eugm 2014 | bekele | adaptive dose finding using toxicity probability intervals

Adaptive Dose Finding Using Toxicity Probability IntervalsProbability Intervals

Neby Bekele, PhDy ,Senior DirectorGil 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 effect y

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 or a e s yp ca y a e p e ea ed, ad a ced oresistant 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 level g 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 level p pas 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 toxicity0 toxicities

Let k=k+1 and go to Step 1.Step 1B: Enroll 3 more patientsat the kAth Dose.

3 patients enrolled atdose 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 oknowledge (and subjective beliefs) and a summary of the observed data



1) Specify statistical model to estimate the ) p yToxicity 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)



4) Treat each successive cohort at the dose j* for ) jwhich 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 understand3. Stops the trial relativelyquickly

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 data2. Stops the trial relativelyquickly

2. May be sensitive to prior assumptions


Adaptive Models Adaptive 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 dToxicity 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 posterior 1 2 i pstandard deviation of pi

Pe: Pr(0 < pi<K1i | data)

Ps: Pr( K1i <pi<K2i | data)

Pd: Pr( K2i <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 enroll stop pto 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

eugm 2014 | bekele | adaptive dose finding using toxicity probability intervals

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