艾昆緯-IQVIA試用設(shè)計器的應(yīng)計建模和自適應(yīng)試用監(jiān)控（英）-2023

WhitePaperAccrual

Modeling

AndAdaptive

Trial

MonitoringWith

IQV

IA

Trial

DesignerIVETA

JAN?IGOVá,MSc,

PhD,ComputationalScientist,

IQVIAERIC

GROVES,MD,PhD,Vice

PresidentofStrategicDrug

DevelopmentforR&D

Solutions,

IQVIATable

of

contentsAbstract12IntroductionIQVIA

Trial

Designer3Dose-escalation3Adaptive

group-sequential

designsSpendingfunctions44Samplesizere-estimation5AccrualmodellingandtrialmonitoringTechnicalspeci?cations56Case

study:AdaptivedesignwithaccrualmonitoringSpendingfunction

approachEarly

stoppingfore?cacy777Early

stoppingforfutility9Samplesizere-estimation

approachModellingaccrual91010111215151516ScenarioI:

Direct

accrualcalculationvs

simulationresultsScenarioII:

MultiplesitesScenarioIII:

Piece-wise

recruitment

rates-patientaccrualmonitoringScenarioIV:

Piece-wise

hazardrates-events

accrualmonitoringConclusionAcknowledgementsReferencesAbstractAdaptive

clinicaltrialdesignscan

be

used

toaddressthe

issueofe?ect

sizenotbeingwellde?ned

beforethe

trialfornew

therapeutics.

When

these

types

oftrialdesignsarecombinedwith

modelsandsimulationsfortheaccrualprocess,

it

ispossibletopredict

thedevelopmentofrecruitment

andendpointcollectionandadjust

strategy

based

oninterimanalysisresults.To

showcasethe

group-sequential

moduleandthe

use

ofaccrualsimulations,inthispaperweconsideranexamplewith

adaptivedesignwithtime-to-event

endpointandthe

underlying

issues.The

accrualmoduleincludesanovelapproachtoaccrualsimulationsonvariouslevelsofgranularitythatareuseful

inthe

designphaseaswellasfortrialmonitoringandadaptation.Wedescribe

IQVIA

TrialDesigner(ITD),

amoderncomplexuser-friendlyweb-based

system

thato?ersabroadrangeofsuchdesignoptions,statisticalmodelsandsimulationsthatstatisticians

can

use

forfast

exploration

anddevelopmentofboth

establishedandnoveltrialdesigns.Moreover,ITD

facilitatescollaborationamongmultipleusers

andstreamlinesthe

trialdesignprocess.Atwin

paperDose-?ndingin

earlyclinicaltrialswithIQVIA

Trial

Designerisalsoavailable.

|

1Introductionbut

still

needed

tocalculatethe

appropriatesamplesize.This

istheminimumsamplesizerequiredtohaveanacceptable(pre-de?ned)

chanceofachievingstatisticalsignificanceforaproposedstudy.Inaclinicaltrial,the

nullhypothesisstates

(inthesimplestcase)thatthe

treatmentarm

isnodi?erentfromthe

controlarm.

The

alternative

hypothesisassumesatreatmentdi?erencebetween

thetwo

armsandso

if

therearesu?cientdata

toreject

thenullhypothesis,

we

conclude

that

the

treatment

is

e?ective.Thereareafewapproachesforhowadaptivegroupsequentialtrialdesigns(GSDs)can

addresstheissueofnothavingenoughinformation,i.e.,havingonlyassumptionsandestimates

ofthee?ect

size(andothernuisanceparameters),Figure1.E?ect

sizeisthe

magnitudeofthealternativehypothesistreatmentdi?erence.Often,

especiallyfornewtreatments,

it

isnotwellde?ned

priortothetrial,Figure1.

Approachestotakewhenthee?ect

sizeisnotwellde?nedatthebeginningoftheclinicaltrialConservativeStop

early(DesignalargetrialtoensureStopfore?cacynecessarystatisticalpowerwithoptiontostopearlyatIA)forfutilityAgileContinue(Startsmall,ifIAresults

arepromising,performsamplesizereestimationandcontinue)recalculatetheneededsamplesizetoachievethedesiredpowerEnrichmentFocus(Strategicallytargetaspeci?csubgroupafterIAreultsare

in)targetaspeci?csub-populationthatbene?tsfromtreatment2

|

Accrual

Modeling

And

Adaptive

TrialMonitoring

With

IQVIA

TrialDesignerfromthestart

ofthetrialorthatthe

recruitment

rateisconstant

overtime.These

accrualassumptionsmayimpact

the

statistical

resolutionofvariousdesigns,especiallytime-to-event

designs.?

Conservative:

Start

big,designalargetrialtoensurethe

necessary

statistical

power,but

includeaninterimanalysis(IA)

partway

throughwith

the

optiontostop

early.The

early

stoppingcan

happenforoneoftwo

reasons:Togetherthismeansthatwhilethe

meanrecruitmentperiod

length

andmeantriallength

mightbe

asdesigned,the

actual

accrualscenariomightbesigni?cantly

di?erentandmightrequirewaitinglongerforenoughevents

tooccurduetopatientsbeingrecruited

moreslowly

at

the

trialbeginning.Additionally,longeraccrualtimeincreasesthe

durationofobservation

ofpatients

accruedearly

inthe

trial,increasingtheirchancetocontributeevents.?

for

e?cacy

-

if

the

results

at

the

interimanalysis

show

statistically

signi?cant

bene?tsto

the

patients17?

forfutility

-if

the

results

at

theinterimanalysisdonotshowsu?cientdi?erencebetween

thetreatmentandthe

controlarm

(orif

toomanyadverse

e?ects

areobserved)5?

Agile:Start

small,designatrialthatwouldnothavesu?cientstatistical

powertodemonstrate

thee?ect,but

includeaninterimanalysis

partway

through.Ifthe

IA

results

arepromising,perform

samplesizere-estimation

todeterminethe

needed

samplesizetoachievethedesiredpowerwith

theupdatedknowledge

ofthe

e?ect

sizeandcontinuethetrialInthispaperwedescribeIQVIA

TrialDesignerandfocusonthe

groupsequentialmoduleandaccrualmodelingtodemonstrate

someofthe

challengesofadaptivedesignandaccrualandhowmodelingandsimulationscan

helpovercomethem.IQVIA

Trial

Designer?

Enrichment:Ifit

isdeterminedat

theinterimanalysisthatthe

e?ect

sizeissmall,but

thesubjectsthatrespondedtothetreatmentsharecertaincharacteristics,

thismaybe

because

thetreatmentisappropriateonly

forasub-population,

perhapsaspeci?c

variantofthedisease.Insuchcase

it

isreasonabletorecruit

morepatients

fromthissub-population,i.e.,enrichthesample.MachinelearningtoolssuchasSOMS

(SubpopulationOptimizationandModellingSolutions)10

can

be

used

toidentify

thecommoncharacteristics

byprocessingtheavailabledata

from

the

?rst

stage

ofthetrialIQVIA

Trial

Designer

(ITD)

is

a

modern

complex

user-11friendly

web-based

system

that

o?ers

a

broad

range

ofdesign

options,

statistical

models

and

simulations

thatstatisticians

can

use

for

fast

exploration

and

developmentof

novel

trial

designs.

Additionally,

it

is

set

up

to

facilitatecollaboration

among

multiple

users/stakeholders.

Ourcompetitors

include

nQuery

and

East

.

In

the

following,204we

brie?y

describe

ITD

capabilities.Dose-escalationWithin

ITD,

the

availabledose-escalation

methodsinclude3+3

(asaspecialcase

ofm+n),i3+3,BOIN,andmTPI-2for?ndingthe

maximumtolerateddose.For?ndingthe

recommendedphaseII

dosewhen

lookingat

both

toxicity

ande?cacy

thereisPRINTE

andincustom

sessionBOIN-based

simpletwo-parametermethod.

Moredetails

about

these

methods,

theircomparisonand

a

case

study

that

highlights

thechallengesand

needforsimulations

indose-findingisavailable

in

a

twinpaperDose-

indinginearlyclinicalInallthese

approaches,data

aregatheredovertime,andstatistical

comparisonsandsubsequentinformeddecisionsaremadewhen

only

portions

ofthe

datahavebeen

collected.

This

?exibility

isoneofthemainadvantages

ofGSDs

over?xeddesigns.However,therearestill

factors

thatare?xedinthese

adaptivedesignsthatmaymakethedesignsinconsistentwithoperationalreality.trialswith

IQVIATrialDesigner

.13For

example,the

GSDpackagemaymakeincorrectassumptionsabout

the

accrualrate.One

mightassumethatallrecruitment

sitesareenrollingpatients

right

|

3Adaptive

group-sequential

designsthe

interimanalyses

andat

?nalstage,

i.e.,whetherlargeramountof

(β)shouldbe

spentat

early

interimanalyses

orat

?nalstage.

The

di?erenttypes

ofspendingfunctions

supported

inthe

applicationare:Inthe

groupsequentialmoduleinITD,

theusercanselect

fromboth

?xedandadaptivedesignswithendpoints:?

Lan-DeMets

approximationtoO’Brien-Flemingfunction

(OF)15?

di?erenceinmeans-forcontinuousvariables,e.g.,blood

pressure,insulinlevels,

etc.?

Lan-DeMets

approximationtoPocockfunction

(PK)15?

Hwang-Shih-DeCani

Gammafunction

family(HS)9?

Haybittle-Peto

boundaries(HP)8?

binomialproportions

(rawdi?erence,odds

ratio,relative

risk)-forbinary

variables,e.g.,proportion

ofpeoplewho

gotinfected,

arefree

ofseizures,etc.?

time-to-event

-forwaitinguntilcertain

eventhappens,e.g.,survival

analysisinoncology,asthmaattacks,

etc.?

piece-wise

linear

user-speci?ed

spending

function

(US)Itmaybe

appropriatetoconsiderdi?erentspendingfunctions

fore?cacy

andforfutility.

As

trialdesigners,weshouldbe

conservative

about

stoppingearlyfore?cacy,

sincewewanttobe

convincedthatthetreatmentindeedworks,

but

wemaybe

morewillingtoacceptanerrorwhen

consideringstoppingthetrialforfutility.There

are

options

to

demonstrate

superiority,

non-inferiority

or

equivalence

of

the

compared

treatments.The

user

can

also

select

if

they

want

to

test

a

one-sidedhypothesis

(to

demonstrate

treatment

over

placebo),two-sided

hypothesis

(when

comparing

two

treatments)or

one-sided

e?cacy

with

non-binding

futility.Another

reasontouse

conservative

spendingfunctioniswhen

the

only

purpose

oftheinterimanalysisistore-estimate

the

samplesize,but

nottostop

early.Insuchcase,

wewantonly

avery

smallportion

oftype

Ierrortobe

spentat

the

interimanalysisandleavemostofit

availableforthe

?nalanalysis.For

the

situation

with

a

binomial

proportions

endpointand

asingle

treatment

arm,

there

is

also

a

simplegroup

sequential

design

with

two

stages

—

Simon’sdesign

—

available

inthe

custom

module.

This

design19minimizesthe

sample

sizeand

uses

a

single

interimanalysis

todetermine

whether

the

trial

should

bestopped

for

futility

or

continue

tothe

second

stage.Simon

Two

stage

designs

are

common

in

phase

Ibbasket

oncology

studies.?

The

OF

function

spendsvery

little

early

andkeepsmoreforthe

?nallook.

Itmightbe

moresuitable

forearly

terminationtoreject

H

infavorofH

(e?cacy)01because

it

reducestheprobability

ofanunfortunatesituationthatcouldpotentiallyhappeninagroupsequentialtrialwhen

onewouldget

ane?ect

sizeatthe

endofthestudy

thatwouldbe

signi?cantif

thiswasa?xeddesignbut

it

isnotbecause

oftheerrorspendingat

the

interimanalysis.

The

boundariesspeci?ed

bythe

OF

function

decreasewith

thenumberoflooks.SPENDINGFUNCTIONSFor

allendpoints,

the

ITD

groupsequentialmoduleo?ers

amultipleinterimanalyses

feature,but

theuserneeds

tobe

awarethatrepeatedhypothesis

testingingroupsequentialdesigns(onceat

eachinterimanalysis)ofaccumulateddata

increasesthe

type

Ierrorrate.Therefore,e?cacy

boundary

points

arechoseninadvanceusingspendingfunctions

thatensurethatthe

overallsigni?canceleveldoes

notexceedthepre-speci?ed

signi?cancelevel

.?

The

PKfunction

isless

conservative

with

the

earlyspending,moresuitable

forearly

terminationwhenwearenotrejecting

H

(futility)

andmoree?cient0Usingdi?erentspendingfunctions,

theusercanspecify

how

(andtype

II

errorrateβincase

ofconsideringstoppingforfutility)

isspentat

eachofoverawider

set

ofsituations.The

boundariesinthiscase

stay

almost

constant.4

|

Accrual

Modeling

And

Adaptive

TrialMonitoring

With

IQVIA

TrialDesigner?

The

familyofHS

functions

parameterizedbyaparameterγallowsforspendingfunctions

thatareless

conservative

thanOF

but

notasaggressiveasPK.

The

morenegative

thevaluesofγarethemoreconservative

spendingfunctions

they

yield,

with

γ=?4

resemblingthe

OF

function;

γ=0spendsthetype

Ierrorlinearlyandγ=1producesaspendingfunction

similartoPK.?

isonly

used

at

the

penultimatelook?

conventionalWaldstatistic

maythenbe

usedwithout

in?atingthe

type

Ierrorif

theconditionalpowerat

the

interimisabove50%?

Cui-Hung-Wang(CHW)

method3?can

be

implementedat

anylooktocontrol

in?ation,thismethod

weighsthe?

HPboundariesareafamilyofp-value

boundariesoften

used

forblind-breaking

samplesizere-estimation.

These

boundariespre-specify

asmall(same)p-value

asthestoppingcriterion

at

theinterimanalyses.

The

?nalp-value

forevaluatingstatistical

signi?canceat

thelast

lookisthencalculatedinsuchawaythattheoveralltype

Ierroristhepre-speci?ed

.?independentWaldstatistics

obtained

at

eachlooktodeterminethe

statistical

signi?cancewith

pre-speci?ed

weights.

Havingdi?erentsets

ofpatientsweighteddi?erently

issometimescontroversialamonginvestigators

notfamiliarwith

the

technicaldetails

ofadaptivemethodology

andissometimesthe

reasonwhy

the

CDLapproachispreferredoverCHW?

An

ITD

usercan

alsospecify

theirown

spendingfunction

byde?ningtheamountof

tobe

spentatvarioustimepoints.

These

valuesarethenlinearlyinterpolatedtoobtain

thespendingfunction

thatcanthenbe

used

when

trying

toreplicateand/ormodifyapreviously

publishedspendingfunction,

e.g.,atruncated

OF.InITD,

both

ofthese

methods

only

recommendincreasesinsample

size(if

needed),

notdecreases—thisisinaccordancewith

the

USFood

andDrugAdministrationguidanceonadaptive

design

.6Accrual

modelling

and

trial

monitoringITD

o?ers

the

accrual

module

to

model

and

simulatethe

recruitment

period

and

also

monitor

the

accrualprogress

of

the

trial.

The

group

sequential

designmodule

and

the

accrual

simulations

give

the

sameresults

on

average,

but

the

accrual

module

o?ers

greaterinsight

into

various

options

that

do

not

?t

the

standardgroup

sequential

design.

These

insights

potentially

canbe

used

to

modify

the

design

assumptions.The

spending

functions

specify

the

nominal

critical

pointsz

and

corresponding

nominal

p-values

1

—

Φ(z)

(in

one-sided

case)

which

if

crossed,

justify

the

early

termination.SAMPLE

SIZE

RE-ESTIMATIONTo

address

the

issue

of

not

having

enough

informationabout

the

e?ect

size

when

performing

the

initial

samplesize

calculation

for

the

trial,

the

ITD

system

enablesboth

blind-breaking

and

blind-preserving

sample

sizere-estimation.

The

blind-preserving

approach

uses

aFor

example,

some

sites

may

not

be

ready

to

openat

trial

start

and

open

later

so

that

the

recruitmentrate

ramps

up

gradually,

which

means

longer

wait

toobserve

the

needed

number

of

events.

These

types

ofconclusions

can

then

be

added

back

into

the

trial

design.so-called

internal

pilot

study

that

typically

updates7the

information

about

variance.

The

blind-breakingapproach

is

available

using

two

methods:ITD

can

helpanswer

the

questions

forhowtostructureaccrualtoassurethatthe

trialwillhaveenoughobserved

events.

This

mayinvolveplanningtoopenmoresites,

oralternatively

toplantoextend

thedurationofobservation

forlongertimethancalculatedfrom

theoriginalGS

design.?

Chen-DeMets-Lan

method

(CDL)2,16?

alsoknown

asthe

PromisingZoneapproach?

calculatesconditionalpower—the

probability

thatwewouldexpect

to?ndsigni?cantp-value

at

the?nallookgiven

what

happenedso

far

|

5The

accrualmodelingforGSDs

isanextension

oftheTechnical

speci?cationsAnisimovapproach.Itallowsthe

usertospecify

the1ITD

isauser-friendlyweb-based

system

relying

onthe

react,

Node.js,nexosandDockertechnologiesforsecureandresponsivedesignandthe

terraforminfrastructure

forcontinuousdeployment.

The

designismodular,?exible

andsupports

integrationofnew

algorithms.

These

aretypically

?rst

tested

inacustom

module,whichcontainsasimpleintegrateddevelopmentenvironment.groupsofsitesandnumberofsitesineachgroup(thegroupscan

havesizeone,thusallowingmodelingonthe

levelofindividual

sites)andtheiropening/closingcharacteristics

andrecruitment

parameters.The

usercan

alsospecify

non-uniform

recruitmentratesoverseveralrecruitment

periods

andforthetime-to-event

endpointalsopiece-wise

hazardrates.Both

piece-wise

recruitment

ratesandpiece-wisehazardratescan

vary

acrossthe

groupsofsites.The

statistical

methods

and

algorithms

areimplemented

in

R18

using

available

open-source

librarieswhere

applicable.

The

calculations

and

simulationsare

performed

using

Amazon

Web

Services

and

theapplication

can

support

10,000

concurrent

requests.6

|

Accrual

Modeling

And

Adaptive

TrialMonitoring

With

IQVIA

TrialDesignerCasestudy:

Adaptivedesignwithaccrual

monitoringthe

trial.Inthisagilecase,

smallerfunds

areneededupfront,

however,the

sponsorneeds

tobe

preparedtomakeareal-time

commitmentforadditionalresourcesonthe

recommendationofDMC

forthe

study

tocontinue.Fromthispointofview,samplesizere-estimation

ismore?exible

thanthe

errorspendingapproach.The

maingoalofstatistical

analysisofclinicaltrialdataistogeneralizefrom

thesamplepopulationtothewhole

population.This

generalizationismorelikelytobe

accurateif

the

samplesizeislarge,howeverinpractice

thereare?nancialandtimeconstraintslimitingthe

samplesize.Also,

thereareethicalconsiderations,i.e.,wedonotwanttounnecessarilyexpose

peopletotreatmentthatmightproveharmfulorine?ective,

thereforethegoalistohavejustsu?cientsamplesize.However,havingtheminimalsamplesizenecessary

reliesontheassumptionsaboutthe

e?ect

size.Traditionally,stoppingforfutility

hasbeen

morecommonlyused

(i.e.,futility-only

designs),butstoppingforearly

e?cacy

isextremely

valuablewhen

appropriatelyused.

Also

notethatsometimesanon-binding

futility

boundisused,

e.g.,sponsormightwanttocontinuethe

trialanyway

forsafetyrecommendationsevenif

thefutility

boundaryiscrossed.Adaptive

trials

can

makecourse-corrections

basedon

all

the

information

as

it

becomes

available

in

thetrial.

As

a

result,

adaptive

trials

can

makebetter

useof

resources

and

allow

early

stopping

if

the

results

areeither

very

promising

or

unpromising.

The

two

di?erentapproaches

(conservative

vs

agile)

to

handling

theuncertainty

in

the

actual

value

of

the

e?ect

size

beforethe

trial

require

two

di?erent

management

strategies.Spending

function

approachInthissection

wedemonstrate

the

valueofanIA

bystoppingfore?cacy

andstoppingforfutility.EARLYSTOPPINGFOREFFICACYConsider

a

phase

III

study

with

the

overall

survival(time-to-event)

endpoint

with

the

true

but

unknownhazard

ratio

HR

=

0.64.

First,

we

consider

a

conservativeTscenario,

in

which

the

hazard

ratio

under

the

alternativeIn

the

conservative

scenario,

when

one

wants

tobe

able

todetect

the

minimalclinically

relevanttherapeutic

e?ect,

the

resulting

sample

sizecan

be

verylarge.

The

study

might

be

overpowered

if

the

actuale?ect

is

higher.The

sponsor

needs

toallocate

andreserve

signi?cant

funds

and

operational

resourcesinadvance

toprepare

for

a

study

with

a

large

samplesize.However,if

it

becomes

clear

during

the

interimanalysis

that

the

e?ect

is

not

there,

the

study

maybeterminated

early.hypothesis

is

H

:

HR

=

0.7and

one

interim

analysis

isplanned

when

50%

of

events

are

observed.

The

inputparameters

are

summarized

in

Table

1.1As

analternative

(agile)approach,if

thesponsorisunableorunwillingtomakealargesamplesizecommitmentup-front

based

onthelimitedpriordata

availableonthe

new

compound,anexpected(optimistic)e?ect

can

be

used

forthe

calculationofthe

samplesize.This

results

inasmallerstudy

with

theexpectation

ofsamplesizere-estimation

at

theinterimanalysis.

An

independentdata

monitoringcommittee(DMC)

willbe

reviewing

theblindbreakingorblindpreserving

interimdata

at

thepre-speci?ed

pointof

|

7Table

1.

Inputparametersforadaptivedesignwithoneinterimanalysis.PARAMETER

NAMEVALUEendpointhazard

ratio

under

H0hazard

ratio

under

H1type

Ierror

(

)time-to-event

(overallsurvival)10.70.025power

(1

?β)0.9proportion

of

events

at

interim

analysisrandomization

ratioupper

(

)spending0.51OF/PKmedian

survival

timemedian

censoring

timeminimumfollow-up

durationtrial

duration12

months

(controlgroup),14

months

(overall)240

months12

months24

monthsThe

samplesizesfor?xedandadaptivedesignsarecontinueuntilthe

?nallookrequiresmoresubjects

andmoreevents.

This

isthetrade-o?

tobe

madeforthepossibility

thatthe

trialmayendearly.calculatedusingthe

methodologiesdescribed

in

.The14results

aresummarizedinTables2and3.

Wesee

thatcomparedtoa?xeddesign,aGS

designthatneeds

toTable

2.

SamplesizeandneedednumberofeventsassumingHR=0.7.TRIAL

DURATION#SUBJECTS#EVENTS(MONTHS)GS

design,

at

?nallook,

OFGS

design,

at

?nallook,

PKFixed

design2459065258733236733024248

|

Accrual

Modeling

And

Adaptive

TrialMonitoring

With

IQVIA

TrialDesignerTable3.

Group

sequential

design

with

one

interimanalysis

using

a

conservative

spending

function

(Lan-DeMetsapproximation

to

O’Brien-Fleming)

and

anaggressive

spending

function

(Lan-DeMets

approximation

to

Pocock).O'BRIEN-FLEMING

SPENDINGPOCOCK

SPENDINGLOOKPROP.(IF)TIME##NOM.PVALUE##EVENTSNOM.PVALUE(MONTHS)SUBJECTSEVENTSSUBJECTS10.5113.2245905901660.00150.02456521840.0155Final3326523670.0139In

case

of

the

OF

spending

function,

the

di?erence

isin

these

n

patients,

the

study

is

stopped.

Otherwise,1small

(590

vs

587

subjects

and

332

vs

330

events)

but

itis

very

unlikely

that

the

trial

would

stop

for

e?cacy

atthe

interim

analysis

at

13.2months

because

the

nominalprobability

is

very

small

p

=

0.0015(z-score

2.96).n

?

n

additional

patients

are

accrued

for

a

total

of1n.

The

nullhypothesis

is

rejected

if

r

+1

or

more2responses

are

observed

inn.

This

design

yields

a

pre-speci?ed

type

I

error

rate

and

pre-speci?ed

powerwhen

the

true

response

rate

is

p.1Incase

ofthe

PKspendingfunction,

thedi?erenceislarger(652vs

587

subjects

and367vs

330

events),but

thepossibility

ofstoppingearly

ismuchmorelikely,sincetheinterimresults

willbe

evaluatedat

asigni?cancelevel0.0155,i.e.,z-score2.157.As

an

alternative

approach,

if

we

wanted

to

have

acontrol

over

the

type

II

error

spending,

possibly

overmore

than

one

interim

analysis,

we

can

consider

adesign

with

Haybittle-Peto

boundary

for

e?cacy

withvery

small

p-value

(e.g.,p

=

0.000001,

so

virtually

noin?ation

at

the

?nal

analysis)

and

PKfunction

to

controlthe

β

spending.

With

HR

=

0.7we

get

the

z

boundaryvalue

for

futility

0.92which

corresponds

to

0.062

type

IIerror

spent

(outof

0.1)

at

the

interim

analysis.

Note

thatin

this

case,

the

needed

number

of

events

is

190at

thetime

of

interim

(and

380

at

the

time

of

?nal

analysis).Wedo

not

expect

stopping

for

e?cacy,

but

we

have

theoption

to

stop

for

futility.EARLYSTOPPINGFORFUTILITYStopping

early

for

futility

is

of

interest

especially

inphase

II