Shaping the Future of Drug Development Flexibility of the BLRM in Dose-Escalation Trials Ursula Garczarek Cytel Inc. | Hagen (DE)
Overview • Bayes logistic regression model (BLRM) • Why people use B LRM • Application for Dose-Escalation trials and demonstration of flexibility – Requirements – Prior elicitation – Extensions of the basic model Arbeitstagung IBS-DR & DVFFA, Hannover 2
Bayesian Logistic Regression Model (BLRM) General Model – Experimental units: n=1,...,N – Y n := 0,1 binary outcome, – X n1 ,...,X nJ := predictors per experimental unit – X n1 ,...,X nJ may come from inputs Z nk , k=1,...,K, K<J 1 = 1 + exp −� � − ∑ ß � � � � � � = 1 �, ß exp � � + ∑ ß � � � � = 1 + exp +� � + ∑ ß � � � � � log 1 − � = � � + � ß � � � � Arbeitstagung IBS-DR & DVFFA, Hannover 3
Why do people use BLRM? • Variable selection 0.125 0.100 0.075 y – E.g. Multimarker diagnostics (Lasso,ML) 0.050 0.025 -10 -5 0 5 10 • Coping with sparse data x 0.125 0.100 – E.g. Analysing adverse events (MBLRM), 0.075 y 0.050 Epidemiology, Genetics,... 0.025 -10 -5 0 5 10 x • Coping with missing values/information – E.g. presence-only data 0.10 y • Adaptive experimentation 0.05 0.00 -10 -5 0 5 10 – Dose escalation x Arbeitstagung IBS-DR & DVFFA, Hannover 4
Dose-Escalation Trials Phase I • Assess dose-toxicity relationship First-in-human studies • • Observe Dose limiting toxicities (DLTs) • Determine maximum tolerated dose (MTD) or recommended phase II dose (RP2D) • MTD := highest dose with toxicity rate lower (or close to) a fixed rate e.g 30% • Formally: • Experimental Units: Patients/Healthy volunteers • Binary outcome: experience of a DLT yes/no • Other characteristic: controlled drug dose Arbeitstagung IBS-DR & DVFFA, Hannover 5
Dose-Escalation Trials Phase I • An sequence of increasing doses d 1 ,d 2 ,…,d J Often: „modified“ 60 40 d Fibonacci: 20 0 0 5 10 seq • Dose d j has an unknown toxicity probability π j • Monotonicity : π j < π j+1 • Goal : Find MTD – π MTD <=0.3, π D>MTD >0.3 Arbeitstagung IBS-DR & DVFFA, Hannover 6
Design requirements Challenge Design Requirement Untested drug in resistant patients Escalating dose cohorts with small #s patients (e.g. 3-6 patients) Primary objective: determine MTD Accurately estimate MTD High toxicity potential: safety first Robustly avoid toxic doses („overdosing“) Most responses occur 80%-120% of MTD* Avoid sub-therapeutic doses while controlling overdosing Find best dose for dose expansion Enroll more patients at acceptable** active doses (flexible cohort sizes) Complete trial in timely fashion Use available information efficiently High toxicity potential: safety first Medical experts are in control Table rows 1-7 from: Satrajit Roychoudhury, Novartis, https://www.slideshare.net/JamesCahill3/eugm-2014-roychaudhuri-phase-1-combination * Joffe and Miller 2008 JCO ** Less than or equal to the MTD determined on study Arbeitstagung IBS-DR & DVFFA, Hannover 7
The 3+3 design (schematic) Image from Hansen et al 2014. Arbeitstagung IBS-DR & DVFFA, Hannover 8
Limitations of 3+3 • Fixed cohort sizes (either 3 or 6) • Pre-defined dose levels to be potentially tested • Ignores dosage history other than previous cohort • Ignores uncertainty: – True DLT rate p=0.5 -> 11% chance of 0 or 1 DLT in 6 patients – True DLT rate p=0.166, 26% chance of >=2 DLT in 6 patients • Cannot re-escalate • Low probability of selecting true MTD (e.g. Thall and Lee. 2003) • High variability in MTD estimates (Goodman et al. 1995) Alessandro Matano, Novartis, http://www.smi-online.co.uk/pharmaceuticals/archive/4-2013/conference/adaptive-designs Arbeitstagung IBS-DR & DVFFA, Hannover 9
Design requirements Challenge Design Requirement Untested drug in resistant patients Escalating dose cohorts with small #s patients (e.g. 3-6 patients) Primary objective: determine MTD Accurately estimate MTD High toxicity potential: safety first Robustly avoid toxic doses („overdosing“) Most responses occur 80%-120% of MTD* Avoid sub-therapeutic doses while controlling overdosing Find best dose for dose expansion Enroll more patients at acceptable** active doses (flexible cohort sizes) Complete trial in timely fashion Use available information efficiently High toxicity potential: safety first Medical experts are in control Table rows 1-7 from: Alessandro Matano, Novartis, http://www.smi-online.co.uk/pharmaceuticals/archive/4-2013/conference/adaptive-designs * Joffe and Miller 2008 JCO ** Less than or equal to the MTD determined on study Arbeitstagung IBS-DR & DVFFA, Hannover 10
Alternatives to 3+3 Arbeitstagung IBS-DR & DVFFA, Hannover 11 Image from Hansen et al 2014.
Why Bayesian in Dose-Escalation Bayesian solution Design Requirement Information can be updated for as small Escalating dose cohorts with small #s and larger groups as one wants patients (e.g. 3-6 patients) Assessable by posterior Accurately estimate MTD Choose next dose based on posterior Robustly avoid toxic doses („overdosing“) Choose next dose based on posterior Avoid sub-therapeutic doses while controlling overdosing Choose next dose based on posterior Enroll more patients at acceptable** active doses (flexible cohort sizes) All information is used + „prior“ Use available information efficiently High toxicity potential: safety first Medical experts are in control Arbeitstagung IBS-DR & DVFFA, Hannover 12
Theoretical and Practical Loss „function“ Dose escalation � d| θ ∈ (0,0.2] � 1 = 1 ����� − � !"�# � d| θ ∈ (0.2,0.35] � 2 = 0 %&�#�%�� % ' L θ, � = � d| θ ∈ (0.35,0.6] � 3 = 1 �'(�!!")� % ' Algorithm � d| θ ∈ (0.6,0.1] � 4 = 2 ��&((��%&+�� % ' in control Interval Probabilities by Dose Interval Probabilities by Dose 1 0.5 0.26 0.24 0.22 Unacceptable 0.16 0.11 0.06 0 0 0 0 0 0 0 0 1 0.8 0.6 Medical 0.4 Excessive Probability 0.16 0.18 0.15 0.16 0.15 0.1 0.12 0.2 0.04 0.01 0.02 0.01 0.01 0.01 0 experts in 1 0.8 0.6 Target control 0.4 0.25 0.24 0.2 0.21 0.19 0.19 0.18 0.18 0.13 0.11 0.2 0.08 0.05 0.06 0 0.94 0.93 0.92 1 0.88 0.86 0.78 x 0.65 0.58 x x x x 0.53 x Under dosing 0.49 x 0.44 0.42 0.5 0.37 x 0 1 2 3.3 5.1 6.6 8.8 11.8 15.6 20.8 27.8 36.8 49 65.2 Dose Pr(Under dosing) Pr(Target) Pr(Excessive) Pr(Unacceptable) Arbeitstagung IBS-DR & DVFFA, Hannover 13
Bayesian Logistic Regression Model Flex 1: Meaningful parametrization • Data: – #DLT/#Patients: r d ~Binomial( π d ,n d ) • Parameter Model: – logit( π d )=log( α )+ß(log(d/d*)) • Prior: – (log( α ),log(ß)) ~ N 2 ( µ 1 , µ 2 , σ 1 , σ 2 , ρ ) Model parameters α and ß can be interpreted as: α: odds of a DLT at d*(reference dose) ß >0: increase log-odds of DLT by unit increase log dose Satrajit Roychoudhury, Novartis, https://www.slideshare.net/JamesCahill3/eugm-2014-roychaudhuri-phase-1-combination Arbeitstagung IBS-DR & DVFFA, Hannover 14
BLRM Flex 2: Plausible functional shapes 1.00 0.60 π 0.35 0.30 0.09 0.00 1.0 2.03.3 5.16.6 8.8 11.8 15.6 20.8 27.8 36.8 49.0 65.2 d Arbeitstagung IBS-DR & DVFFA, Hannover 15
BLRM Flex 2: Plausible functional shapes 1.00 Prior information d*=11.8 Odds: 0.1 0.60 π 0.35 0.30 0.09 0.00 1.0 2.03.3 5.16.6 8.8 11.8 15.6 20.8 27.8 36.8 49.0 65.2 d Arbeitstagung IBS-DR & DVFFA, Hannover 16
BLRM Flex 2: Plausible functional shapes 1.00 linetype ß=0.1 ß=0.5 0.60 ß=1 ß=2 π colour ß=0.1 ß=0.5 0.35 ß=1 0.30 ß=2 0.09 0.00 1.0 2.0 3.3 5.16.6 8.8 11.8 15.6 20.8 27.8 36.8 49.0 65.2 d Arbeitstagung IBS-DR & DVFFA, Hannover 17
BLRM Flex 3=1+2: Prior elicitation There has to be knowledge on lowest dose and on dose range 1. Minimal informative 2. Somewhat informative • P( π d1 <=0.6 ) = 0.95 • P( π d1 <=0.05 ) = 0.5 – B (1,log(0.05/0.4)) – B (1,log(0.05/0.5)) • P( π dJ <=0.2 ) = 0.05 • P( π MTD <=0.3 ) = 0.5 – B (log(0.05/0.2),1) – B (log(0.3/0.5),1) Prior medians for the other Prior medians for the other doses by basic model doses by basic model – B (a,b),j=2,...,J-1 – B (a,b),j=2,...,J without d=MTD Best approximating Best approximating N 2 ( µ 1 , µ 2 , σ 1 , σ 2 , ρ ) N 2 ( µ 1 , µ 2 , σ 1 , σ 2 , ρ ) Arbeitstagung IBS-DR & DVFFA, Hannover 18
Dose-Escalation Trials Phase I Assess dose-toxicity relationship • • First-in-human (FIH) studies – single agent Determine maximum tolerated dose (MTD) or • recommended phase II dose (RP2D) • Observe Dose limiting toxicities (DLTs) • Combination dose finding studies (Phase Ib) • Same primary objective as FIH studies • Combination of two (or more) drugs • Addition of a new drug to a registered treatment to increase efficacy http://www.bayes-pharma.org/bayes2014docs/Day1/Jullion.pdf Arbeitstagung IBS-DR & DVFFA, Hannover 19
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