1. Theis Lange and Shanmei Liao
Dose Escalation Design in Combo Studies: Adjusted AAA and TBSC (Two Stage, Bayesian Method, Split Cohort)
Theis Lange and Shanmei Liao
JSM 2019

2. Needs Drug A: new compound, safety profile in clinic unknown
Drug B: studied compound, safety profile in clinic well known
Hint from preclinical:
Combo with Drug A might require Drug B to decrease 1 level from its RP2D (recommended dose for phase 2).
Need 2 MTDs
One with Drug B at RP2D, one with Drug B at RP2D-1

3. AAA and adjAAA AAA desing (Lyu 2017*) adjAAA Bayesian model based
Incorporate mono info into combo
Allow two cohorts to be started at the same time if deemed both optimal.
Models for the efficacy estimation (ie. risk-benefit tradeoff)
Insert unplanned dose level
adjAAA
Keep the feature 1-3, and provide 2 MTDs at the end (with RP2D and RP2D- 1 in Drug B)
* Lyu, J., Ji, Y*., Zhao, N*, Catenacci, DVT. AAA: Triple-adaptive Bayesian designs for the identification of optimal dose combinations in dual-agent dose-finding trials. (revision) JRSS-C

4. Parameters Drug A: 6 levels, i.e. 20, 40, 80, 160, 300 and 600mg
Drug B: 2 levels: 160mg and 80mg
Target tolerable DLT rates: 20% tox for mono and 30% for combo.
The most expected case is shown below, with MTDs as (Drug A=300, Drug B=160), (Drug A= 600, Drug B= 80) and (Drug A= 600) for combo and mono.
True tox (scenario 0)
Dose Drug A 20 40 80
160
300
600
Dose Drug B
0.10
0.15
0.20
0.25
0.30
0.35
0.06
0.19
0.23
0.28
0.01
0.05
0.09
0.13
0.16
The true tox probs are constructed by fixing 4 cells values (landmark tox rates, yellow highlighted) based on above assumptions and then do linear interpolation (on log values for Drug A dose).

5. Illustration
STAGE I: Each cohort includes 3 persons. 3+3 in mono followed by diagonal up-dose
Dose escalation will stop if observe 2 out of 3 pts in one cohort with DLT.
True tox (scenario 0)
Dose Drug A 20 40 80
160
300
600
Dose Drug B
0.10
0.15
0.20
0.25
0.30
0.35
0.06
0.19
0.23
0.28
0.01
0.05
0.09
0.13
0.16
Cohort ID
Dose Drug A
Dose Drug B
Event count 1 20 2 40 3 80 4
160 5 6
300
Cohort ID
Dose Drug A
Dose Drug B
Event count 7
600 8 20 80 9 40
160 1 10 11 12
300 2
Stage I stopped because we saw two events in a single cohort.

6. Illustration (2) STAGE II
At end of Stage I a Bayesian analysis said combo with predicted tox level closest to target was Drug A=300 for Drug B=80 and Drug A=160 for Drug B=160.
These two cohorts were therefore started.
After each pair of cohorts (Drug B = 80 and 160) new optimal doses were estimated.
We stop when the limit (36 pt) for combo part have been reached.
Cohort ID
Dose Drug A
Dose Drug B
Event count
Best Drug A (Drug B=80)
Best Drug A (Drug B=160) 13
300 80 1
600
160 14 15 2 16 17 18 19 20

7. Compare With Other Methods
We will consider the following designs for the dose escalation:
3+3 for both mono and combo
3+3 for mono and BLRM (the Bayesian Logistic Regression Method) design for combo.
3+3 for mono combined with the adjAAA
Three different tox scenarios will be explored: most expected, low tox and high tox
Besides the prob of choosing the correct MTD, study duration and total sample size will also be compared among the three models.

8. Scenario 0 – Most Expected
Assumed true tox
Results
Dose Drug A 20 40 80
160
300
600
Dose Drug B
0.10
0.15
0.20
0.25
0.30
0.35
0.06
0.19
0.23
0.28
0.01
0.05
0.09
0.13
0.16
adjAAA
Dose Drug A 20 40 80
160
300
600
Dose Drug B
0.05
0.11
0.18
0.23
0.26
0.07
0.22
0.29
0.36
 Triple 3+3
Dose Drug A 20 40 80
160
300
600
Dose Drug B
0.28
0.23
0.21
0.16
0.08
0.05
0.13
0.20
0.19
0.14
0.18
BLRM
Dose Drug A 30 80
160
300
600
Dose Drug B
0.02
0.07
0.09
0.04
0.01
0.05
0.21
0.23

9. Scenario 1 – Low Tox Assumed true tox Results Dose Drug A 20 40 80 160
300
600
Dose Drug B
0.10
0.13
0.16
0.19
0.22
0.25
0.06
0.09
0.12
0.23
0.01
0.05
0.20
adjAAA
Dose Drug A 20 40 80
160
300
600
Dose Drug B
0.06
0.11
0.15
0.26
0.35
0.12
0.03
0.14
0.25
0.45
 Triple 3+3
Dose Drug A 20 40 80
160
300
600
Dose Drug B
0.24
0.17
0.15
0.11
0.13
0.16
0.29
 BLRM
Dose Drug A 30 80
160
300
600
Dose Drug B
0.01
0.05
0.10
0.09
0.15
0.001
0.03
0.11
0.17
0.29

10. Scenario 2 – High Tox Assumed true tox Results Dose Drug A 20 40 80
160
300
600
Dose Drug B
0.10
0.17
0.23
0.30
0.36
0.43
0.06
0.11
0.28
0.34
0.01
0.16
0.20
0.25
 adjAAA
Dose Drug A 20 40 80
160
300
600
Dose Drug B
0.02
0.15
0.31
0.27
0.17
0.07
0.03
0.14
0.36
 Triple 3+3
Dose Drug A 20 40 80
160
300
600
Dose Drug B
0.31
0.26
0.23
0.13
0.05
0.02
0.15
0.20
0.24
0.12
0.09
 BLRM
Dose Drug A 30 80
160
300
600
Dose Drug B
0.03
0.06
0.09
0.05
0.01
0.11
0.33
0.20
0.12

11. Sample Size and Number of DLTs
Under Scenario 0 (the most expected case) we examine the number of patients required for each of the methods.
In design for adjAAA, we only fixed the dose escalation in combo and stage 2 as n=36, the sample size needed or mono dose escalation in not controlled. Same to the BLRM.
Mean sample size
Mean Number of DLT events
Scenario
adjAAA
Triple 3+3
BLRM
57.5
56.1
56.5
9.8
8.1
8.9 1
57.3
57.9
56.6
8.5
7.4
8.0 2
57.2
54.3
56.2
11.3
8.7
10.1
Sample size used in adjAAA is similar to those in the triple 3+3 and BLRM.
The average DLT numbers are slightly higher in adjAAA compared to the other two. While this is also related to a higher probability of identifying the true MTDs in adjAAA.

12. Study Duration
Since all three models explored are fixing cohort at size 3, with same sample size, the one allowing parallel cohort dosing will have relatively shorter study duration.
In this case, adjAAA could have shorter study duration with the adaptive feature 3, start cohorts simultaneously.
If we can decide from medical perspective, how soon we can start the combo exploration after certain dose is explored in mono, that will further shorten our study duration.

13. Looking Forward and Broader
Similar to the previous case, in current competitive drug development environment, new info might coming up during or after the dose escalation study.
One single MTD combo is no longer enough for a better prediction of ultimate successful dose combo when other aspects comes in to play, i.e. late onset AEs, efficacy, PK, ...
Instead of limited ourselves to one single point, we should look forward and look broader.
We suggest new paradigm where next dose is chosen by establish how best to minimize
uncertainty on the clinical relevant
parameters upon trial completion.
Two Stage, Bayesian Method, Split Cohort
(TBSC) Designs

14. The New Goal
The ultimate goal in a combo-dose escalation trial is to determine the location of the curve P(DLT=1)=30% in the two-dimensional dose space.
Perhaps restricted to a pre-specified target-box.
If we knew the red-curve we would know all doses with the desired tox-level.
Target box
P(DLT=1)=0.3

15. The Procedure – Overview
Stage I
A rule base approach (say 3+3) along a pre-defined escalation trajectory (eg. diagonal).
Combo dose can be tested before all mono levels are tested.
Possibly to run a mono escalation trial in parallel.
Stage II
Fit a Bayesian logistic regression on all data.
Compute credibility area for the 30%-tox curve (green area below).
Pick next dose such that we minimize the expected size of the credibility area
Repeat 1-3 until predefined sample size reached.
Target box
P(DLT=1)=0.3

16. Illustration After stage 1 (reached highest combo) we have:
Proposed new dose combo (drug A, drug B)
Expected new area of credibility interval
(20, 80)
0.757
(20, 120)
0.766 …
(800, 120)
0.746
(800, 200)
0.814
Red line is true tox curve (30%), blue dots are current best guess, while circles are all doses inside the current 95% credibility interval for having 30% tox risk.
This dose will be used next.

17. Illustration (2) After next cohort this is status:
Proposed new dose (drug A, drug B)
Expected new area of credibility interval
(20, 80)
0.655
(20, 120)
0.639 …
(600, 160)
0.637
(800, 200)
Red line is true tox curve (30%), blue dots are current best guess, while circles are all doses inside the current 95% credibility interval for having 30% tox risk.
This dose will be used next.

18. Illustration (3) Keep going and after 57 patients:
Red line is true tox curve (30%), blue dots are current best guess, while circles are all doses inside the current 95% credibility interval for having 30% tox risk.
It can be seen that we have now practically uncovered the unknown red-curve (true tox).

19. Scenario 0 – Most Expected
Assumed true tox
Results: probability of chosen as MTD
True tox
Dose Drug A 20 40 80
160
300
600
Dose Drug B
0.1
0.15
0.20
0.25
0.30
0.35
0.06
0.10
0.19
0.23
0.28
 TBSC
Dose Drug A 30 80
160
300
600
Dose Drug B
0.018
0.062
0.134
0.265
0.086
0.014
0.006
0.073
0.231
0.111
TBSC – 2 parallel cohorts
Dose Drug A 30 80
160
300
600
Dose Drug B
0.024
0.07
0.121
0.285
0.068
0.009
0.01
0.088
0.219
0.107
 Model BLRM
Dose Drug A 30 80
160
300
600
Dose Drug B
0.017
0.068
0.091
0.07
0.037
0.007
0.053
0.209
0.212
0.233

20. TBSC – 2 parallel cohorts
Scenario 1 – Low Tox
Assumed true tox
Results: probability of chosen as MTD
True tox
Dose Drug A 20 40 80
160
300
600
Dose Drug B
0.10
0.13
0.16
0.19
0.22
0.25
0.06
0.09
0.12
0.23
 TBSC
Dose Drug A 30 80
160
300
600
Dose Drug B
0.002
0.027
0.070
0.307
0.344
0.014
0.007
0.028
0.094
0.107
TBSC – 2 parallel cohorts
Dose Drug A 30 80
160
300
600
Dose Drug B
0.002
0.038
0.074
0.307
0.314
0.006
0.005
0.027
0.093
0.135
 Model BLRM
Dose Drug A 30 80
160
300
600
Dose Drug B
0.011
0.050
0.101
0.091
0.145
0.001
0.028
0.108
0.173
0.291

21. TBSC – 2 parallel cohorts
Scenario 2 – High Tox
Assumed true tox
Results: probability of chosen as MTD
True tox
Dose Drug A 20 40 80
160
300
600
Dose Drug B
0.10
0.17
0.23
0.30
0.36
0.43
0.06
0.11
0.16
0.21
0.26
0.31
 TBSC
Dose Drug A 30 80
160
300
600
Dose Drug B
0.021
0.090
0.149
0.141
0.024
0.014
0.029
0.166
0.287
0.079
TBSC – 2 parallel cohorts
Dose Drug A 30 80
160
300
600
Dose Drug B
0.025
0.084
0.160
0.131
0.029
0.009
0.036
0.153
0.298
0.077
 Model BLRM
Dose Drug A 30 80
160
300
600
Dose Drug B
0.021
0.045
0.058
0.026
0.011
0.013
0.086
0.317
0.222
0.198

22. Trial Properties Sample size and DLT event counts:
For TBSC the termination criterion is total sample size and therefore constant.
Study duration:
The TBSC design can naturally initiate multiple in parallel cohorts (illustrated in TBSC-2) and can therefore complete faster in cases where patient requirement speed is not a bottleneck.
The only limitations on the number of parallel running cohorts is safety/ethical aspect.
Mean sample size
Mean DLT event count
Scenario
TBSC
TBSC-2
BLRM
Most expected 57
56.5
11.9
12.1
8.9
Low tox
56.6
9.9
10.1
8.0
High tox
56.4
13.0
13.1
9.4

23. Summary
Both adjAAA and TBSC methods are aiming to leave more true options for future when other info are gathered, late onset AEs, efficacy, PK, formulation properties from the compound or other info from other compounds in the same class.
TBSC methods are aiming to doing so with a more thorough goal in design.
The two methods out-performed their competitors in the current simulations by obtaining more probability for true MTDs.
With the property of can having two cohorts initiated at the same time, these two can also shorten the dose escalation duration.
While as a result of not being very conservative, both methods are having more DLT events than the competitors.