Download Bayesian Adaptive Methods

Carrie Deis
Nadine Dewdney
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Phase I clinical trials
Standard Designs
Adaptive Designs
Bayesian Approach
Traditional vs. Bayesian
Hybridization
FDA Guidance
Conclusion
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Conducted to determine toxicity for the
dosing of the new intervention
First time the drug is tested in humans
Small number of patients, 20 to 50
Depending on the nature of the new drug,
patients are usually healthy volunteers
A higher dose is assumed to be more effective
Goal is to find maximum tolerable dose (MTD)
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Known prior to the start of the trial:
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Starting dose
Toxicity profile and Dose-limiting toxicity
Target toxicity level
Dose Escalation Scheme
Starting dose commonly chosen as:
◦ 1/3 lowest toxic dose in dogs
◦ 1/10 of the LD10 in mice
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Dose escalation is done incrementally
◦ Increments are pre-determined
◦ Modified Fibonacci sequence – increase rate
diminishing as the dose gets higher
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Patients are assigned to dose levels according
to predefined rules
◦ Allow for only escalation and de-escalation of dose
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Doses selected such that, D1,…, DK would be
close to MTD
MTD is determined statistically as the dose at
which 1/3 of the subjects develop toxicity
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Subjects are randomized
The number of subjects, ri, developing
toxicity would be observed
pi = ri/ni, is used to calculate the proportions
exhibiting toxicity
Dose-response is modeled based on the
probability of toxicity
The MTD would be fitted to this model
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Ethical concerns with the traditional approach
◦ Patients might be treated excessively and
unnecessarily at low doses
◦ Too many patients may be treated at doses that are
too high or too low
◦ Highly likely most subjects are treated at low doses
◦ Not clear that the estimated MTD is the correct dose
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Adjustments and modifications can be made
after the trial has started
◦ Does not affect the integrity of the trial
◦ Goal is to improve upon the probability of success of
the trial and correctly identify the clinical benefits of
the intervention under investigation
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Prospective adaptations include
◦ Stopping a trial early for safety or lack of efficacy
◦ Dropping the loser - Inferior treatments dropped
◦ Sample size re-estimation
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Modifications hypothesis might be necessary
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Inclusion/exclusion criteria
Dose/regimen
Treatment duration
Endpoints
Several types of adaptive designs
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Group sequential
Sample size adjustable design
Drop-the-losers design
Adaptive treatment allocation design
Bayesian adaptive methods
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Based on Bayes Theorem:
◦ Expresses how a subjective degree of belief should
rationally change to account for evidence
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Used as a statistical inferential tool in
adaptive designs
Strength of the Bayesian approach
◦ Decision on trial continuation is made as data
accumulates
◦ Sample size not determined in advance although a
maximum size might be specified
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Drawbacks
◦ Analysis after each subject is treated
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Calculates the predictive probability that the
patient will respond to treatment
Specifies a prior distribution then updates it
as information becomes available
Uses the likelihood function and the prior
distribution to obtain a posterior distribution
MTD is determined from the posterior
distribution
Studies are based on costs and public health
benefits
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Prior Distribution
Logistic model:
p(d) = exp (3 + ad)/[ 1 + exp(3 + ad)]
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Power model:
p(d) = dexp(a)
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p(d) is the probability of DLT
d is the dose
a is a model parameter
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Once the posterior distribution is calculated:
◦ The MTD is revised based on the distribution of a
◦ The mode of the posterior distribution is used to
estimate the next dose
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Each patient is treated at the dose which is
closest to the MTD
Toxicity profile is updated after each patient is
treated
The sequence is repeated until a precise
estimate of parameter a is obtained or the
sample size is exhausted
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Example: A dose-finding escalation design
from an oncology trial
Traditional approach
◦ The 3+3 traditional escalation rule (TER)
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Bayesian approach
◦ The continual reassessment method (CRM)
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The objective is to determine the MTD for a
new drug using the least amount of patients
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Results from animal studies:
◦ The dose limiting toxicity rate was determined to
be 1% for the starting dose of 25 mg/m2, 1/10 of
the lethal dose
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The MTD is estimated to be 150 mg/m2
The dose limiting toxicity rate is defined as
0.25
Selected Model: A logistic toxicity model
Dose sequence was chosen with interim
factors = 2, 1.67, 1.33, 1.33, 1.33, 1.33,
1.33, 1.33, 1.33
Summary of simulation results for the designs
Assumed
True MTD
Mean
Predicted
MTD
Mean
number of
Patients
Mean
number of
DLTs
3+3 TER
100
86.7
14.9
2.8
CRM
100
99.2
13.4
2.8
3+3 TER
150
125
19.4
2.9
CRM
150
141
15.5
2.5
3+3 TER
200
169
22.4
2.8
CRM
200
186
16.8
2.2
Method
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Both approaches underestimate the true MTD
◦ However, the Bayesian approach was much closer to
the true value for all dose levels
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At all three dose levels the Bayesian approach
required less patients
The mean number of DLTs for the Bayesian
approach was either less than or equal to the
traditional approach at all dose levels
The Bayesian CRM approach proved to be
more favorable
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The Bayesian approach can be used alone or
as a hybrid with the classic approach
As a hybrid, the Bayesian approach is used to
increase the probability of success
Example: Two-arm parallel design
◦ Compares a test treatment and a control
◦ Use data from 3 clinical trials with similar sample
sizes
◦ Prior probabilities for the effect size are 0.1, 0.25,
and 0.4 with 1/3 probability for each trial
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The classic approach:
◦ Mean of the effect size, = 0.25, is used to calculate
the sample size. For the design with β = 0.2:
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The Bayesian approach:
The power of the effect size is
Φ is the c.d.f. of the standard normal distribution
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Prior, π(ε), is the uncertainty of ε, the
expected power
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Assuming, one-sided α = 0.025,
Pexp =0.66
With the hybrid approach the power is less
than the 80% power stated in the frequentist
approach, recall β = 0.2. In order to reach the
expected power of 80%, the sample size
needs to be increased
The Bayesian approach piece is used to
increase the probability of success given that
the final criterion is p ≤ α = 0.025
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Prior information and Assumptions
Criterion for success for safety and effectiveness
Justification for the proposed sample size
Prior probability of the study claim
◦ This is the probability of the study claim before
seeing any new data, and it should not be too high
◦ Ensures the prior information does not overwhelm
the current data, potentially creating a situation
where unfavorable results from the proposed study
get masked by a favorable prior distribution
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Program Code
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Operating characteristics
◦ Provide tables of the probability of satisfying the study
claim, given “true” parameter values and sample sizes
for the new trial
◦ Provides an estimate of the probability of a type I error
in the case where the true parameter values are
consistent with the null hypothesis, or power in the
case where the true parameter values are consistent
with the alternative
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Effective Sample Size
◦ Quantifies the efficiency you are gaining from using
the prior information and gauges if the prior is too
informative
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Bayesian full approach is more beneficial in
Phase I studies
◦ Inherent adaptive nature of the design
◦ Conditions are more dynamic than other phases
and the flexible nature of the Bayesian approach
allows for unexpected changes
◦ Produces a posterior probability which is useful in
decision making and the transitioning from one
phase to the next
◦ Dose levels can be modified which could be
beneficial for a phase I cancer study
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Even without using a full Bayesian method,
hybridization results in increased probability
of success in trials
Maintaining the validity and integrity of the
study and control of the type I error in
applications of the method is important
Feasibility should be evaluated in order to
prevent abuse of this method in applications
such as endpoints or hypotheses changes
The FDA is cautious of the growing trend of
Bayesian designs and continues to set
guidelines for its use in Phase I trials
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Chang, Mark (2008). Adaptive Design Theory and Implementation
Using SAS and R. Boca Raton: Chapman & Hall/CRC
Berry, Scott M., Carlin, Bradley P., Lee, J.Jack, Muller, Peter (2011).
Bayesian Adaptive Methods for Clinical Trials. Boca Raton:
Chapman & Hall/CRC
Chow, Shein-Chung and Chang, Mark (2008). Adaptive Design
Methods in Clinical Trials – A Review. Orphanet Journal of Rare
Diseases, 3 11
Cook, Thomas D. and DeMets, David L. (2008). Introduction to
Statistical Methods for Clinical Trials. Boca Raton: Chapman &
Hall/CRC
The FDA Center for Drug Evaluation and Research, and Center for
Biologics Evaluation and Research, Guidance for Industry:
Adaptive Design Clinical Trials for Drugs and Biologics:
www.fda.gov