implementation of bayesian logistic regression for dose escalation at novartis oncology

Implementation of Bayesian Logistic Regression for dose escalation at Novartis Oncology

Glen Laird, Novartis OncologyWorkshop in Phase I designs October 2, 2009With contributions from Beat Neuenschwander, Bill Mietlowski, Jyotirmoy Dey, and Stuart Bailey.

2 | Novartis implementation of Bayesian Logistic Regression | Phase 1 Workshop | Oct 2nd, 2009 |

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

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


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


Summary of MCRM: impact of exponent alpha

•

ALPHA0.1 0.2 0.3 0.4 0.50.7 1.0 2.0 3.0 4.0AAA

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1 2 3 4 5 6

A A A A A A A

A

A

A

AA 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


One Novartis experience with MCRMMotivating 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.


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!


One Novartis experience with CRM- Case study Results


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?


Statistical Aspects


Combination of clinical and statistical expertiseInformed decisions: clinical, data, historical knowledge and statistics

DLT ratesp1, p2,...,pMTD,...

(uncertainty!)

HistoricalData

(prior info)

Model based dose-DLT

relationship

Trial Data0/3,0/3,1/3,...

ClinicalExpertise

Dose recommen-

dations

DecisionsDose Escalation

Decision

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) ?


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

Dose that maximizes probability that true DLT rate

p is in target interval e.g. (0.166, 0.333)

… with overdose control e.g., less than 25%

probability that true DLT rate p exceeds 0.333

1 2


Quantifying the uncertainty in DLT ratesCharacterizing 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%





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)





Data: 1/6

Summary for p: 0.17 (0.02,0.53)95%



• 16.8% probability for overdosing: DLT rate p>1/3




Conclusions- Considerable uncertainty due to sparse data- Therefore: good decisions require synergy of clinical and statistics expertise


Data: 1/6

Summary for p: 0.17 (0.02,0.53)95%



• 16.8% probability for overdosing: DLT rate p>1/3

• 48.3% probability for underdosing:DLT rate p<1/6


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%)


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


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)


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.)


PriorsTypical priors represent different types of information

Uninformative Prior• wide 95%-intervals• (default prior)

Bivariate normal prior for (log(),log()) prior for DLT rates p1,p2,…




Historical Prior• Data from historical trials

(discounted due to between-trial variation!)





Historical Prior• Data from historical trials

(discounted due to between-trial variation!)

Mixture Prior• Different prior information

(pre-clinical variation)• different prior weights



OutputInterval Probabilities: underdosing, targeted toxicity, overdosing

Top Panelprobability of overdosingfailed overdose criterion in red! Pr( true DLT rate p >0.333) > 25%

Middle Panelprobability of targeted toxicity

Bottom Panelprobability of underdosing

Recommended Dose 15 (max target w/ overdose<25%)

overdosingtargeted toxicity

underdosing


Summary

ModelPrior

Expertise

1. Substantial uncertainty in MTD finding requires statistical component2. Input: standard model (logistic regression) + prior3. Inference: probabilistic quantification of DLT rates, a requirement that

leads to informed recommendations/decisions4. Dose Recommendations are based on the probability of targeted

toxicity and overdosing. • Overdose criterion is essential.

Input Inference Recommendations


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)


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


Novartis experience case study revisited – BLR Results


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


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!)


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


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


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())


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%

20 .973 .025 .002 .034 .045 .001 .018 .164

30 .831 .142 .027 .090 .088 .004 .062 .337

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

Most excessive dose of 45 mg (narrowly) avoided despite mean being clearly below the targeted toxicity rate of 30%.


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”


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

Study conductPatient enrollment / observation for each dose cohort


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


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.


Combination of clinical and statistical expertiseInformed decisions: clinical, data, historical knowledge and statistics

DLT ratesp1, p2,...,pMTD,...

(uncertainty!)

HistoricalData

(prior info)

Model based dose-DLT

relationship

Trial Data0/3@1 mg

ClinicalExpertise

Dose recommen-

dationsDecisions

Dose EscalationDecision

Additionalstudy data – AE,PK, BM, Imaging

con-meds


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


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). Platelet-derived 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

implementation of bayesian logistic regression for dose escalation at novartis oncology

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