Randomized dose-escalation design for drug combination cancer trials with immunotherapy

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1 Randomized dose-escalation design for drug combination cancer trials with immunotherapy Pavel Mozgunov, Thomas Jaki, Xavier Paoletti Medical and Pharmaceutical Statistics Research Unit, Department of Mathematics and Statistics, Lancaster University, UK and INSERM, Institut Gustave Roussy, Villejuif, France Acknowledgement: This project has received funding from the European Union s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No P. Mozgunov, T.Jaki and X.Paoletti WDE-based approaches to dose-escalation 1 / 20

2 Immunotherapy in Phase I clinical trials Phase I conventional paradigm: the more the better Important exceptions: molecularly targeted agents (e.g. immunotherapy). Immune system can regulate/eliminate tumours Low toxicity profile Example: immune-checkpoint proteins blocker anti-programmed-death-receptor-1 (PD1) Pembrolizumab None of the trials reached MTD Plateau found. Same toxicity/activity probability for 2 and 10 mg/kg FDA requested to focus on a lower dose level P. Mozgunov, T.Jaki and X.Paoletti WDE-based approaches to dose-escalation 2 / 20

3 Immunotherapy in Phase I clinical trials Phase I conventional paradigm: the more the better Important exceptions: molecularly targeted agents (e.g. immunotherapy). Immune system can regulate/eliminate tumours Low toxicity profile Example: immune-checkpoint proteins blocker anti-programmed-death-receptor-1 (PD1) Pembrolizumab None of the trials reached MTD Plateau found. Same toxicity/activity probability for 2 and 10 mg/kg FDA requested to focus on a lower dose level P. Mozgunov, T.Jaki and X.Paoletti WDE-based approaches to dose-escalation 2 / 20

4 Combinations with immunotherapy Immunotherapy is enough not efficacious in cancer treatment by itself Current investigations: the added value of immune checkpoint blockers to backbone therapy the added value of a new drug to an immune checkpoint blocker. One drug is administered at full dose while the other is escalated. Objectives of the trial: To find the maximum tolerated combination (MTC) To detect clinically significant difference between the MTC and standard therapy alone (required by EMA) To detect a possible dose effect in the combination P. Mozgunov, T.Jaki and X.Paoletti WDE-based approaches to dose-escalation 3 / 20

5 Combinations with immunotherapy Immunotherapy is enough not efficacious in cancer treatment by itself Current investigations: the added value of immune checkpoint blockers to backbone therapy the added value of a new drug to an immune checkpoint blocker. One drug is administered at full dose while the other is escalated. Objectives of the trial: To find the maximum tolerated combination (MTC) To detect clinically significant difference between the MTC and standard therapy alone (required by EMA) To detect a possible dose effect in the combination P. Mozgunov, T.Jaki and X.Paoletti WDE-based approaches to dose-escalation 3 / 20

6 Combinations with immunotherapy Immunotherapy is enough not efficacious in cancer treatment by itself Current investigations: the added value of immune checkpoint blockers to backbone therapy the added value of a new drug to an immune checkpoint blocker. One drug is administered at full dose while the other is escalated. Objectives of the trial: To find the maximum tolerated combination (MTC) To detect clinically significant difference between the MTC and standard therapy alone (required by EMA) To detect a possible dose effect in the combination P. Mozgunov, T.Jaki and X.Paoletti WDE-based approaches to dose-escalation 3 / 20

7 Current approach Current design: one parameter CRM design for single agent trial Advantages: Ability to find MTC with high probability Well-known properties Disadvantages: Strong monotonicity assumption No possibility of a plateau detection Does not allow a statistical comparison of toxicities P. Mozgunov, T.Jaki and X.Paoletti WDE-based approaches to dose-escalation 4 / 20

8 Current approach Current design: one parameter CRM design for single agent trial Advantages: Ability to find MTC with high probability Well-known properties Disadvantages: Strong monotonicity assumption No possibility of a plateau detection Does not allow a statistical comparison of toxicities P. Mozgunov, T.Jaki and X.Paoletti WDE-based approaches to dose-escalation 4 / 20

9 Current approach Current design: one parameter CRM design for single agent trial Advantages: Ability to find MTC with high probability Well-known properties Disadvantages: Strong monotonicity assumption No possibility of a plateau detection Does not allow a statistical comparison of toxicities P. Mozgunov, T.Jaki and X.Paoletti WDE-based approaches to dose-escalation 4 / 20

10 Proposals Flexible model: E max model A plateau in a dose-toxicity relation Ability to model the toxicity probability on the single agent alone independently Randomization between a control and an investigation arm control is standard therapy prevents a selection bias allows statistical comparison of the toxicity ethical P. Mozgunov, T.Jaki and X.Paoletti WDE-based approaches to dose-escalation 5 / 20

11 Proposals Flexible model: E max model A plateau in a dose-toxicity relation Ability to model the toxicity probability on the single agent alone independently Randomization between a control and an investigation arm control is standard therapy prevents a selection bias allows statistical comparison of the toxicity ethical P. Mozgunov, T.Jaki and X.Paoletti WDE-based approaches to dose-escalation 5 / 20

12 Bayesian CRM Combination of A (fixed) and B: d 0 = {a, b 0 }, d 1 = {a, b 1 },..., d m = {a, b m } Model p i = ψ(d i, θ); d i is a unit-less amount of drug θ is a vector of parameters Given binary outcomes, the CRM updates the posterior f j (θ) The posterior mean (!) f j 1 (θ)l(d, y, θ) f j (θ) = f R d j 1 (u)l(d, y, u)du ˆp (j) k = E(ψ(d k, a) Y j ) = (1) R d ψ(d k, u)f j (u)du (2) Main debate: choice of model ψ(d k, a) P. Mozgunov, T.Jaki and X.Paoletti WDE-based approaches to dose-escalation 6 / 20

13 Bayesian CRM Combination of A (fixed) and B: d 0 = {a, b 0 }, d 1 = {a, b 1 },..., d m = {a, b m } Model p i = ψ(d i, θ); d i is a unit-less amount of drug θ is a vector of parameters Given binary outcomes, the CRM updates the posterior f j (θ) The posterior mean (!) f j 1 (θ)l(d, y, θ) f j (θ) = f R d j 1 (u)l(d, y, u)du ˆp (j) k = E(ψ(d k, a) Y j ) = (1) R d ψ(d k, u)f j (u)du (2) Main debate: choice of model ψ(d k, a) P. Mozgunov, T.Jaki and X.Paoletti WDE-based approaches to dose-escalation 6 / 20

14 Bayesian CRM Combination of A (fixed) and B: d 0 = {a, b 0 }, d 1 = {a, b 1 },..., d m = {a, b m } Model p i = ψ(d i, θ); d i is a unit-less amount of drug θ is a vector of parameters Given binary outcomes, the CRM updates the posterior f j (θ) The posterior mean (!) f j 1 (θ)l(d, y, θ) f j (θ) = f R d j 1 (u)l(d, y, u)du ˆp (j) k = E(ψ(d k, a) Y j ) = (1) R d ψ(d k, u)f j (u)du (2) Main debate: choice of model ψ(d k, a) P. Mozgunov, T.Jaki and X.Paoletti WDE-based approaches to dose-escalation 6 / 20

15 E max model ψ(d i, E 0, E max, λ, ED 50 ) ψ(d i, θ) = E 0 + E 0 is the probability of toxicity on the control E max + E 0 is the maximum probability of toxicity ED 50 is the combination which produces E 0 + Emax 2 λ 0 is the slope factor d λ i E max d λ i + ED λ 50 (3) Skeleton construction: ( d i = ED ˆ (0) 50 ˆp i (0) Ê (0) 0 Ê (0) max + Ê (0) 0 ˆp i (0) ) 1 ˆλ (0) By definition, ˆp 0 (0) Ê (0) 0 d i = 0 P. Mozgunov, T.Jaki and X.Paoletti WDE-based approaches to dose-escalation 7 / 20

16 E max model ψ(d i, E 0, E max, λ, ED 50 ) ψ(d i, θ) = E 0 + E 0 is the probability of toxicity on the control E max + E 0 is the maximum probability of toxicity ED 50 is the combination which produces E 0 + Emax 2 λ 0 is the slope factor d λ i E max d λ i + ED λ 50 (3) Skeleton construction: ( d i = ED ˆ (0) 50 ˆp i (0) Ê (0) 0 Ê (0) max + Ê (0) 0 ˆp i (0) ) 1 ˆλ (0) By definition, ˆp 0 (0) Ê (0) 0 d i = 0 P. Mozgunov, T.Jaki and X.Paoletti WDE-based approaches to dose-escalation 7 / 20

17 E max model ψ(d i, E 0, E max, λ, ED 50 ) ψ(d i, θ) = E 0 + E 0 is the probability of toxicity on the control E max + E 0 is the maximum probability of toxicity ED 50 is the combination which produces E 0 + Emax 2 λ 0 is the slope factor d λ i E max d λ i + ED λ 50 (3) Skeleton construction: ( d i = ED ˆ (0) 50 ˆp i (0) Ê (0) 0 Ê (0) max + Ê (0) 0 ˆp i (0) ) 1 ˆλ (0) By definition, ˆp 0 (0) Ê (0) 0 d i = 0 P. Mozgunov, T.Jaki and X.Paoletti WDE-based approaches to dose-escalation 7 / 20

18 Randomization Assignment cohort-by-cohort c = c 1 + c 2 c 1 be the number of patients assigned to the current best combination c 2 be the number of patients assigned to the control, d 0. For instance, taking c 1 = 3 and c 2 = 1, one will end up with 25% of the total sample size being assigned to the control. CRM with randomization results in the majority of patients on two combinations: control and MTC. P. Mozgunov, T.Jaki and X.Paoletti WDE-based approaches to dose-escalation 8 / 20

19 Randomization Assignment cohort-by-cohort c = c 1 + c 2 c 1 be the number of patients assigned to the current best combination c 2 be the number of patients assigned to the control, d 0. For instance, taking c 1 = 3 and c 2 = 1, one will end up with 25% of the total sample size being assigned to the control. CRM with randomization results in the majority of patients on two combinations: control and MTC. P. Mozgunov, T.Jaki and X.Paoletti WDE-based approaches to dose-escalation 8 / 20

20 Randomization Assignment cohort-by-cohort c = c 1 + c 2 c 1 be the number of patients assigned to the current best combination c 2 be the number of patients assigned to the control, d 0. For instance, taking c 1 = 3 and c 2 = 1, one will end up with 25% of the total sample size being assigned to the control. CRM with randomization results in the majority of patients on two combinations: control and MTC. P. Mozgunov, T.Jaki and X.Paoletti WDE-based approaches to dose-escalation 8 / 20

21 Simulations setting Sample size n = 48 m = 7 combinations Target probability γ = 0.25; Clinically significant difference τ = 0.05 Confidence level α = 0.9 c 1 = 3, c 2 = 1 25% on the control treatment. P. Mozgunov, T.Jaki and X.Paoletti WDE-based approaches to dose-escalation 9 / 20

22 Characteristics (i) Proportion of correct recommendations (ii) Proportion of times the clinically significant difference is found (iii) Goodness of fit measure P P (P (p MTC p control τ) > α) (4) NMSE = 1 N N j=1 n i=1 (p i ψ(d i, ˆθ (j) )) 2 n i=1 (p i ˆp opt i ) 2 (5) P. Mozgunov, T.Jaki and X.Paoletti WDE-based approaches to dose-escalation 10 / 20

23 Prior and comparators Skeleton P 0 = [0.08, 0.25, 0.35, 0.45, 0.55, 0.65, 0.70, 0.75] T Information to construct prior distributions for model parameters: (i) Control: upper bound of the 95% credibility interval is (ii) Prior MTC: upper bound of the 95% credibility interval is E 0 B(0.8, ); λ Γ(1, 1); E max E 0 U[0, 1 E 0 ]; ED 50 Γ(0.4, 0.4); P. Mozgunov, T.Jaki and X.Paoletti WDE-based approaches to dose-escalation 11 / 20

24 Comparators (P1) One-parameter power model (no randomization): (L2) Two-parameter logistic models with (R) and without randomization. ψ(d i, z) = d z i. ψ(d i, β 1, β 2 ) = exp(log(β 1) + β 2 d i ) 1 + exp(log(β 1 ) + β 2 d i ) P. Mozgunov, T.Jaki and X.Paoletti WDE-based approaches to dose-escalation 12 / 20

25 Scenarios Scenario 1 Scenario 2 Scenario 3 Toxicity Scenario 4 Scenario 5 Scenario 6 Toxicity combination combination combination P. Mozgunov, T.Jaki and X.Paoletti WDE-based approaches to dose-escalation 13 / 20

26 Results (I) d 0 d 1 d 2 d 3 d 4 d 5 d 6 d 7 TR Sc E max (R) L2(R) L P Sc E max (R) L2(R) L P P. Mozgunov, T.Jaki and X.Paoletti WDE-based approaches to dose-escalation 14 / 20

27 Results (II) d 0 d 1 d 2 d 3 d 4 d 5 d 6 d 7 TR Scenario E max (R) L2(R) L P Scenario E max (R) L2(R) L P P. Mozgunov, T.Jaki and X.Paoletti WDE-based approaches to dose-escalation 15 / 20

28 Results (III) Sc 1 Sc 2 Sc 3 Sc 4 Sc 5 Sc 6 E (R) P 74.7% 16.3% 66.7% 71.5% 67.9% 24.2% NMSE L2 (R) P 71.8% 14.4% 59.7% 64.1% 74.9% 20.9% NMSE L2 P1 P 61.5% 15.7% 50.1% 50.2% 64.7 % 18.1% NMSE P 99.9% 93.7% 99.7% 99.7% 99.4% 95.3% NMSE P. Mozgunov, T.Jaki and X.Paoletti WDE-based approaches to dose-escalation 16 / 20

29 Fitted curves Scenario 1. Emax (R) Scenario 1. Logit (R) Scenario 1. Logit Toxicity Toxicity Toxicity Scenario 4. Emax (R) Scenario 4. Logit (R) Scenario 4. Logit Toxicity Toxicity Toxicity Scenario 6. Emax (R) Scenario 6. Logit (R) Scenario 6. Logit Toxicity Toxicity Toxicity combination combination combination P. Mozgunov, T.Jaki and X.Paoletti WDE-based approaches to dose-escalation 17 / 20

30 Sensitivity analysis Prior distributions: E 0 B(0, 8, ), λ Γ(c 1, c 2 ), E max E 0 U[0, 1 E 0 ], ED 50 Γ(c 3, c 4 ). Recommendation: An informative for λ and an uninformative for ED 50 Randomization proportion Recommendation: 20%-25% on the control arm P. Mozgunov, T.Jaki and X.Paoletti WDE-based approaches to dose-escalation 18 / 20

31 Conclusions Randomization and E max model allow to identify clinically significant differences with higher probability than alternatives. The cost of randomization: a small reduction in the proportion of correct recommendations in some scenarios. The randomization helps to overcome problems with fitting This design should be considered if not only MTC identification is of interest P. Mozgunov, T.Jaki and X.Paoletti WDE-based approaches to dose-escalation 19 / 20

32 Further work Large variance of number of patients on the MTC. Further investigation on the fitting problem Phase II trials: a statistical comparison of the optimal combination and control effectivenesses P. Mozgunov, T.Jaki and X.Paoletti WDE-based approaches to dose-escalation 20 / 20