MPTI Talk

Adaptive Dose Finding Using Toxicity
Probability IntervalsProbability Intervals
Neby Bekele, PhDy ,
Senior Director
Gil d S iGilead Sciences
1Phase I & TPI. Oct, 2014.

Outline of TalkOutline of Talk
 Phase I Clinical Trials in Oncologygy
 Overview of common methods
– 3+3 Design3 3 Design
– Model Based Alternatives
 Overview of the TPI method Overview of the TPI method
 Implementation and Software Demonstration
 Concluding Remarks

Phase I Clinical Trials in OncologyPhase I Clinical Trials in Oncology
 Given a set of doses of a new agent find a dose
with an “acceptable” level of toxicityy
 Underlying Assumptions:
– We explicitly assume that the probability of toxicityWe explicitly assume that the probability of toxicity
increases with dose
– While implicitly assuming that the probability of
response increases with dose

Phase I Clinical Trials in OncologyPhase I Clinical Trials in Oncology
 Implications of underlying assumptions:
A higher dose is worse because it is more likely toA higher dose is worse, because it is more likely to
cause toxicity while also being better because it is
more likely to have an anti-tumor effecty
Goal: Finding the dose that balances benefit
relative to risk (i.e., the MTD)( )

Practical Considerations for Phase I Oncology
Clinical TrialsClinical Trials
 For ethical reasons doses must be selected For ethical reasons, doses must be selected
sequentially, for small cohorts of patients
 It may be the case that no dose is safe It may be the case that no dose is safe
 The maximum sample size is usually very small
 Patient heterogeneity is usually ignored
 Little is known about the dose-toxicity curvey
 Evaluating toxicity usually takes weeks
 Whil t i iti f i t d
 While toxicities are of various types and
severities, this is usually ignored

Practical Considerations for Phase I Oncology
Clinical TrialsClinical Trials
 For ethical reasons doses must be selected For ethical reasons, doses must be selected
sequentially, for small cohorts of patients
 Phase I is often ethical only for patients with Phase I is often ethical only for patients with
little or no therapeutic alternative
– Patients typically are pre-treated, with advanced ora e s yp ca y a e p e ea ed, ad a ced o
resistant disease, little chance of response
– Dose-finding typically is done in terms of toxicity
only to find a “maximum tolerated dose”only, to find a maximum tolerated dose

Typical Phase I Oncology Clinical Trial SetupTypical Phase I Oncology Clinical Trial Setup
 The investigator chooses the starting levelg g
based on clinical judgment, & possibly animal or
in vitro data
 Treat patients in cohorts of 1, 2, or 3
 Escalate & de-escalate using reasonable rules & g
 If the lowest dose is too toxic, stop the trial, or
add lower dose levelsadd o e dose e e s

The 3+3 DesignThe 3+3 Design
 Example of an Up-and-Down Designp p g
 Algorithm based
– “If I see this then I do this”If I see this then I do this
 Up-and-down designs based on 1948 paper by
Mood and Dixon (applications dealt withMood and Dixon (applications dealt with
explosives and lethal toxicities!)
 Easy to understand Easy to understand
 Easy to implement

Example 3+3 Decision Rules (Approach I)Example 3+3 Decision Rules (Approach I)
# Patients with DLT Decision
0/3 Escalate one level
1/3 Treat 3 more1/3 Treat 3 more
at the same level
2/3 or 3/3 Stop & choose previous levelp p
as the MTD
1/3 + {0/3} Escalate one level
1/3 + {1/3} Stop & choose previous level
as the MTD
1/3 + { 2/3 or 3/3 } Stop & choose previous level
as the MTD

Example 3+3 Decision Rules (Approach II)Example 3+3 Decision Rules (Approach II)
Step 1: Enroll 3Step 1: Enroll 3
patients at the kth
Dose
More than
3 patients
>1 toxicities1 toxicity
0 toxicities
Let k=k+1 and go to Step 1.
Step 1B: Enroll 3 more patients
at the kAth Dose.
3 patients
enrolled at
dose k-1?
No Yes
>2 toxicities for
all patients at
k dose
Declare the
previous dose
the MTD
Enroll 3 more
patients at
previous dose. Let
k = k-1Go to Step 1
0 toxicity for
current cohort

High Level Process for Implementing a 3+3
MethodMethod
Decision RuleData
Decision
Framework for
Toxicity Data
making dosing
decisions
Toxicity Data

Problems with the 3+3 DesignProblems with the 3+3 Design
 Ignores most of the data
St th t i l l ti l i kl Stops the trial relatively quickly
 Unreliable and increases the risk of choosing an
i ff ti dineffective dose
 Is not flexible in that it does not allow the
h t h th t t d t i it ilresearcher to change the targeted toxicity easily.

Model Based AlternativesModel Based Alternatives
 Much more reliable than 3+3 algorithms
M d l b d th d iti t Model based methods are sensitive to
underlying assumptions about the dose-toxicity
relationshipp
 Minimally, requires expertise in the
implementation of model based methodsp e e tat o o ode based et ods
 May requires specialized software for trial
conduct (including web-based software)
co duct ( c ud g eb based so t a e)

Adaptive Dose findingAdaptive Dose-finding
 Write Down a Probability Model
D fi t f t ti ti i d l d Define a set of statistics using your model and a
set of decision rules to choose doses adaptively
At th d f th t d th d l t d l At the end of the study use the model to declare
an MTD
W it ft f d t f T i l d f Write software for conduct of Trial and perform a
simulation study to ensure the method can find
appropriate doses.
app op ate doses

Bayesian Models
(Commonly Used in Phase I Dose Finding)(Commonly Used in Phase I Dose-Finding)
 All Bayesian inferences follow from Bayes’
Theorem:
posterior  prior • likelihood
 The posterior is a product of our prior e poste o s a p oduct o ou p o
knowledge (and subjective beliefs) and a
summary of the observed data

Bayesian Models
1) Specify statistical model to estimate the) p y
Toxicity probabilities
p1 < p2 < … < pkp1 p2 pk
corresponding to the k dose levels
2) S if t t T i it b bilit *2) Specify a target Toxicity probability, pTOX*
3) Prob(Toxicity | dose j) = pj , j=1,…,k,
*O’Quigley, Pepe, Fisher. (Biometrics, 1990)

Bayesian Models
4) Treat each successive cohort at the dose j* for) j
which pj* is closest to pTOX*.
5) The dose satisfying (4) at the end of the trial is
the selected to be the MTDthe selected to be the MTD

Pros and Cons of the Two Model Based
ApproachesApproaches
3+3 Design Model Based Approaches
Pros:
1. Easy to Implement
Pros:
1. More reliable
2. Easy to understand
3. Stops the trial relatively
quickly
Cons:
1. Requires specializedquickly
Cons:
1 Ignores most of the data
1. Requires specialized
software for both trial setup
and conduct
2 May be sensitive to prior1. Ignores most of the data
2. Stops the trial relatively
quickly
2. May be sensitive to prior
assumptions

Adaptive ModelsAdaptive Models
 Assume you decide to use an Adaptive Model
 Which model should you use? Keeping up with
ll th h i b bit i d b liall the choices can be a bit mind-boggling
 How should the model interface with the user?

High Level Process for Implementing a Model
Based Method: Statistician as InterfaceBased Method: Statistician as Interface
ModelData Statistician
Statistician as User
Statistical
Framework for
Toxicity Data
Interface Model making dosing
decisions
Toxicity Data

High Level Process for Implementing a Model
Based Method: Graphical InterfaceBased Method: Graphical Interface
Data Model User
Interface
Graphical User
Statistical
Framework for
k d
Toxicity Data
Interface Modelmaking dosing
decisions
Toxicity Data

Pros and Cons of the Two Model Based
ApproachesApproaches
Statistician as Interface Graphical User Interface
Pros:
1. Relatively Easy to
Pros:
1. Easy to Scale up
Implement
Cons:
Cons:
1. Requires expertise in bothCons:
1. Difficult to Scale up (may
be difficult to use in a
multicenter setting)
1. Requires expertise in both
statistics (to build the model)
and computer programming
(to build the GUI and to havemulticenter setting)
2. Risk of data entry error
(to build the GUI and to have
the data communicate with
the model)
2. Risk of data entry error

Middle Ground: Toxicity Probability IntervalsMiddle Ground: Toxicity Probability Intervals
 Combines model based methods with simple
up-and-down rules similar to the 3+3 algorithmp g
 A simple spreadsheet can be used to monitor
Escalation Rules

Toxicity Probability Intervals (mTPI)Toxicity Probability Intervals (mTPI)
 A priori, assumes that pi follows a non-
informative beta(0.0005,0.0005) distribution( , )
A t i i th d l th t f ll A posteriori, the model assumes that pi follows a
beta(xi+.0005,ni-xi+0.0005) distribution

Toxicity Probability Intervals (TPI)Toxicity Probability Intervals (TPI)
K1 and K2 are constants and i is the posterior1 2 i p
standard deviation of pi
Pe: Pr(0 < pi<K1i | data)
Ps: Pr( K1i <pi<K2i | data)
Pd: Pr( K2i <pi< 1 | data)
Pstop: Pr(pi> | data)

Modified Toxicity Probability Intervals (mTPI)Modified Toxicity Probability Intervals (mTPI)
 A priori, assumes that pi follows a uniform
beta(1,1) distribution( , )
A t i i th d l th t f ll A posteriori, the model assumes that pi follows a
beta(xi+1,ni-xi+1) distribution

Modified Toxicity Probability Intervals (mTPI)Modified Toxicity Probability Intervals (mTPI)
Pe: Pr(0 < pi<1 | data)/(1)
Ps: Pr( 1<pi<2 | data)/(2  1)
Pd: Pr( 2<pi< 1 |data)/(1   2)
Pstop: Pr(pi> | data)

Toxicity Probability Intervals (TPI):
Decision RulesDecision Rules
If Pstop>.9 then do not allow additional patients to enrollstop p
to the ith dose
If Pe is largest then escalate to the next dose
If Ps is largest then stay at the current dose
If Pd is largest then de-escalate

Toxicity Probability Intervals (TPI):
Decision RulesDecision Rules
Decision Rules lead to the exact same decisions as a
Decision-Theoretic framework in which the loss
functions are defined as:

Toxicity Probability Intervals Limitations(?)Toxicity Probability Intervals Limitations(?)
 Toxicity rates are modeled independently
 Monotone dose-toxicity curve imposed at the
d f th t dend of the study
 Need to define 1 and 2

mTPI: Example CalculationsmTPI: Example Calculations
 What do you need to Implement the method:y p
 Software
 Define max sample size
 Define Pstop threshold
 Define (target toxicity)
 Define 1 and 2

mTPI: Example CalculationsmTPI: Example Calculations

Concluding RemarksConcluding Remarks
 mTPI is a middle ground between up-and-down
designs and model based designsg g
 mTPI is easy to implement
O ti ll t d t d Operationally easy to understand
 Is flexible
 Does not require software while trial is ongoing
 Has good operating characteristics
 Has good operating characteristics

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