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

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

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

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).

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.

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

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.

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

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

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

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.

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.

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

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

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

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.

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.

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).

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

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

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

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

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.