) | |
6a | EWOC | 52.04 | 52.19 | 32.83 (1.00) | 32.67 (1.47) |
CRM | 50.45 | 50.98 | 34.98 (2.77) | 34.65 (3.50) | |
6b | EWOC | 61.04 | 61.17 | 32.85 (1.20) | 32.70 (2.00) |
CRM | 59.11 | 59.32 | 34.91 (2.20) | 34.63 (4.40) |
Scenario 01 | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|
Dose Level | Z = 1 | Z = 2 | ||||||||
1 | 2 | 3 | 4 | 5 | 1 | 2 | 3 | 4 | 5 | |
5 | 0.50 | 0.44 | 0.38 | 0.31 | 0.24 | 0.45 | 0.53 | 0.60 | 0.68 | 0.75 |
4 | 0.53 | 0.49 | 0.43 | 0.35 | 0.26 | 0.40 | 0.46 | 0.53 | 0.63 | 0.70 |
3 | 0.58 | 0.57 | 0.51 | 0.43 | 0.36 | 0.33 | 0.36 | 0.44 | 0.53 | 0.59 |
2 | 0.65 | 0.57 | 0.55 | 0.47 | 0.44 | 0.20 | 0.33 | 0.38 | 0.48 | 0.53 |
1 | 0.68 | 0.65 | 0.58 | 0.53 | 0.48 | 0.15 | 0.20 | 0.33 | 0.40 | 0.47 |
Scenario 02 | ||||||||||
Dose Level | Z = 1 | Z = 2 | ||||||||
1 | 2 | 3 | 4 | 5 | 1 | 2 | 3 | 4 | 5 | |
5 | 0.36 | 0.44 | 0.48 | 0.41 | 0.34 | 0.28 | 0.35 | 0.42 | 0.52 | 0.60 |
4 | 0.30 | 0.39 | 0.43 | 0.45 | 0.38 | 0.22 | 0.23 | 0.33 | 0.43 | 0.45 |
3 | 0.24 | 0.27 | 0.31 | 0.43 | 0.49 | 0.17 | 0.20 | 0.21 | 0.33 | 0.39 |
2 | 0.15 | 0.27 | 0.28 | 0.37 | 0.44 | 0.11 | 0.14 | 0.19 | 0.25 | 0.30 |
1 | 0.10 | 0.25 | 0.28 | 0.30 | 0.38 | 0.08 | 0.13 | 0.15 | 0.21 | 0.27 |
Scenario 01 | ||||||||
Criterion | Model | PS | S-3 | S-2 | S-1 | AV | % Grade 2 | Average DLT Rate |
(% Excessive DLT) | ||||||||
EWOC | Binary | 57.2 | 9.5 | 29.0 | 64.6 | 84.8 | 54.33 | 31.91 (1.27) |
Ordinal | 71.7 | 26.7 | 54.7 | 92.2 | 82.4 | 54.81 | 31.59 (1.63) | |
CRM | Binary | 54.2 | 8.2 | 25.3 | 62.7 | 82.4 | 53.74 | 32.92 (1.66) |
Ordinal | 70.5 | 26.2 | 61.9 | 91.6 | 81.1 | 53.86 | 32.87 (2.43) | |
Scenario 02 | ||||||||
Criterion | Model | PS | S-3 | S-2 | S-1 | AV | % Grade 2 | Average DLT Rate |
(% Excessive DLT) | ||||||||
EWOC | Binary | 26.6 | 3.3 | 12.5 | 40.1 | 64.2 | 30.14 | 21.11 (0.00) |
Ordinal | 38.4 | 38.2 | 58.4 | 84.9 | 63.9 | 30.95 | 21.30 (0.00) | |
CRM | Binary | 29.2 | 3.7 | 12.6 | 40.0 | 68.8 | 31.57 | 23.24 (0.04) |
Ordinal | 44.7 | 49.9 | 69.4 | 90.5 | 71.3 | 32.77 | 23.33 (0.00) |
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Diniz, M.A.; Kim, S.; Tighiouart, M. A Bayesian Adaptive Design in Cancer Phase I Trials Using Dose Combinations with Ordinal Toxicity Grades. Stats 2020, 3, 221-238. https://doi.org/10.3390/stats3030017
Diniz MA, Kim S, Tighiouart M. A Bayesian Adaptive Design in Cancer Phase I Trials Using Dose Combinations with Ordinal Toxicity Grades. Stats. 2020; 3(3):221-238. https://doi.org/10.3390/stats3030017
Chicago/Turabian StyleDiniz, Márcio A., Sungjin Kim, and Mourad Tighiouart. 2020. "A Bayesian Adaptive Design in Cancer Phase I Trials Using Dose Combinations with Ordinal Toxicity Grades" Stats 3, no. 3: 221-238. https://doi.org/10.3390/stats3030017