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Implementation of Bayesian Logistic
Regression for dose escalation at Novartis
Oncology
Glen Laird, Novartis Oncology
Workshop in Phase I designs
October 2, 2009
With contributions from Beat Neuenschwander, Bill
Mietlowski, Jyotirmoy Dey, and Stuart Bailey.
Outline of Presentation
 Background on Phase I needs
 CRM/MCRM background
•
One Novartis experience
 FDA feedback on potential issues w/ CRM
•
Example studies cited
 Novartis implementation of Bayesian Logistic Regression
•
Statistical model
•
Protocol planning and Study execution
•
Decision making during dose-escalation teleconference
 Comparison of Bayesian Logistic and CRM methods
 Key messages
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Flexible Phase I Oncology Designs
Requirements for dose-escalation
Challenges of Oncology Phase I Trials
 Accurately determine the Maximum Tolerated Dose (MTD)
 Untested drug in resistant patients
• Unknown potential for toxicity – Avoid “overdosing” while trying to
test a wide dose-range and learn about dose-toxicity relationship
• Avoid sub-therapeutic doses while controlling “overdosing”
• Identify active and acceptable doses for phase II/III
 Rare and very-ill patients
• Use as few patients as possible – cohorts of 3-6
• Inability to distinguish tox due to condition from tox due to drug
• Ph 1 pts also hope for therapeutic benefit
• Use all available information efficiently
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CRM/MCRM background: implementation at
Novartis
 Many versions of CRM/MCRM exist. Novartis implementation used a
power model

Prior probabilities of DLT at dose levels (“skeleton”) input

Learning model (posterior): P{DLT} = pi mean() , where pi are the initial
“skeleton” estimates of P{DLT}

Target DLT rate often 33% at Novartis

Prior uncertainty about  usually specified by lognormal distribution.

Starting at lowest dose

Not skipping doses

Enrolling in cohorts (often size 3-6)
 Emerging DLT data  updated estimate of exponent 
 Updated   Updated posterior probabilities of DLT
•
 > 1 decreases probabilities of DLT for all doses
•
 < 1 increases probabilities of DLT for all doses
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Summary of MCRM: impact of exponent alpha
•
1.0
A
0.9
A
0.8
0.7
A
0.6
0.5
A
0.4
0.3
0.2
A
0.1
0.0
A
A
1
A
A
A
A
2
ALPHA
0.1
0.7
A
3
0.2
1.0
4
0.3
2.0
0.4
A
A
A
3.0
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5
6
0.5
4.0
A
CRM/MCRM background
 CRM/MCRM uses 1-parameter model
• depends on correct specification of skeleton (log posterior
probability DLT proportional to log prior skeleton)
• Serious mis-specification of skeleton can lead to excessive
dosing
• On-study recommendations may be impractical (or not
followed by clinicians) even if final dose recommendation
would be reasonable.
 CRM/MCRM ignores precision of updated estimate of
exponent 
• Same updating if estimate of  came from cohorts of 1, 3, 6,
or 12 patients
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One Novartis experience with MCRM
Motivating example (from Neuenschwander, et al, 2008)
 open-label, multicenter, non-comparative, dose-escalation
cancer trial designed to characterize the safety, tolerability
and PK profile of a drug and to determine its MTD.
 The pre-defined doses were 1, 2.5, 5, 10, 15, 20, 25, 30,
40, 50, 75, 100, 150, 200 and 250 mg. Target P(DLT)=.3.
 The first cohort of patients was treated at 1mg. No DLTs
were observed for the first four cohorts of patients.
 clinical team decided to skip 2 doses to 25mg (contradicting the
planned MCRM in which doses were not supposed to be skipped)
 Both patients dosed at 25 mg experienced DLT
• MCRM recommended further escalation, to the dismay of the team.
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Case study – CRM Results
 Recommendation:
• from original pi: dose = 40 or 30 (not favored by team!)
• from equidistant pi: dose = 25 (questionable)
• Note: the pi are structural assumptions, should not be changed!
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One Novartis experience with CRM- Case study
Results
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FDA concern about CRM methods

Raji Sridhara and/or Sue-Jane Wang from FDA raise concerns
about 3 trials using CRM methods.
1. Companion studies of 9-aminocamptothecin : 9 out of 17 patients
experience DLTs and 12 out of 18 patients experience DLTs.
(Piantadosi, et al, 1998)
2. Time to event (TITE) CRM model has 4 out of 8 patients at highest
dose experience DLTs (Muler, et al, 2004)
3. Gleevec prostate trial has 8 out of 10 patients enrolled above MTD
experience DLT (Matthew, et al).
Use of multi-parameter models more technically feasible for
widespread use than in years past.
 Could more flexible Bayesian methods be developed that retain
some of the improvements over 3+3 type methods?
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Flexible Phase I Oncology Designs
Statistical Aspects
Combination of clinical and statistical expertise
Informed decisions: clinical, data, historical knowledge and statistics
Historical
Data
(prior info)
Trial Data
0/3,0/3,1/3,...
DLT rates
p1, p2,...,pMTD,...
(uncertainty!)
Model based
dose-DLT
relationship
Dose
recommendations
Decisions
Dose Escalation
Decision
Clinical
Expertise
How certain are we that
(1) True DLT rate for recommended dose is in target interval (0.166,0.333), (2) not an overdose (>0.333) ?
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Quantifying the uncertainty in DLT rates
Recommendations rely on relevant inferential summaries
 Inference: for each dose we want to know
• how likely is it that true DLT rate is in target interval?
• how likely is it that true DLT rate is an overdose?
•  Example (next slide)
 Dose recommendation: for next cohort, select dose that
fulfills the following criteria
Two criteria
1
Dose that maximizes
probability that true DLT rate
p is in target interval
 e.g. (0.166, 0.333)
2 … with overdose control
 e.g., less than 25%
probability that true DLT rate
p exceeds 0.333
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Quantifying the uncertainty in DLT rates
Characterizing DLT rates requires us to go beyond point estimates
• Example: 1 DLT in 6 patients. What do we really know about p?
 Uninformative prior: 0.25 (0.00,0.95)95%
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Quantifying the uncertainty in DLT rates
Characterizing DLT rates requires us to go beyond point estimates
• Example: 1 DLT in 6 patients. What do we really know about p?
 Uninformative prior: 0.25 (0.00,0.95)95%
 Data: 1/6
 Summary for p: 0.17 (0.02,0.53)95%
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Quantifying the uncertainty in DLT rates
Characterizing DLT rates requires us to go beyond point estimates
• Example: 1 DLT in 6 patients. What do we really know about p?
 Uninformative prior: 0.25 (0.00,0.95)95%
 Data: 1/6
 Summary for p: 0.17 (0.02,0.53)95%
 Additional information: there is a
• 35% probability for targeted
toxicity:
p in target interval in (0.166,0.333)
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Quantifying the uncertainty in DLT rates
Characterizing DLT rates requires us to go beyond point estimates
• Example: 1 DLT in 6 patients. What do we really know about p?
 Uninformative prior: 0.25 (0.00,0.95)95%
 Data: 1/6
 Summary for p: 0.17 (0.02,0.53)95%
 Additional information: there is a
• 35% probability for targeted
toxicity:
p in target interval in (0.166,0.333)
• 16.8% probability for overdosing:
DLT rate p>1/3
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Quantifying the uncertainty in DLT rates
Characterizing DLT rates requires us to go beyond point estimates
• Example: 1 DLT in 6 patients. What do we really know about p?
 Uninformative prior: 0.25 (0.00,0.95)95%
 Data: 1/6
 Summary for p: 0.17 (0.02,0.53)95%
 Additional information: there is a
• 35% probability for targeted toxicity:
p in target interval in (0.166,0.333)
• 16.8% probability for overdosing:
DLT rate p>1/3
• 48.3% probability for underdosing:
DLT rate p<1/6
Conclusions
- Considerable uncertainty due to sparse data
- Therefore: good decisions require synergy of clinical and statistics expertise
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Methodology - Overview
Inference: model-based. Recommendations: target toxicity, overdose control
 Model: logistic regression
 Inference is Bayesian
 Priors
• “uninformative”
• priors based on historical data
• mixture priors accounting for pre-clinical variability
 Dose recommendations: balancing target toxicity & safety
• Target toxicity: recommend dose that is in target interval with high
probability
• Safety: dose must fulfill overdose criterion
• Note: this approach is safer than recommending dose with an
estimated DLT rate that is closest to target toxicity (e.g. 25%)
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Models
Reasonably flexible model is needed to ensure good performance
 Basic model: logistic regression
• DLT rate p, dose = d: logit(p) = log(p/(1-p)) = log() + .log(d),  , > 0
• reasonably flexible 2-parameter model
 Extensions of basic model
• Covariates X (): logit(p) = log() + .log(d) + X
- e.g. dose regimen or patient characteristics
- e.g. levels of combination partner (Bailey, et al, 2009)
• Combination setting: DLT rate for combination of two compounds
• Ordinal Data: e.g. no DLT, low-grade toxicity, DLT
• Joint Safety-Efficacy model
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Protocol development
 Pre-define provisional dose escalation steps
• Provisional doses decided on expected escalation scheme typically indicate maximum one-step jump. Intermediate doses
may be used on data-driven basis
 Minimum cohort-size – typically 3.
• Allow enrollment of additional subjects for dropouts or cohort
expansion
 Simulation tool exists to test operating characteristics
• Performance of the design in terms of correct dose-determination,
gain in efficiency under various assumed dose-toxicity
relationships (truths)
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Protocol development
 Stopping rules (“rules for declaring the MTD”)
• At least 6 evaluable patients at the MTD level with at least 21
patients evaluated in total in the dose escalation phase
or
• At least 9 patients evaluated at a dose level with a high precision
(model recommends the same dose as the highest dose that is
not an overdose with 50% posterior probability in the target
toxicity interval.)
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Priors
Typical priors represent different types of information
 Bivariate normal prior for (log(),log())  prior for DLT rates p1,p2,…
Uninformative Prior
• wide 95%-intervals
• (default prior)
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Priors
Typical priors represent different types of information
 Bivariate normal prior for (log(),log())  prior for DLT rates p1,p2,…
Uninformative Prior
• wide 95%-intervals
• (default prior)
Historical Prior
• Data from historical trials
(discounted due to
between-trial variation!)
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Priors
Typical priors represent different types of information
 Bivariate normal prior for (log(),log())  prior for DLT rates p1,p2,…
Uninformative Prior
• wide 95%-intervals
• (default prior)
Historical Prior
• Data from historical trials
(discounted due to
between-trial variation!)
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Mixture Prior
• Different prior information
(pre-clinical variation)
• different prior weights
Output
Interval Probabilities: underdosing, targeted toxicity, overdosing
overdosing
targeted
toxicity
underdosing
Top Panel
probability of overdosing
failed overdose criterion in red!
Pr( true DLT rate p >0.333) > 25%
Middle Panel
probability of targeted toxicity
Bottom Panel
probability of underdosing
Recommended Dose
15 (max target w/ overdose<25%)
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Summary
Model
Prior
Expertise
Input

Inference

Recommendations
1. Substantial uncertainty in MTD finding requires statistical component
2. Input: standard model (logistic regression) + prior
3. Inference: probabilistic quantification of DLT rates, a requirement that
leads to informed recommendations/decisions
4. Dose Recommendations are based on the probability of targeted
toxicity and overdosing.
•
Overdose criterion is essential.
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Comparison of Operating characteristics to
CRM/MCRM (Neuenschwander, et al, 2008)
 Simulations performed comparing
• CRM (with 27% target rate);
• MCRM;
• Logistic Regression based on 27% target rate (LRmean).
• Logistic Regression maximizing target toxicity (LRcat);
• Logistic Regression maximizing target toxicity with 25% overdose
control (LRcat25);
 Eight scenarios studies using 7 dose levels.
• “true” MTD (27% DLT rate) varied from dose level 1,2,4,6, or 7
• Flat and steep true curves studied
• Same prior medians and vague priors used
• Fixed sample size of 24 or 36 patients.
• Older version of target toxicity used (20% - 35% DLT rate)
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Comparison of Operating characteristics to
CRM/MCRM
 Performance
• LRcat25 and MCRM have lower average number of DLTs than the
more aggressive CRM, LRmean, and LRcat methods
• LRcat25 selected correct dose with similar frequency as the more
aggressive methods
- It was slightly lower (approximately 6%-10% lower) for “flat” toxicity curves
in which the true MTD was high (dose 6)
• MCRM had worse targeting than other methods when the true dose
was a high dose level.
 By being more aggressive only when the full posterior
summary justifies it, LRcat25 appears to combine some of
the added safety of the MCRM with the superior targeting
of the CRM, LRmean, and LRcat methods.
 Thall and Lee (2003) also compared performance
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Novartis experience case study revisited – BLR
Results
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Case study - comparison
Priors
 Prior for BLR chosen
to be similar to prior for
CRM
Posteriors
 CRM: “too” narrow
intervals for doses
where no data have
been seen. Similar
things happen for other
1-parameter models
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Case study: Summary
 CRM not able to react to the toxicity data due to less
flexibility in 1-parameter model
• Lack of uncertainty at high (never tested) doses
 BLR does not suffer from the same issue and makes
sensible on-study recommendations in this case
• Parameterization allows uncertainty to remain at doses never tested
and therefore model can adapt more easily
 BLR approach to estimating the MTD is more suitable in
this case study than the CRM approach
• Provide better estimation of the full dose response curve (still not the
primary goal though!)
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FDA concern about CRM methods
•
Data from Mathew, et al study:
cohort
dose
patients
DLTs
1
30
6
0
2
45
4
3
3
35
6
5
4
30
6
3
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Analysis of first cohort of Mathew et al data
alpha= 6.077
DoseLevel PtoxPrior Npat Ntox Ptox
1
20
0.07
0
0
0.000
2
25
0.16
0
0
0.000
3
30
0.30
6
0
0.001
4
35
0.40
0
0
0.004
5
40
0.46
0
0
0.009
6
45
0.53
0
0
0.021
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Re-examination of Mathew et al data using Novartis
methodology
 Re-examined Mathew et al data using Novartis method.
• assume same prior medians as actual study design.
• Match prior percentiles for 2.5%, median, and 97.5% percentiles as
closely as possible to a bi-variate normal prior for (log(),log())
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Analysis of Mathew et al data using Novartis
methodology, cont’d
dose 0-.16 .16-.33 .33-1
mean sd
2.5% 50% 97.5%
.034 .045
.001 .018 .164
20
.973
.025
.002
30
.831
.142
.027
35
.687
.225
.088
.136 .126
.006 .097 .470
40
.553
.268
.179
.190 .170
.009 .139 .640
45
.450
.273
.278
.246 .210
.012 .185 .785
.090 .088
.004 .062 .337
 Most excessive dose of 45 mg (narrowly) avoided despite
mean being clearly below the targeted toxicity rate of 30%.
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Implementation message taken from JSM
 Dan Sargent noted at JSM 2009 that the differences
between Bayesian methodologies are not as important as
the need to replace “3+3” methods with some form of
Bayesian method.
 Good to continue to search for better dose escalation
methods, but don’t let that stop the implementation of
methods that are at least better than “3+3”
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Study conduct
Patient enrollment / observation for each dose cohort
 To assure patient safety during the conduct of the study a
close interaction within clinical team is required

Clinician, statistician, clinical pharmacologist, etc

Investigators

Clinical trial leader provides regular updates on accrual:

For each cohort enroll subjects per minimum cohort-size, typically 3

May enroll additional subjects up to a pre-specified maximum

In the case of unexpected or severe toxicity all investigators will
be informed immediately

The model will be updated in case the first 2 patients in a cohort
experience DLT
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Discussion at the dose escalation conference (DETC)
Discussion with investigators during the DETC
 Investigators and sponsor review all available data (DLT, AE,
labs, VS, ECG, PK, PD, efficacy) particularly from current
cohort as well as previous cohorts
 Agree on total number of DLTs and evaluable subjects for
current cohort
 Statistician informs participants of the highest dose level one
may escalate to per statistical analysis and protocol
restrictions
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Dose escalation decision
 Participants decide if synthesis of relevant clinical
data justifies a dose escalation and to which dose
(highest supported by the Bayesian analysis and
protocol or intermediate)
 Decisions are documented via minutes and
communicated to all participants.
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Combination of clinical and statistical expertise
Informed decisions: clinical, data, historical knowledge and statistics
Trial Data
0/3@1 mg
Historical
Data
(prior info)
DLT rates
p1, p2,...,pMTD,...
(uncertainty!)
Model based
dose-DLT
relationship
Dose
recommendations
Clinical
Expertise
Additional
study data – AE,
PK, BM, Imaging
con-meds
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Decisions
Dose Escalation
Decision
Flexible Phase I Oncology Designs
Concluding remarks
Key Messages
 Patient safety is the primary objective
• Statistical approach quantifies knowledge about DLT data only
• Statistical inference is used as one component of a decision-making
framework
- Provides upper bound for potential doses based on uncertainty statements
- To reduce risk of overdose  obtain more information at lower doses
 Application of our approach can be protocol/drug specific
• Maximum escalation steps, minimum and maximum cohort sizes,
stopping rules are pre-specified
 Studies require active review of ongoing study data by Novartis
and investigators
 Novartis method appears to have good targeting properties while
preserving patient safety
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References
 Bailey, Neuenschwander, Laird, Branson (2009).
A Bayesian case study in oncology phase I combination dose-finding using logistic regression
with covariates. Journal of Biopharmaceutical Statistics, 19:369-484
 Mathew, Thall, Jones, Perez, Bucana, Troncoso, Kim, Fidler, and Logothetis (2004). Plateletderived Growth Factor Receptor Inhibitor Imatinib Mesylate and Docetaxel: A Modular Phase I
Trial in Androgen-Independent Prostate Cancer Journal of Clinical Oncology, 16, 3323-3329.
 Muler, McGinn, Normolle, Lawrence, Brosn, Hejna, and Zalupski (2004) 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 Onocology,
22:238-243.
 Neuenschwander, Branson, Gsponer (2008)
Critical aspects of the Bayesian approach to Phase I cancer trials. Statistics in Medicine,
27:2420-2439.
 Piantadosi, Fisher, and Grossman (1998) Validation Of Doses Selected Using The Continual
Reassessment Method (Crm) In Patients With Primary Cns Malignancies. ASCO meeting
abstract. Abstract #819.
 Thall, Lee (2003) Practical model-based dose-finding in phase I clinical trials: methods based
on toxicity. Int J Gynecol Cancer 13: 251-261
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