shaping the future of drug development...ethical requirement eugm - march 2016 4 “the major...

Shaping the Future of Drug Development

Bayesian-Based Dose Escalation Designs:

Determining the Optimal Approach and Design

Pantelis Vlachos, Ph.D. Cytel Inc. | Geneva

Agenda

• Introduction to Phase I Dose Escalation • Methods considered in East® ESCALATE

• Single Agent • Dual Agent

• Demo • Q&A

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Phase I dose-escalation (single agent)

Only consider trials with fixed doses. • A sequence of K doses, d1,d2,…,dK, as

candidates. • Dose i has a toxicity probability of pi (unknown). • Monotonicity : pi < pi+1 • Goal: to find the MTD , defined as the highest

dose with toxicity rate lower (or close to) a fixed rate, pT, e.g., pT = 0.30.

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Ethical Requirement

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“The major difficulty in phase I trial design and conduct is the ethical requirement that the number of patients in the trial who experience toxicity must be limited.”

Phase I Trial Challenges

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Alessandro Matano, Novartis, http://www.smi-online.co.uk/pharmaceuticals/archive/4-2013/conference/adaptive-designs

Rule-based vs Model-based

• Rule-based – 3+3 Design

• Model Based – Continual Reassessment Method (CRM) – Bayesian Logistic Regression Model (BLRM)

• Hybrid – Modified Toxicity Probability Interval (mTPI)

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Rule-based vs Model-based

Rule-based Model-based

Applicability Easy More complex due to statistical component (e.g. evidence-based prior derivation)

Flexibility Not very flexible • Fixed cohort size • Fixed doses

Flexible: allows for • Different cohort sizes • Intermediate doses

Extensibility Rather difficult Easily extendable • 2 or more treatment arms • combinations

Inference for true DLT rates

Observed DLT rates only

Full inference, uncertainty assessed for true DLT rates

Statistical requirements None “reasonable” model, “good” statistics

Decisions Algorithm decides Clinically-driven recommendations

(Based on Matano. Bayesian Adaptive Designs for Oncology Phase 1 Trials, 2013)

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Why model-based? more flexible (eg., different cohort sizes) Bayesian statistical inferences But, more complex (need for user-friendly software!)

3+3 (Prevalence)

• Over 98% of published Phase 1 trials (1991-2006) use variations of 3+3

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The 3+3 design (schematic)

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Yuan Ji, KOL Lecture Oct. 2013

Limitations of 3+3 • Ignores dosage history other than previous cohort

– 0/3, 0/3, 0/3, 0/3, 0/3, 2/6 provides more information than 0/3, 2/6 • Same action under qualitatively different situations

– 0/3 and 1/6 lead to same action (escalate to the next provisional dose) – 2/3, 3/3, 2/6, 3/6, and 4/6 lead to same action (de-escalate)

• Ignores uncertainty: – If true DLT rate is p=0.5, 11% of the time we will see 0 or 1 DLT in 6

patients – If true DLT rate is p=0.166, 26% of the time we will see at least 2 DLT in 6

patients • Cannot re-escalate • Fixed cohort sizes (either 3 or 6) • Pre-defined dose levels to be potentially tested • Low probability of selecting true MTD (e.g. Thall and Lee. 2003) • High variability in MTD estimates (Goodman et al. 1995)

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Alessandro Matano, Novartis, http://www.smi-online.co.uk/pharmaceuticals/archive/4-2013/conference/adaptive-designs

Target Toxicity? • Common misconception target toxicity is fixed (eg., 17%, or

33%). • He et al. (2006) showed via simulation that the expected toxicity

level at the MTD for the 3+3 is between 19-22%.


Regulatory Guidelines • FDA Guidance (Clinical Considerations for Therapeutic Cancer

Vaccines)

• EMEA / CHMP Guideline on Clinical Trials in Small Populations


Bayesian Framework

(Based on Matano. Bayesian Adaptive Designs for Oncology Phase 1 Trials, 2013) EUGM - March 2016 13

The Continual Reassessment Method (CRM)

• Bayesian model-based method (O'Quigley et al. 1990)

• Uses all available information from doses to guide dose assignment

• Inputs to specify: – Target toxicity pT (usually at 33%) – A single-parameter (θ) dose-toxicity curve – prior distribution for θ – prior mean probabilities at each dose (“skeleton”)

• Next recommended : posterior toxicity probability closest to target


CRM: The process

1. Patient cohorts treated at each dose level 2. Toxicity outcome observed 3. Using Bayes theorem, prior distribution and

observed outcomes are used to calculate the posterior mean of the probability of toxicity at each dose level, 𝑝�𝑖

4. Next cohort of patients assigned to dose level that has its 𝑝�𝑖 closest to target toxicity

5. Repeat 1-4 until termination criteria met


Modified CRM


Uncertainty in toxicity rate

• CRM relies on point estimate, ignores uncertainty. • eg, same posterior mean, but Pr(p > 0.6) = 0.168 vs

0.002


Bayesian Logistic Regression Model (BLRM)

• Two parameter logistic: • is the “reference dose”


Bayes Risk


• Choose dose that minimizes posterior expected loss.

Escalation with Overdose Control (EWOC)


• Choose dose that maximizes targeted toxicity probability, given not overdosing.

Prior Specification (direct vs indirect)

• Enter directly bivariate normal for log(α) and log(β):

• Enter “best guess” for P(d1) and MTD:


Prior Specification (indirect)

• Assuming logits of toxicity are linear, calculate prior probabilities of toxicity (predicted median) at each dose level

• Assign a “minimally informative unimodal” Beta distribution at each dose level (Neuenschwander et al., 2008 Appendix A)

• Generate n sets of logits from Beta distributions, to obtain n estimates of log(α) and log(β) using least squares

• Use sample means, variance, correlation for bivariate normal


Posterior Sampling Methods


modified Toxicity Probability Interval (mTPI)

• mTPI is Bayesian like CRM and BLRM, but rule-based like 3+3 • Challenges for model-based methods: complexity (esp for non-

statisticians); sensitivity to priors


Trial Monitoring Table


Yuan Ji, KOL Lecture Oct. 2013

modified Toxicity Probability Interval (mTPI)

• Probability of toxicity at each dose modeled by independent Beta distributions

• Set of decision intervals specified (like in BLRM) • Dosing decisions determined by 'normalized' posterior

probability in each interval at the current dose di : – Escalate to di+1 if di is 'underdosing' – Stay at di if 'proper dosing' – De-escalate to di-1 if di is 'overdosing'


Equivalence Intervals • The Equivalence Interval (EI) is defined as [pT-ε1; pT +ε2] • pT-ε1 is the lowest toxicity probability that the physician would

be comfortable using to treat future patients without dose escalation

• pT +ε2 is the highest toxicity probability that the physician would be comfortable using to treat future patients without dose de-escalation


Unit Probability Mass

• UPM (interval) = Post Pr(interval) / length(interval)


What about combination trials? • Recent FDA draft guidance on “Co development of two or more

unmarketed investigational drugs for use in combination” – “Combination therapy is an important treatment modality in many

disease settings, including cancer, cardio-vascular disease, and infectious diseases. Recent scientific advances have increased our understanding of the pathophysiological processes that underlie these and other complex diseases. This increased understanding has provided further impetus for new therapeutic approaches using combinations of drugs directed at multiple therapeutic targets to improve treatment response or minimize development of resistance.”


About combination therapies • Becoming increasingly common in the treatment of many

diseases (e.g. cancer, HIV) • Many designs are still quite naïve

– e.g. fix dose of one agent, and dose-escalate the other (using single-agent designs)

• Require simultaneous dose-escalation • Aims and objectives must differ from single-agent trials

– Multiple MTDs may exist – More prior information (from single-agent trials) – Interaction


Methods in East


comb2BLRM

PIPE

The general approach • Specify an initial dose-combination for first cohort, x =

(xA,xB) • Record the observed number of toxicities • Given a parametric dose-toxicity model, π(x, θ), with priors

on the parameter vector θ – Update inferences to obtain new posterior distribution

• Choose next dose combination based on – A set of admissible dose combinations – A decision rule to choose between admissible doses, using the

posterior distribution • Continue recruiting patients until either

– a fixed sample size is obtained – A stopping rule is satisfied


comb2BLRM: Model components • Model has three components which stand for

1. Single-agent 1 toxicity, represented by parameters α1, β1

2. Single-agent 2 toxicity, represented by parameters α2, β2

3. Interaction, represented by parameter η.

• π12 is the probability of a DLT for dose combination (d1, d2),

odds12 = π12 /(1 - π12 ) = α1 d1 β1 + α2 d2

β2 + α3(d1 β1 d2

β2 ) β3

To ensure interpretation of the parameters, we simplify the model as

odds12 = odds12 0 x exp(η d1 d2)


Prior distribution • For the single-agent parameters proceeds as in the univariate

BLRM

• For the interaction log-odds multiplier η we use η ~ N(mη, s2

η) which allows for synergistic and antagonistic interaction • mη, s2

η determined from two prior quantiles of η, for example the median (set to 0 for the case of no a priori evidence for interaction) and 97.5% quantile.

• If it is known that only synergistic interaction is possible, a prior for η confined to positive values could be used (e.g., log-normal).


PIPE: Design components • Target a MTD contour (MTC) • A-priori and a-posteriori the probability of toxicity (π12) at a

specific dose combination is a Beta random variable • Posterior probability of toxicity at each dose level easily

calculated • MTC needs to satisfy monotonicity assumption to drive dose

escalation • Next dose combination is chosen from a set of admissible doses

that are “close” to the MTC


MTC for Discrete Space*


* Mander (2015) Finding the right dose in response adaptive trials

Process


• Dose a new cohort of patients on best combination • Record the number of DLTs • For each dose/day combination calculate the posterior DLT

probability • Calculate the probability of being above the TTL (averaged

over the contour distribution) for Safety • Use the most likely contour for Decision making

* Mander (2015) Finding the right dose in response adaptive trials

Summary • Almost all trials to date have used rule-based methods • Rule-based methods (eg, 3+3) are easy to implement and

simple to explain • Model-based methods (eg, CRM, BLRM) are more flexible

and efficient, but performance may depend on prior information

• mTPI may be a useful compromise

• East ESCALATE provides two modes: 1. Simulations for comparing and evaluating designs 2. Interim Monitoring for executing designs and analyzing data


References 3+3

B.E. Storer. Design and analysis of phase I clinical trials. Biometrics, 45:925-937, 1989. mTPI

Y. Ji, P. Liu, Y. Li, and N. Bekele. A modified toxicity probability interval method for dose finding trials. Clinical trials, 7:653-656, 2010.

CRM J. O’Quigley, M. Pepe, and L. Fisher. Continual reassessment method: A practical design for phase I clinical trials in cancer. Biometrics, 46:33-48, 1990. S.N. Goodman, M.L. Zahurak, and S Piantadosi. Some practical improvements in the continual reassessment method for phase I studies. Statistics in Medicine, 14:1149-1161, 1995

BLRM B. Neuenschwander, M. Branson, and T. Gsponer. Clinical aspects of the Bayesian approach to phase I cancer trials. Statistics in Medicine, 27:2420-2439, 2008. L. W. Huson and N. Kinnersley. Bayesian fitting of a logistic dose– response curve with numerically derived priors. Pharmaceutical Statistics , 8: 279–286, 2009

Combination B. Neuenschwander, et al. A Bayesian Industry Approach to Phase I Combination Trials in Oncology. Statistical Methods in Drug Combination Studies, 95-135, 2015 A.P. Mander and M.J. Sweeting. A product of independent beta probabilities dose escalation design for dual-agent phase I trials. Statistics in Medicine, 34:1261-1276, 2015


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