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BOIN: A Novel Platform for Designing EarlyPhase Clinical Trials

Ying Yuan

Department of BiostatisticsThe University of Texas, MD Anderson Cancer Center

Ying Yuan BOIN: A Novel Platform for Designing Early Phase Clinical Trials

Introduction Method Simulation Summary

Outline

IntroductionBayesian optimal interval (BOIN) designsSoftware and practical implementation



Phase I clinical trials

The objective of phase I clinical trials is to find themaximum tolerated dose (MTD) that has a target toxicityrate φ.

Target toxicity rate



Performance vs Simplicity

Easy Difficult Implementa)on

Performance

Poor

Good

3+3

CRM



Performance vs Simplicity

Easy Difficult Implementa)on

Performance

Poor

Good

3+3

CRM

BOIN



Objective

To introduce the BOIN design as a platform that is easy toimplement in a transparent way as the 3+3 design, butyields better performance comparable to morecomplicated, model-based designs, such as the CRM.Can handle both single-agent trials and drug-combinationtrials (to find a single MTD or the MTD contour).



BOIN design

DLT rate at the current dose = No. of patients experienced DLT at the current doseNo. of patients treated at the current dose



Escalation/de-escalation boundaries

Table: The escalation/de-escalation boundaries (λe, λd ) under theBOIN design for different target toxicity rates*.

Target toxicity rate φboundaries 0.15 0.2 0.25 0.3 0.35 0.4

λe 0.118 0.157 0.197 0.236 0.276 0.316λd 0.179 0.238 0.298 0.358 0.419 0.479

* using the default underdosing toxicity rate φ1 = 0.6φ and overdosing toxicity rate

φ2 = 1.4φ.



BOIN design with target toxicity rate of 25%




Statistical principle behind BOIN design

How are dose escalation trials conducted in practice?

Start the trial by treating the 1st cohort at the lowest orpre-specified dose.

ThenThree possible decisions:

1 Escalation

2 Retaining the current dose

3 Deescalation



Statistical principle behind BOIN design

How are dose escalation trials conducted in practice?

Start the trial by treating the 1st cohort at the lowest orpre-specified dose.Then

Three possible decisions:1 Escalation

2 Retaining the current dose

3 Deescalation



The oracle design

If we knew the true toxicity probability of the current doselevel j , denote as pj .

We should

escalate the dose if pj < φ.

retain the dose if pj = φ.

deescalate the dose if pj > φ.



The oracle design

If we knew the true toxicity probability of the current doselevel j , denote as pj .We should






The oracle design

Then,




......



The oracle design

If pj was known, we obtain the oracle designNo decision errorOptimize dosing for each patient

In reality, the oracle design does not exist because pj isunknownWe have to estimate pj based the observed data and makethe decision

For example, use the observed toxicity rate pj = mj/nj asan estimate of pj , where mj is the number of patientsexperienced toxicity at dose j , and nj is the number ofpatients treated at those j



Decision errors

The decision is often incorrectEscalate/retain when the current dose is above the MTDDeescalate/retain when the current dose is below the MTDEscalate/deescalate when the current dose is the MTD

Such decision errors cannot be completely avoidedbecause of small sample size and estimation uncertainty

When the truth toxicity = 30%, there is 34% to observe 0/3having toxicity.

What is the best we can do in practice?

Minimize incorrect decisions and get as close aspossible to the oracle design!

This is the motivation of the BOIN (Bayesian OptimalINterval) design



Decision errors

The decision is often incorrectEscalate/retain when the current dose is above the MTDDeescalate/retain when the current dose is below the MTDEscalate/deescalate when the current dose is the MTD

Such decision errors cannot be completely avoidedbecause of small sample size and estimation uncertainty

When the truth toxicity = 30%, there is 34% to observe 0/3having toxicity.

What is the best we can do in practice?Minimize incorrect decisions and get as close aspossible to the oracle design!

This is the motivation of the BOIN (Bayesian OptimalINterval) design



A class of nonparametric designs

1 The first cohort are treated at the lowest dose level.2 At the current dose level j :

if pj ≤ λ1j , escalateif pj ≥ λ2j , deescalateotherwise, i.e., λ1j < pj < λ2j , retain

where λ1j ≡ λ1j(nj , φ) and λ2j ≡ λ2j(nj , φ) denote theprespecified dose escalation and deescalation boundaries.

3 Repeat step 2 until the maximum sample size is reached.



A family of nonparametric designs







A class of nonparametric designs





Because λ1j and λ2j freely vary across the dose and nj , thisclass of designs include all possible nonparametric designs thatdo not impose a dose-toxicity curve.



Notations and setup

Specify three point hypotheses

H0 : pj = φ

H1 : pj = φ1

H2 : pj = φ2,

φ1 is the highest toxicity probability that is deemedsubtherapeutic (i.e., below the MTD) such that doseescalation should be madeφ2 is the lowest toxicity probability that is deemed overlytoxic such that dose deescalation is requiredExample: φ = 0.25, φ1 = 0.15 and φ2 = 0.35.



Remarks on the hypotheses

The purpose of specifying three hypotheses, H0,H1 andH2, is not to represent the truth and conduct hypothesistesting.H1 and H2, or more precisely δ1 = φ1 − φ and δ2 = φ2 − φ,represent the minimal differences (or effect sizes) ofpractical interest to be distinguished from the target toxicityrate φ (or H0), under which we want to minimize theaverage decision error rate for the trial conduct.This is analogous to power calculation.



Remarks on the hypotheses

In practice, we should avoid setting φ1 and φ2 at valuesvery close to φ because of the limited power due to smallsample sizes of phase I trials.

At the significance level of 0.05, we have only 3% power todistinguish 0.35 from 0.25 with 30 patients.

As default values, we recommend φ1 = 0.6φ andφ2 = 1.4φ.

e.g., when φ = 0.25, φ1 = 0.15 and φ2 = 0.35.



Correct and incorrect decisions

The correct decisions under H0, H1 and H2 are R, E andD, respectively, where R, E and D denote dose retainment(of the current dose level), escalation and deescalation.The incorrect decisions under H0, H1 and H2 are R, E andD, where R denotes the decisions complementary to R(i.e., R includes E and D), and D and R are definedsimilarly.



Decision error rate

The probability of making an incorrect decision (or decisionerror rate) at each of the dose assignments is given by

α ≡ pr(incorrect decision on dosing)

= pr(H0)pr(R|H0) + pr(H1)pr(E |H1) + pr(H2)pr(D|H2)

= pr(H0){Bin(njλ1j ; nj , φ) + 1− Bin(njλ2j − 1; nj , φ)}+ pr(H1){1− Bin(njλ1j ; nj , φ1)}+ pr(H2)Bin(njλ2j − 1; nj , φ2)



Optimal interval boundaries

Assuming the non-informative prior that the current dose isequally likely to be below, above or equal to the MTD, theoptimal dose escalation/deescalation boundaries thatminimize decision error are given by

λe ≡ λ1j = log(

1− φ1

1− φ

)/log

(φ(1− φ1)

φ1(1− φ)

)λd ≡ λ2j = log

(1− φ1− φ2

)/log

(φ2(1− φ)

φ(1− φ2)

).

The optimal escalation/deescalation boundaries areindependent of nj and j !!This makes BOIN extremely simple because the samepair of escalation/de-escalation boundaries can be usedthroughout of the trial.



Flowchart of the BOIN design




Statistical properties of the BOIN

CoherenceThe BOIN design is (long-memory) coherent in the sense thatthe design will never escalate the dose when the observedtoxicity rate pj at the current dose is higher than the targettoxicity rate φ; and will never deescalate the dose when theobserved toxicity rate pj at the current dose is lower than thetarget toxicity rate φ

Example: suppose target toxicity rate = 30%, if 1/3 hastoxicity, the BOIN design will never escalate dose; if 0/3has toxicity, the design will never deescalate dose.

ConsistenceUnder the BOIN design, dose allocation and selection convergeto the target dose.



Selection of the MTD

At the end of the trial, based on all observed data, weselect as the MTD dose j∗, whose isotonic estimate oftoxicity rate pj∗ is closest to φ;For patient safety, we impose the following doseelimination rule when implementing the BOIN design

If pr(pj > φ|mj ,nj) > 0.95 and nj ≥ 3, dose levels j and

higher are eliminated from the trial, and the trial is terminated

if the first dose level is eliminated,

where pr(pj > φ|mj ,nj) can be evaluated based on abeta-binomial model.



BOIN drug-combination design

The BOIN design has been extended to handledrug-combination trials to find a single MTD (Lin and Yin,2016) or the MTD contour (Zhang and Yuan, 2016).The BOIN drug-combination designs make the decision ofdose escalation/de-escalation based on the same rule asthe single-agent BOIN design described previously, thusare easy to implement and possess desirable statisticalproperties (Yuan and Zhang, 2017).



Simulation

6 doses, sample size = 36, target φ = 0.2 or 0.3.Considered 1000 does-toxicity scenarios randomlygenerated using the pseudo-uniform algorithm (Clertantand O’Quigley, 2017)Simulated 2000 trials under each of the 1000 scenariosCompared the BOIN to CRM. It is known that the CRM hasgood performance close to the theoretical optimal bound



Dose-toxicity scenarios

1 2 3 4 5 6

0.0

0.2

0.4

0.6

0.8

1.0

(a)

Dose Level

Toxi

city

pro

babi

lity

1 2 3 4 5 60.

00.

20.

40.

60.

81.

0

(b)

Dose Level

Toxi

city

pro

babi

lity

Figure: Panel (a) shows 50 randomly selected dose-toxicity curves,and panel (b) shows the distribution of the toxicity probabilities bydose level from the 1000 scenarios with 6 dose levels.



Percentage of correct selection (PCS)

Difference between BOIN and CRM

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φ=0.20 φ=0.30

−40

−20

020

40

BOIN−CRM in Percentage of correct selection

Per

cent

age

of c

orre

ct s

elec

tion

(%)

(a) Percentage of correct selectionof the target

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φ=0.20 φ=0.30−

40−

200

2040

BOIN−CRM in PCS within 5%

PC

S w

ithin

5%

(%

)

(b) Percentage of correct selectionwithin 5% of the target



Patient allocation


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φ=0.20 φ=0.30

−20

−10

010

20

BOIN−CRM in Percentage of patients treated at MTD

Per

cent

age

of p

atie

nts

trea

ted

at M

TD

(%

)

(c) Number of patients allocated tothe target dose

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●

φ=0.20 φ=0.30−

20−

100

1020

BOIN−CRM in Percentage of patients treated at doses within 5% of target

Per

cent

age

of p

atie

nts

trea

ted

at d

oses

with

in 5

% o

f tar

get

(d) Number of patients allocated toto the doses within 5% of the target



Overdose control


(e) Number of patients allocated tothe doses above the MTD

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φ=0.20 φ=0.30−

50

510

BOIN−CRM in Risk of overdosing 80%

Ris

k of

ove

rdos

ing

80%

(%

)

(f) The probability of allocating>80% patients to the doses abovethe MTD



Software

Windows desktop program freely available at MDAnderson Biostatistics software download websitehttps://biostatistics.mdanderson.org/softwaredownload/SingleSoftware.aspx?Software_Id=99

Web applications at http://www.trialdesign.orgR package "BOIN" available at CRAN


https://biostatistics.mdanderson.org/softwaredownload/SingleSoftware.aspx?Software_Id=99



http://www.trialdesign.org


Software for novel trial designs



BOIN Desktop Program



BOIN Desktop Program: Combination Trials



BOIN Desktop Program



Web App

http://www.trialdesign.orgAn integrated platform for designing clinical trials


http://www.trialdesign.org


Summary

BOIN provides a novel platform to design phase Isingle-agent and drug combination clinical trials.BOIN is extremely simple to implement and yields goodperformance comparable to more complicatedmodel-based designs.Windows desktop program, Web App and R package arefreely available to implement the design.



Reference

Liu S. and Yuan Y. (2015) Bayesian Optimal Interval Designs for Phase I ClinicalTrials, Journal of the Royal Statistical Society: Series C, 64, 507-523.

Yuan Y., Hess, K., Hilsenbeck S.G. and Gilbert M.R. (2016) Bayesian OptimalInterval Design: A Simple and Well-performing Design for Phase I OncologyTrials, Clinical Cancer Research, 22, 4291-4301.

Lin R. and Yin G. (2016) Bayesian Optimal Interval Designs for Dose Finding inDrug-combination Trials, Statistical Methods in Medical Research, in press

Zhang, L. and Yuan, Y. (2016) A Practical Bayesian Design to Identify theMaximum Tolerated Dose Contour for Drug Combination Trials. Statistics inMedicine, 35, 4924-4936.

Yuan, Y. and Zhang, L. (2017) Designing Early-Phase Drug Combination Trials.Handbook of Methods for Designing, Monitoring, and Analyzing Dose FindingTrials, edited by O’Quigley J., Iasonos, A and Bornkamp, B., Chapter 6,p109-p126.



Thank you !


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