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Jouni Kerman
Statistical Methodology Group / Novartis, Switzerland
May 27, 2011 / MBDD Conference, Stockholm
Bayesian modeling in clinical trials: from early development to Phase III
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Acknowledgements
Beat Neuenschwander (Oncology)
Michael Branson (Translational Sciences)
Roland Fisch (Statistical Methodology)
Björn Bornkamp (Statistical Methodology)
Heinz Schmidli (Statistical Methodology)
Amy Racine (Modeling and Simulation)
Marc Vandemeulebroecke (Modeling and Simulation)
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About the Novartis Statistical Methodology group
Role of “the Methods” group
• 11 members in the Basel headquarters and in the U.S.
• Consult statisticians on actual projects
• Promote innovative methods (adaptive/seamless designs, Bayesian methods, ...)
• Also an external focus: conferences, papers
• Keep up dialogue / scientific discussions with regulators
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Contents
Introduction: a need for better statistical methods
• Shortcomings of conventional statistics at Pharma
The Bayesian approach – what and why
• And, how
Use of Bayesian statistics at Novartis
• Cases: From Phase 1 to Phase 3
Summary and conclusion
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Introduction:
A need for better statistical methods
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Step back and ask: what‟s our business?
Our challenge, as a business
• Make informed decisions in the face of uncertainty
• This involves taking all relevant information into account
Our reason for existence, as statisticians
• Help making informative decisions by quantifying the uncertainty affecting decision making
• This involves incorporating all relevant information into our statistical analyses
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Example: disconnect of statistics and reality
TeGenero TGN1412 First-in-Man Trial (2006)
• 8 healthy volunteers: 2 on placebo, 6 on TGN1412 (a monoclonal antibody)
• all 6 TGN patients had severe adverse reactions from a cytokine storm; neither of the 2 placebo patients had any AEs
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But Fisher‟s
exact test gave
a p-value of
3.5% so it‟s not
significant at
2.5% level
Cytokine storm?!
I am 100% sure
that this is due to
the drug!
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Example: disconnect of statistics and reality
TGN1412 data analysis: what was missing?
• Cytokine storm is very rare; the clinician took this into account but the statistician didn‟t for the sake of “objectivity.” Who is right?
• Suppose we only had data from ONE patient – what can we say?
Cytokine storm?!
I am 100% sure
that this is due to
the drug!
Sorry,
insufficient
data!
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Does traditional statistics deliver?
Reality vs. Hypotheses: Success ≠ Power
• Language of statistics ≠ language of clinicians (or business)
• Traditional hypothesis testing framework is awkward and “misses the point”
What is our
chance of
success??
I can‟t say, but you‟ve
got 80% probability
to reach a statistically
significant result,
given that your
alternative
hypothesis is true
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Does traditional statistics deliver?
Significance ≠> Success
• P-value by itself is meaningless
• We are always interested in the magnitude of the effect as well • If ignored, this has implications to sample size...
We got a p-
value of
0.04, great!
Hold it!
The point estimate
was 0.2, while the
alternative was 0.5.
Do you think we got
a successful study?
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Does traditional statistics deliver?
Meaningless tests
• Do we really need a study to test μ=0 vs μ≠0 ?
The result
was not
significant.
What does
it mean?
We can only
conclude that the
sample size was
too small.
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The Bayesian way:
complete modeling of uncertainty
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Bayesian modeling is not just “modeling” ...
Bayesian modeling = modeling of uncertainty
• Not just modeling of curves / shapes / time series / dependencies ...
• Bayesians model uncertainty using probability models – involving all relevant information
Uncertainty is quantified by a probability distribution
• All quantities (parameters) that have uncertainty are modeled to have a distribution: treatment effect, responder rate...
• Allows you to incorporate external information
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-20 0 20 40 60 80 100 120
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How the Bayesian approach helps
Better confidence in the trial results
• Quantify uncertainty (or, „confidence‟) properly
• Don‟t ignore available information – and don‟t ignore lack of it!
• Use all available external information in the design and analysis
Better communication by direct focus on the scientific / business questions
• Formulate criteria and scientific questions directly in terms of quantities of interest
• No need for meaningless null hypotheses that make no sense in clinical trials
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Example of a Bayesian approach to CTs
“What is the clinical definition of success?”
• “Treatment difference Δ must be better than placebo, and of clinically relevant magnitude”
Δ >0 and Δ ≥ δ
“What is the model for the data?”
y ~ N(Δ, s2)
“What do we know?”
• We have information on Δ and s, based on past trials and publications: introduce uncertainty distributions for Δ and s
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Example of a Bayesian approach to CTs
“How many subjects do we need?”
• We recruit as many as needed to satisfy our requirements for precision:
Pr( Δ > 0 | data ) ≥ 95%
Pr( Δ ≥ δ | data ) ≥ 50%
• We can also compute Type 1 and 2 errors given some relevant scenarios
• The starting point of the design should however always be the definition of clinical success
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-20 0 20 40 60 80 100 120
δ 0
Posterior of Δ
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Bayesians and frequentists: a peaceful coexistence
Role of Bayesian statistics / modeling
• Sponsor / Study-level trial design
• Provides for a sound framework to defining a well-behaved statistical procedure that takes into account all relevant information and its uncertainty as well
Role of frequentist statistics
• Regulatory perspective
• Provides a framework for evaluating the false positive error rate and the power of the trial
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Bayes at Novartis:
Some examples
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Proof-of-Concept studies
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Early phase: Proof-of-Concept (PoC) trials
PoC: a translational step from “research” to “clinic”
• Early answer to key scientific questions:
• “Does the mechanism of the drug work”?
• “Does the drug work in this indication”?
Key decision point within the development strategy
• “Do we have enough confidence to invest further in the development of the candidate drug?”
Obvious platform for Bayesian models
• Trials are always quite small– it will pay off including external information in the model
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Historical controls in PoC (and elsewhere)
Reuse information about the effect of a known drug (control)
• Combine information from many sources of information: in-house trials, publications
• Quantify the existing effect via a meta-analytic (hierarchical) Bayesian model
• Predict the effect for the future study
• Down-weight the information appropriately taking the size of the future trial into account
• Take this distribution as the prior information and incorporate it into the (Bayesian) analysis model
Fewer
patients in
control arm
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Example: PoC in Crohn‟s disease (An inflammatory bowel disease)
Population:
• Male and female patients with moderate to severe active CD
Design:
• Multicenter, double-blind, randomized, 2 parallel groups (placebo or high dose), immediate readout after 2 iv infusions 3 weeks apart
Primary endpoint:
• Crohn„s Disease Activity Index (CDAI) • Gold standard, composite disease activity score, low scores are good
• Comprises assessments of stool, pain, well-being, signs and symptoms, treatment for diarrhea, abdominal mass, hematocrit and body weight
• Clinically meaningful scores:
• <150 (remission), <220 (mild), <450 (moderate)
• decrease by 70 or 100 points (response)
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Example: PoC in Crohn‟s disease
Model
• CDAI change from baseline ~ N(q, s2)
• Quantity of interest: Δ = – (qActive – qPlacebo)
Prior information
• qActive – noninformative (prior with very little information)
• qPlacebo ~ N(50, 882/20), based on 671 placebo patients from 6 studies, “discounted” to a prior with 20 patients‟ worth of information
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Example: PoC in Crohn‟s disease
PoC criteria
• CDAI change from baseline ~ N(q, s2)
• Quantity of interest: Δ = – (qActive – qPlacebo)
-20 0 20 40 60 80 100 120
Positive PoC if
P(Δ ≥ 50 | data ) ≥ 50%
and
P(Δ > 0 | data ) ≥ 95%
Thresholds
Levels of proof
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-20 0 20 40 60 80 100 120
Example: PoC
Points to note
• We take into account both “significance” (Δ > 0) and magnitude of the effect (Δ ≥ 50)
• Thresholds are the important clinically relevant ones
• Levels of proof are adjusted to match required precision of estimates => sample size follows
• False negative/positive errors are controlled at acceptable levels
• Note: in PoC, false positive of 20% may be acceptable!
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Phase I dose finding in oncology
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Phase I dose finding in Oncology
Phase I dose escalation cancer trials
• Goal: identify the Maximum Tolerated Dose (MTD) while monitoring for dose-limiting toxicity (DLT)
• Small: often 15 – 30 patients
• Adaptive: dose escalations depend on data from past cohorts
• Large uncertainty during and at end of trial – external information may help
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Phase I dose finding in Oncology
Traditional dose escalation schemes
• Algorithmic (e.g. 3+3) • Simplistic: does not take into account of all past
information
• Used to be “the gold standard”
• Not used anymore at Novartis
• Continual Reassessment Method (CRM) • Bayesian, but not without problems...
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Phase I dose finding in Oncology
“Are model-based designs too aggressive?”
• Muler et al. (2004) JCO
• One-parameter Continual Reassessment Method (CRM)
• MTD recommendation from CRM: 50 mg!
• Is it justified? No!
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20mg 30mg 40mg 50mg
Data: DLT/n 0/5 0/5 4/8
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Phase I dose finding in Oncology
Bad Bayesian modeling is still bad
• One-parameter CRM model is inappropriate!
• Too simplistic models are too constraining, possibly leading to bad decisions within a trial
• Even though the operating characteristics (Type 1, 2 error control) may look fine, this does not guarantee that the “on-study characteristics” make sense
• On-study performance is also important!
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Phase I dose finding in Oncology
Modeling the probability of a DLT at a given dose
• Logit(p(dose)) = log α + β log(dose/dose*) • with α, β > 0. dose* = reference dose
• A more realistic representation of the dose-toxicity curve
• The Bayesian model yields posterior distributions conditioned on the dose
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p(dose)
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Phase I dose finding in Oncology
Decisions are based on posterior summaries of the probability of DLT
• Three main regions of interest: under-dosing, targeted dosing, overdosing
• The model yields probabilities for each possibility
• Dose recommendation relies on maximizing probability of targeted dosing while keeping the probability of overdosing at < 25%
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Phase I dose finding in Oncology
Improved performance
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20mg 30mg 40mg 50mg
Data: DLT/n 0/5 0/5 4/8
overdosing
target
under-dosing
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Phase I dose finding in Oncology
“But are you actually using Bayesian methods in your cancer trials?”
Yes. 100% of the Phase 1 trials in Oncology
at Novartis are now Bayesian
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Probability of success in Phase III
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Probability of success in Phase 3
“What are our chances of success in Phase 3?”
• This is a question that calls for a probability that is essentially Bayesian: not a long-run frequency!
• This is a conditional probability: probability of success later given what we know today (at end of Phase 2)
• This is needed for an internal decision – no regulatory constraints (and no Type 1 error control) here!
• We are obliged to use the prior information that we believe reflects the uncertainty appropriately
Probability of Success
• = the (posterior) predictive probability of a success criterion being fulfilled at the end of a future Phase 3 study
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Probability of success in Phase 3 Case study: a compound for acute heart failure
Calculating the probability of success
• Sampling distributions were set up to simulate a data-generating process and unknown parameters were modeled as prior distributions – derived from the Phase II data
• A Bayesian probability model was used to predict the data that could be obtained in a future study of 800, 1000, 1200, 1400, or 1600 patients
• Outcomes such as “Study success”, “Dyspnea demonstrated”, and “Early submission” were computed based on the actual analyses that would be used in Phase III (e.g. chi-square test, log-rank test)
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Bayesian clinical trial simulation Case study: a compound for AHF
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Simulation of trial outcomes
• Set up a joint prior distribution of the unknowns (θ) given Phase 2 data, capturing their uncertainty
• Generate a sequence of S draws θ(i) from the distribution– then for each θ(i) a data set of N patients was simulated.
Computing the PoS
• Compute a Success / No success decision di
(0 or 1) for each trial outcome
• Obtain the PoS by averaging over the di
• Uncertainty in the parameters is then propagated to the simulated trial data points
y(1), ...,y(S)
Σdi/S = 0.89
0, 1, 1, ..., 0, 1
θ
θ(1), ..., θ(S)
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Challenges and opportunities
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Challenges in adopting the Bayesian approach
• Ignorance / lack of acceptance • Misconceptions
• Lack of regulatory guidelines / acceptance
• Mathematical expertise required • Some distribution calculus / likelihood formulations...
• Modeling expertise required • Biostatistics: lots of opportunities for creative modeling – lots of variety
• Every problem has its own special features – few models fit all problems
• Best solutions are not necessarily trivial, but some trivial solutions may be good enough in many cases!
• Computational expertise required • No standard “tests” available! – prepare to do lots of programming
• Simulation methods are used almost for every trial design
• MCMC / convergence issues / speed
• WinBUGS, R, SAS
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Challenge => opportunity
Trends
• Increasing competition and outsourcing
• Statisticians must strive to offer higher and higher value
• Statisticians must evolve - and offer better and better solutions
A chance for industry statisticians!
• Bayesian expertise is in demand
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Conclusion
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Conclusion Take-home points
Bayesian modeling approach offers ...
• Better informed decisions via more realistic and precise modeling of sources of uncertainty
• Better communication to clinicians and stakeholders via intuitive probabilistic formulation of scientific / business questions
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Tack! Kiitos! Thank you!
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References
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References: textbooks / general
Textbooks
• Berry, Carlin, Lee, Müller (2011) Bayesian Adaptive Methods for Clinical Trials. Chapman & Hall / CRC Press.
• Spiegelhalter, Abrams, Myles (2004) Bayesian Approaches to Clinical Trials and Health-Care Evaluation. Wiley (Statistics in Practice)
• Gelman, Hill (2007). Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press
General discussion about Bayes in clinical trials
• Clinical Trials Special Issue 2005, 2:271-378
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References: some papers on specific issues
Papers
• Neuenschwander, Branson, Gsponer (2008) Critical aspects of the Bayesian approach to phase I cancer trials. Statistics in Medicine 27:2420-2439
• Neuenschwander, Capkun-Niggli, Branson, Spiegelhalter (2010) Summarizing historical information on controls in clinical trials. Clinical Trials 7:5-18.
• Muler, McGinn, Normolle et al. Phase I trial using a time-to-event continual reassessment strategy for dose escalation of Cisplatin combined with Gemcitabine and radiation therapy in pancreatic cancer. Journal of Clinical Oncology 2004.
• Bailey, Neuenschwander, Laird, Branson. A Bayesian case study in oncology phase I combination dose-finding using logistic regression with covariates. JBS 2009.
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