1. Statistical Methods for Biotechnology Products II
Phase I and II Cancer Clinical Trials
Instructor: Jen-pei Liu, Ph.D.
Division of Biometry
Department of Agronomy
National Taiwan University, and
Division of Biostatistics and Bioinformatics
National Health Research Institutes
2018/12/8
copyright by Jen-pei Liu, PhD

2. copyright by Jen-pei Liu, PhD
Outlines
Introduction
Characterization of Cancer Trials
Phase I Trials
Single Stage
Two Stage
Bayesian Approach
Phase II Trials
Multi-stage Designs
Randomized Phase II Trials
2018/12/8
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3. copyright by Jen-pei Liu, PhD
Introduction
Characterization of Cancer Trials
Patient population – life-threatening and irreversible
Treatments – cytotoxic agents:
No efficacy at lower doses but with severe immunosuppression, hepatic, renal, and cardiac toxicity
Efficacious at high doses but with possible fatal or life-threatening AEs
2018/12/8
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Introduction
Criteria
Minimize exposure of subjects to the investigational new cancer interventions
Select efficacious cytotoxic agents with an acceptable safety profile in the most efficient way
2018/12/8
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Cancer Phase I Studies
Maximum Tolerable Dose (MTD)
The maximum dose with an acceptable and manageable safety profile
Dose-Limiting Toxicity (DLT)
The unacceptable or unmanageable safety profile
Pre-defined by some criteria – NCI Common Toxicity Criteria (CTC)
Grade 3 or greater hematological toxicity
2018/12/8
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Cancer Phase I Studies
Designs for the maximum tolerable dose
For PhaseⅠcancer chemotherapy
Pre-selected fixed dose levels
Maximum Tolerable Dose (MTD)
Quantitative Definition
Some percentile of a tolerance distribution w.r. to some definitive dose-limiting clinical toxicity
Storer (1989), Korn, et al (1994)
2018/12/8
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Cancer Phase I Studies
2018/12/8
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2018/12/8
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9. copyright by Jen-pei Liu, PhD
Cancer Phase I Studies
Starting dose (Storer, 1997)
1/10 – 1/3 of the mouse LD10
Subsequent Doses
The modified Fibonacci sequence
{2, 1.67, 1.5, 1.4, 1.33….}
2018/12/8
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Cancer Phase I Studies
Considerations of Cancer Phase I Trials
Critically ill patients
Limited availability of patients
Heterogeneous patient population
A screening process of potential cancer drugs
Serious, irreversible, life-threatening, and maybe fatal AEs
2018/12/8
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11. Standard Dose Escalation Design
Step 1
A group of three patients are treated with the initial dose
Step 2
If no toxicity is observed in all three patients, then the dose for the next group of three patients is escalated to the next higher dose level. Otherwise, the next group of three patients is treated at the same dose.
2018/12/8
copyright by Jen-pei Liu, PhD

12. Standard Dose Escalation Design
Step 3
The dose of the next group of three patients is escalated to the next higher dose level, if the pre-specified clinical toxicity is observed at most one patient of the six patients from both step 1 and 2, otherwise the trial stops.
Step 4
Repeat step 2 and 3 two consecutive groups of three patients until the trial stops.
Traditionally from the standard design, the MTD is defined to be either the dose at which the trial stops or the next lower dose.
2018/12/8
copyright by Jen-pei Liu, PhD

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2018/12/8
copyright by Jen-pei Liu, PhD

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2018/12/8
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2018/12/8
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16. Drawbacks of the Current Practice for Standard Design
No room for de-escalation
No further analysis of data
No objective estimation of MTD with statistical models
No sampling error and no confidence interval
Slow escalation
2018/12/8
copyright by Jen-pei Liu, PhD

17. Accelerated Titration Designs Richard Simon (1997)
Rationale
Address the flaws of traditional designs
Attempt to obtain information about inter-patient variability and cumulative toxicity - stay for 3 courses to allow for intra-patient dose modifications
Distinguish between moderate and dose-limiting toxicities
2018/12/8
copyright by Jen-pei Liu, PhD

18. Accelerated Titration Designs Richard Simon (1997)
Scheme
The first stage
1 patient per level until 1 DLT or 2 moderate toxicities
The second stage
Traditional design, i.e. add 2 patients to the current dose that triggered the switch.
2018/12/8
copyright by Jen-pei Liu, PhD

19. Accelerated Titration Designs Richard Simon (1997)
MTD
Estimated as the highest dose where at most 1/6 patients developed DLT
Compared to traditional designs
Go through the lower doses quickly, and thus reduces under-treated patients in absolute sense and speed up the completion
Obtain similar estimate of MTD
Provide more information. Upon completion, a model can be fitted to estimate inter- and intra-patient variability
Require careful patient management to track the toxicity over multiple course
2018/12/8
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20. Issues of PhaseⅠDesigns for MTD
Complete the trials with
Minimum amount of patients, and
Minimum amount of time
Recognize differential dosing-limiting clinical toxicity
Include a stopping rule to allow flexibility to extend to higher or lower dose levels
Investigators and regulatory agencies dictate the dose level for the first patient
2018/12/8
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21. copyright by Jen-pei Liu, PhD
Cancer PhaseⅠStudies
Designs for determination of maximum tolerable dose
For PhaseⅠcancer chemotherapy
Pre-selected fixed dose levels
Maximum Tolerable Dose (MTD)
Quantitative Definition
Some percentile of a tolerance distribution w.r. to some definitive dose-limiting clinical toxicity Storer (1989), Korn, et al (1994)
2018/12/8
copyright by Jen-pei Liu, PhD

22. copyright by Jen-pei Liu, PhD
2018/12/8
copyright by Jen-pei Liu, PhD

23. Standard Dose Escalation Design
Step 1
A group of three patients are treated with the initial dose
Step 2
If no toxicity is observed in all three patients, then the dose for the next group of three patients is escalated to the next higher dose level. Otherwise, the next group of three patients is treated at the same dose.
2018/12/8
copyright by Jen-pei Liu, PhD

24. Standard Dose Escalation Design
Step 3
The dose of the next group of three patients is escalated to the next higher dose level, if the pre-specified clinical toxicity is observed at most one patient of the six patients from both step 1 and 2, otherwise the trial stops.
Step 4
Repeat step 2 and 3 two consecutive groups of three patients until the trial stops.
Traditionally from the standard design, the MTD is defined to be either the dose at which the trial stops or the next lower dose.
2018/12/8
copyright by Jen-pei Liu, PhD

25. copyright by Jen-pei Liu, PhD
2018/12/8
copyright by Jen-pei Liu, PhD

26. Drawbacks of the Current Practice for Standard Design
No room for de-escalation
No further analysis of data
No objective estimation of MTD with statistical models
No sampling error and no confidence interval.
2018/12/8
copyright by Jen-pei Liu, PhD

27. Bayesian Sequential Design
The Continual Reassessment Method (CRM)
O’Quigley, Pepe, Fisher (1990), O’Quigley (1992), Moller (1995)
Step 1
Determine the dose-toxicity relationship
Select fixed dose levels
Determine the prior probability of slope
Choose a fixed sample size
Step 2
Determine the dose for the first patient as the dose level which produces the prior probability of dose-limiting clinical toxicity closest to p.
2018/12/8
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28. Bayesian Sequential Design
Step 3
Update the posterior distribution of slope after each patient’s toxicity result becomes available. The dose level for the next patient is the one which gives the posterior probability of dose-limiting clinical toxicity closest to p.
Step 4
Repeat Step 3 until the results of the last patient are available.
Step 5
The estimated MTD is determined as the dose which minimizes some pre-selected criterion such as some quadratic error loss function with respect to the probability of dose-limiting clinical toxicity.
2018/12/8
copyright by Jen-pei Liu, PhD

29. Advantages of Continual Reassessment Method
Try to accommodate the situations
Patients at high risk of death
Fatal toxicity of new drug at high doses
No efficacy at lower doses
No information about dose range
A well-defined goal of estimating a percentile of the dose-toxicity relationship
It should converge to percentile with increasing sample size.
2018/12/8
copyright by Jen-pei Liu, PhD

30. Issues of Continual Reassessment Method
Assumption of a homogeneous patient population for the prior distribution of parameters
It treats patients in cohorts of 1
It takes too long to complete the trial
It is less conservative so that it may treat patients at very high dose levels
Difficulty in choice of a criterion metric
2018/12/8
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31. copyright by Jen-pei Liu, PhD
Simulated comparison of five possible methods of escalation/estimation for a phaseⅠtrial
Dose level
True probability of toxicity
Method
Standard minimum number of patients treated at the MTD
Continual reassessment targeted probability (θ)of dose-limiting toxicity for the MTD 6 3
Θ=0.25
Θ=0.20
Θ=0.15
Recommended (MTD) dose level (%) - 1
0.05 10 9 5 20 2
0.10 39 35 22 33 42
0.25 32 38 25 4
0.35 15 18 23 16
0.50
0.70
Dose levels treated at (%) 24 13 28 26 30 27 21 12 8
Average number of patients treated (25th percentile, 75th percentile)
(12, 18)
(12, 18)
(12, 15)
(11, 15)
(11, 15)
Average number of toxicities
Probability of toxicity
Average number of cohorts
3.3
0.20
5.1
2.8
4.7
3.5
0.26
13.4
3.1
0.23
13.2
2.7
0.21
12.7
Source: Vorn et al (1994)
2018/12/8
copyright by Jen-pei Liu, PhD

32. copyright by Jen-pei Liu, PhD
Simulated comparison of five possible methods of escalation/estimation for a phaseⅠtrial
Dose level
True probability of toxicity
Method
Standard minimum number of patients treated at the MTD
Continual reassessment targeted probability (θ)of dose-limiting toxicity for the MTD 6 3
Θ=0.25
Θ=0.20
Θ=0.15
Recommended (MTD) dose level (%) - 1
0.00 2
0.01
0.04 9 8 11 4
0.09 39 35 16 28 40 5
0.24 44 46 59 53 41
0.49 10 22 12
Dose levels treated at (%) 14 15 17 21 19 20 24 23 34 32
Average number of patients treated (25th percentile, 75th percentile)
(21, 24)
(18, 21)
(11, 15)
(12, 15)
(12.15)
Average number of toxicities
Probability of toxicity
Average number of cohorts
3.0
0.14
7.2
2.6
0.13
6.4
0.20
13.3
2.4
0.18
13.7
2.1
0.15
13.8
Source: Vorn et al (1994)
2018/12/8
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33. copyright by Jen-pei Liu, PhD
Simulated comparison of five possible methods of escalation/estimation for a phaseⅠtrial
Dose level
True probability of toxicity
Method
Standard minimum number of patients treated at the MTD
Continual reassessment targeted probability (θ)of dose-limiting toxicity for the MTD 6 3
Θ=0.25
Θ=0.20
Θ=0.15
Recommended (MTD) dose level (%) - 56 50 32 31 1
0.30 35 43 53 61 2
0.40 10 13 19 7
0.52 4
0.61 5
0.76
0.87
Dose levels treated at (%) 62 60 59 64 29 30 27 25 21 8 9 11
Average number of patients treated (25th percentile, 75th percentile)
(6,12)
(6, 9)
(7, 12)
(6, 11)
(6, 11)
Average number of toxicities
Probability of toxicity
Average number of cohorts
2.9
0.35
2.8
2.5
2.4
3.6
0.38
9.6
3.4
0.37
9.2
3.2
0.36
8.9
Source: Vorn et al (1994)
2018/12/8
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34. copyright by Jen-pei Liu, PhD
Modifications of CRM
Goodman, Zahurak & Piantadosi (1995)
> 1 patient per cohort, dose increase is limited to 1 level, start at the lowest level
Moller (1995)
Combined with a preliminary up-and-down design, limit escalation to 1 level.
Piantadosi & Liu (1996)
Incorporate pharmacokinetics parameters
Some of other simulation studies for comparing CRM’s with nonparametric approach: O’Quigley & Chevret (1991), Chevret (1993), Ahn (1996)
2018/12/8
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35. copyright by Jen-pei Liu, PhD
Cancer Phase II Trials
Allows early termination for inactivity or high activity.
Define
P0: undesirable level (lower bound)
P1: target level
2018/12/8
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36. copyright by Jen-pei Liu, PhD
Simon’s design
Procedure
Stage 1: If X1 > r go to stage 2
≦ r stop and reject the drug
Stage 2: If X1+X2 is ≦ r reject the drug
> r accept the drug
Given p0, p1, α, β, then (n1, n2, r1, r) are optimized to minimize either
The expected sample size under p0, or
The maximal sample size n1 + n2
Not readily evaluable, but tables of designs under different values of parameter are available from the paper.
2018/12/8
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37. copyright by Jen-pei Liu, PhD
Designs for p1 – p0 = 0.20
Optimal Design
Minimax Design
Reject Drug if Response Rate P1 p0
≦ r1/n1
≦ r/n
EN(p0)
PET(p0)
0.05
0.25
0/9
2/24
2/17
3/30
14.5
12.0
16.8
0.63
013
012
015
2/20
2/16
3/25
1634
13.8
20.4
0.51
0.54
0.46
0.10
0.30
1/12
1/10
2/18
5/35
5/29
6/35
19.8
15.0
22.5
0.65
0.74
0.71
1/16
1/15
2/22
4/25
5/25
6/33
19.5
26.2
0.55
0.62
0.20
0.40
3/17
3/13
4/19
10/37
12/43
15/54
26.0
20.6
30.4
0.75
0.67
3/19
4/18
5/24
10/36
10/33
13/45
28.3
22.3
31.2/
0.50
0.66
7/22
5/15
8/24
17/46
18/46
24/63
29.9
23.6
34.7
0.72
0.73
7/28
6/19
7/24
15/39
16/39
21/53
35.0
25.7
36.6
0.36
0.48
0.56
0.60
7/18
7/16
11/25
22/46
23/46
32/66
30.2
24.5
36.0
/0.56
11/28
17/34
12/28
20/41
20/39
27/54
33.8
34.4
38.1
0.91
0.64
0.70
11/21
8/15
13/24
26/45
26/43
36/61
29.0
23.5
34.0
11/23
12/23
14/27
23/39
23/37
32/53
31.0
27.7
36.1
0.80
6/11
7/11
12/19
26/38
30/43
37/53
25.4
20.5
29.5
0.47
0.69
18/27
8/13
15/26
24/35
25/35
32/45
28.5
20.8
35.9
0.82
0.90
6/9
4/6
11/15
22/28
22/27
29/36
17.8
14.8
21.2
0.58
11/16
19/23
13/18
20/25
21/26
26/32
20.1
23.2
22.7
0.95
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38. copyright by Jen-pei Liu, PhD
Designs for p1 – p0 = 0.15
Optimal Design
Minimax Design
Reject Drug if Response Rate P1 p0
≦ r1/n1
≦ r/n
EN(p0)
PET(p0)
0.05
0.20
0/12
0/10
1/21
3/37
3/29
4/41
23.5
17.6
26.7
0.54
0.60
0.72
0/18
0/13
1/29
3/32
3/27
4/38
26.4
19.8
32.9
0.40
0.51
0.57
0.10
0.25
2/21
2/18
7/50
7/43
10/66
31.2
24.7
36.8
0.65
0.73
2/27
2/22
3/31
6/40
7/40
9/55
33.7
28.8
40.0
0.48
0.62
0.35
5/27
5/22
8/37
16/63
19/72
22/83
43.6
35.4
51.4
0.69
6/33
6/31
8/42
15/58
15/53
21/77
45.5
40.4
58.4
0.50
0.53
0.30
0.45
9/30
9/27
13/40
29/82
30/81
40/110
41.7
60.8
0.59
0.70
16/50
16/46
27/77
25/69
25/65
33/88
56.0
49.6
78.5
0.68
0.81
0.86
0.55
16/38
11/26
19/45
40/88
40/84
49/104
54.5
44.9
64.0
0.67
18/45
28/59
24/62
34/73
37/70
45/94
57.2
60.1
78.9
0.56
0.90
0.47
18/35
15/28
22/42
47/84
48/83
60/105
53.0
43.7
62.3
0.63
0.71
19/40
39/66
28/57
41/72
40/68
54/93
58.0
66.1
75.0
0.44
0.95
0.75
21/34
17/27
47/71
46/67
64/95
47.1
39.4
55.6
25/43
18/30
48/72
43/64
43/62
57/84
54.4
43.8
73.2
0.46
0.85
14/20
14/19
18/25
27/31
26/29
37/42
20.8
17.7
24.4
0.42
0.76
5/7
7/9
31/35
35/40
34.4
48.5
2018/12/8
copyright by Jen-pei Liu, PhD