Bayesian response-adaptive designs for basket trials Department of - PowerPoint PPT Presentation

Bayesian response-adaptive designs for basket trials Department of Biostatistics Dana-Farber Cancer Institute Harvard T.H. Chan School of Public Health Lorenzo Trippa Joint work with Brian Alexander and Steffen Ventz ONCOSTAT-2018

Example1: INSIGhT, a Bayesian trial in GBM (PI: Brian Alexander)

Trial Design Progression– RT + TMZ à Eligibility Adjuvant TMZ free survival Genotyping for R Newly diagnosed biomarker A glioblastoma RT + TMZ à subgrouping N adjuvant nera#nib D Unmethylated Overall O MGMT survival M RT+ CC-115 à I IDH1 nega#ve adjuvant CC-115 Z E RT + TMZ à adjuvant abemaciclib Hypothesis - An experimental agent will result in improved overall survival in q combina#on with RT, following RT, or both compared with standard of care therapy for pa#ents with newly diagnosed, MGMT promoter unmethylated, glioblastoma and that this therapeu#c effect may be limited to genomic biomarker groups

Categories not mutually exclusive EGFR PIK3Ca/ CDK4/6 TCGA DF/BWCC amplification/ PIK3R1 amplification estimate (n=37) mutation mutations/ /P16 loss (n=91) PTEN loss + + + 19% 19% + - + 22% 0% + + - 1% 8% + - - 3% 3% - + - 14% 25% - - + 12% 5% - + + 15% 22% - - - 13% 19% 45% vs. 34% 49% vs. 69% 65% vs. 43% TCGA 2008 DFCI Alexander, Ramkissoon

Bayesian Adaptive Randomization A B 0.60 0.60 40th patient 40th patient Arm 1 Random Assignment Probabilities Arm 1 Random Assignment Probabilities 90th patient 90th patient 140th patient 140th patient A r m 1 : T R U E H R , 0 . 6 A r m 2 : T R U E H R , 1 . 0 0.25 0.25 0 0.6 1.0 1.2 1.8 2.4 0 0.6 1.0 1.2 1.8 2.4 Estimated HR for Arm 1 v Control Estimated HR for Arm 2 v Control Trippa et al. 2012 JCO

Arm-specific sample size Control arm Treatment 1, relative hazard, 1.0 Treatment 2, relative hazard, 1.0 Treatment 3, relative hazard, 0.6 10 20 30 40 50 60 70 Arm − Specific Sample Size (no. of patients) Fig 3. Number of patients assigned to each arm across simulations: median,

Detail-2: Adding Arms Vs New Trials [Ventz et al.2017 JCO] (A) independent two-arm trials (B) rolling-arms design - - - - - - 1st 2-arm trial initial therapy - - - 2nd 2-arm trial 1st added arm - - - 3th 2-arm trial 2nd added arm - - time since 1st enrollment to 1st trial time since 1st enrollment - control arm - experimental arm interim analysis

Example2: endTB, a Bayesian trial in Tuberculosis (PI: Carol Mitnick)

endTB, a Bayesian trial in Tuberculosis [Cellammare et al.2017 Int. J. Lung D.]

Arm-Specific Sample Size [Cellammare et al.2017 Clinical Trials]

Bayesian uncertainty directed (BUD) designs

BUD or BAR ? heuristic exploration/exploitation vs myopic decisions a b c BUD: 0.657 BUD: 0.003 BUD: 0.002 BAR: 0.347 BAR: 0.022 BAR: 0.013 6 6 6 BUD: 0.087 BUD: 0.724 BUD: 0.257 BAR: 0.159 BAR: 0.287 BAR: 0.151 BUD: 0.255 BUD: 0.273 BUD: 0.741 BAR: 0.494 BAR: 0.691 BAR: 0.836 posterior density posterior density posterior density 4 4 4 2 2 2 0 0 0 0.00 0.25 0.50 0.75 1.00 0.00 0.25 0.50 0.75 1.00 0.00 0.25 0.50 0.75 1.00 arm 1 arm 2 arm 3 best arm

Basket Designs [Trippa and Alexander, 2017, JCO] Traditional Balanced Adaptive Two Stage Bayesian Basket Basket Randomization Patient 1 Patient n Biomarker only Biomarker agnostic

Decision theory − → BUD ◮ Sequential experiment t = 1 , . . . , T . ◮ Actions A t ∈ A . ◮ Observations Y t ∼ p ( Y t | A t , θ ) . ◮ Parameter space θ ∈ Θ . θ ∼ π

Decision theory − → BUD ◮ D is set of candidate decision functions: (Σ t ) → A . examples: PW, BAR ◮ u = u ( d , Y , θ ) indicates the utility function, ( d ∈ D ). example: balance of toxicity and efficacy d ⋆ ∈ D : d ⋆ = arg max E [ u ( d , Y , θ )] . d ∈D Definition: BUD designs are myopic approximations of d ⋆ .

BUD Definition: BUD designs are myopic approximations of d ⋆ . Step (1) - Action space: example : randomization probabilities Step (2) - Information metric: ◮ u ( · ) quantifies the acquired information trough the data Σ t , ◮ Large values of u (Σ t ) correspond to low uncertainty, u ( p ( θ ∈ · | Σ t )) , u (Σ t ) = ˜ Assumption: u ( w × p 1 + (1 − w ) × p 2 ) ≤ w × ˜ u ( p 1 ) + (1 − w ) × ˜ ˜ u ( p 2 ) .

Step (1) - Action space. Step (2) - Information metric. Step (3) - Myopic approximation: ◮ Convexity, u ( w × p 1 + (1 − w ) × p 2 ) ≤ w × ˜ ˜ u ( p 1 ) + (1 − w ) × ˜ u ( p 2 ) ◮ Information Increments, E [ u (Σ t +1 ) | Σ t , A t +1 ] ≥ ˜ u ( E [ p ( · | Σ t +1 ) | Σ t , A t +1 ]) = u (Σ t ) ∆ t ( a ) = E [ u (Σ t +1 ) | A t +1 = a , Σ t ] − u (Σ t ) ≥ 0 . ◮ BUD decisions p ( A t +1 = a | Σ t ) ∝ ∆ t ( a ) h ( t ) .

Examples Examples Multi-arm trials: ◮ a multi-arm A = { 0 , . . . , K } study with binary endpoints having mean θ k . ◮ γ a = θ a − θ 0 , a = 1 , . . . , K , � K − Var( γ a I ( γ a > 0) | Σ t ) . u (Σ t ) = a =1 Dose-finding trial: ◮ K candidate dose levels A = { a k } K 1 ◮ we let θ R , k and θ T , k denote the probabilities of response and toxicity. ◮ score R k = w θ R , k + (1 − w )(1 − θ T , k ). ◮ the dose k ⋆ = arg max k R k has the highest score, and u (Σ t ) = E [ − log p ( R k ⋆ | Σ t ) | Σ t ] .

utility regret 0 0 0 0 0 0 0 0 0 . . . . . . . . . 4 4 4 4 4 0 0 0 0 8 8 8 8 8 0 0 1 1 0 2 4 6 8 0 5 0 5 ORACLE 0 BUD 50 scenario 1 scenario 1 BR 100 BAR DBCD1 150 DBCD2 200 ORACLE 0 BUD 50 scenario 2 BR scenario 2 BUD 100 BAR DBCD1 BR 150 DBCD2 sample size BAR 200 ORACLE 0 BUD DBCD1 50 scenario 3 BR scenario 3 BAR 100 DBCD2 DBCD1 150 DBCD2 ORACLE 200 0 BUD scenario 4 50 BR scenario 4 BAR 100 DBCD1 DBCD2 150 200 T = 336

◮ simulation study for a 4-arm trial with T = 336 patients. Control Arm 1 Arm 2 Arm 3 ESS (SD) Power MSE ESS (SD) Power MSE ESS (SD) Power MSE Design ESS (SD) Scenario 1 : no effective arm ( θ 0 , θ 1 , θ 2 , θ 3 ) = ( 0.4 , 0 . 4 , 0 . 4 , 0 . 4) BR 84 (8) 84 (8) 04.0 5.89 84 (8) 04.1 5.86 84 (8) 03.2 5.74 BUD 118 (3) 73 (3) 03.8 5.44 73 (3) 03.8 5.43 73 (3) 04.0 5.52 BAR 97 (8) 80 (21) 03.9 7.33 79 (21) 03.6 7.30 80 (21) 03.8 7.28 DBCD1 84 (4) 84 (4) 03.8 5.93 84 (4) 03.8 5.85 84 (4) 03.6 5.82 DBCD2 84 (6) 84 (6) 03.6 5.89 84 (6) 03.9 5.92 84 (6) 03.5 5.82 Scenario 2: one superior arm ( θ 0 , θ 1 , θ 2 , θ 3 ) = ( 0.4 , 0.6 , 0 . 4 , 0 . 4) BR 85 (8) 84 (8) 78.6 5.75 83 (8) 04.2 5.75 84 (8) 03.3 5.80 BUD 118 (3) 73 (3) 82.2 5.48 73 (3) 03.6 5.46 73 (3) 03.8 5.40 BAR 100 (10) 103 (14) 87.5 4.89 67 (18) 03.2 7.65 66 (18) 03.6 7.96 DBCD1 84 (4) 84 (4) 79.8 5.99 84 (4) 03.9 6.07 84 (4) 04.0 6.02 DBCD2 80 (6) 97 (6) 81.2 5.63 80 (6) 03.4 6.16 80 (6) 03.7 6.09 Scenario 3: one superior and one inferior arm ( θ 0 , θ 1 , θ 2 , θ 3 ) = ( 0.4 , 0.6 , 0 . 4 , 0 . 2) BR 84 (8) 84 (8) 78.9 5.92 84 (8) 03.6 5.70 84 (8) 0.00 4.72 BUD 122 (4) 75 (3) 84.3 5.10 75 (3) 03.6 5.22 63 (5) 0.00 4.68 BAR 111 (10) 117 (13) 90.6 4.40 75 (20) 04.0 7.22 32 (11) 0.00 8.12 DBCD1 88 (4) 88 (4) 81.1 5.69 88 (4) 03.7 5.66 72 (7) 0.00 5.20 DBCD2 85 (7) 104 (6) 83.8 5.25 85 (7) 03.8 5.95 61 (8) 0.00 5.76 Scenario 4: three superior arms ( θ 0 , θ 1 , θ 2 , θ 3 ) = ( 0.4 , 0.6 , 0.65 , 0.7 ) BR 84 (8) 85 (8) 79.4 5.89 84 (8) 92.5 5.86 84 (8) 98.6 5.74 BUD 120 (3) 74 (3) 83.6 5.34 72 (3) 95.1 5.18 70 (4) 99.1 5.14 BAR 90 (4) 80 (9) 79.2 7.33 82 (8) 93.4 7.30 83 (8) 98.6 7.28 DBCD1 86 (4) 86 (4) 80.4 5.93 84 (5) 94.0 5.85 80 (5) 98.6 5.82 DBCD2 70 (6) 85 (5) 75.8 5.89 89 (5) 91.7 5.92 92 (5) 98.4 5.82

K arms with binary primary outcomes: Asymptotics: � K � K 1 u (Σ t ) = − Var( θ a | Σ t ) = − , σ − 2 + t � p a , t × σ − 2 a a =0 a =0 Proportion-of-assignments( a ) → ρ a 2 h 1+2 h σ a ρ a = � K 2 h 1+2 h ℓ =0 σ ℓ

Traditional Balanced Adaptive Two Stage Bayesian Basket Basket Randomization Patient 1 Patient n Biomarker only Biomarker agnostic

BUD: Basket Design ◮ K experimental therapies in biomarker subgroups X t ∈ { 0 , 1 } B . ◮ binary endpoints p ( Y t = 1 | X t = x , A t = a , θ ) = θ x , a . ◮ Drug a = 1 , . . . , K targets biomarker 1 ≤ b a ≤ B . ◮ Prior � � � { θ x , a > θ x , 0 } E ℓ, a = 1 , ℓ = 1 , 0 x ba = ℓ E C E 1 , a 1 , a ν × λ ν × λ E 0 , a 0 E C ν × (1 − λ ) (1 − ν ) 1 − ν × λ 0 , a � � � p ( E 1 , a = 1 | Σ t ) + w × H as p ( E 0 , a = 1 | Σ t ) utility = H as