Description

The Direct Assignment Option as a Modular Design Component: An Example for the Setting of Two Predefined Subgroups

All materials on our website are shared by users. If you have any questions about copyright issues, please report us to resolve them. We are always happy to assist you.

Related Documents

Share

Transcript

Research Article
The Direct Assignment Option as a Modular Design Component: An Example for the Setting of Two Predefined Subgroups
Ming-Wen An,
1
Xin Lu,
2
Daniel J. Sargent,
3
and Sumithra J. Mandrekar
3
Department of Mathematics, Vassar College, Raymond Avenue, Poughkeepsie, NY , USA
Emory University, Atlanta, GA , USA
Mayo Clinic, Rochester, MN , USA
Correspondence should be addressed to Ming-Wen An; mian@vassar.eduReceived November ; Revised December ; Accepted December Academic Editor: Maria N. D. S. CordeiroCopyright © Ming-Wen An et al. Tis is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the srcinal work is properly cited.
Background
. A phase II design with an option or direct assignment (stop randomization and assign all patients to experimentaltreatment based on interim analysis, IA) or a predened subgroup was previously proposed. Here, we illustrate the modularity o the direct assignment option by applying it to the setting o two predened subgroups and testing or separate subgroup maineﬀects.
Methods
. We power the -subgroup direct assignment option design with IA (DAD-) to test or separate subgroup maineﬀects, with assessment o power to detect an interaction in a post-hoc test. Simulations assessed the statistical properties o thisdesign compared to the -subgroup balanced randomized design with IA, BRD-. Diﬀerent response rates or treatment/controlin subgroup (./.) and in subgroup (./., ./.) were considered.
Results
. Te -subgroup DAD- preserves powerand type I error rate compared to the -subgroup BRD-, while exhibiting reasonable power in a post-hoc test or interaction.
Conclusion
. Te direct assignment option is a exible design component that can be incorporated into broader design rameworks,while maintaining desirable statistical properties, clinical appeal, and logistical simplicity.
1. Introduction
Te primary goal o phase II clinical trials is to betterunderstand a treatment’s eﬃcacy and saety prole to inorma phase III go/no-go decision. Te phase II design withoption or direct assignment (i.e., stop randomization andassign all patients to the experimental arm based on one ortwo interim analyses (IA)) or a single predened subgroupwas previously proposed []. In theory, such a design canbe readily incorporated into existing and broader designrameworks.Specically,theoptionordirectassignmentcanbe integrated into any design with an IA where a decisionmust be made or how to allocate treatment to patients(typically the decision is between continuing to randomizepatients to one o the treatments and stopping the trial dueto either eﬃcacy or utility). In this paper, we present thedirect assignment option as a modular design component by applying it to the setting o two predened subgroups.In some therapeutic settings, we may expect treatmentheterogeneity across subpopulations identied by some ac-tor, or example, biomarker status. Specically, the treatmentmay be eﬀective in one subgroup but ineﬀective in another(qualitative treatment-subgroup interaction), or the treat-ment may be eﬀective in both subgroups but with diﬀerentmagnitude (quantitative treatment-subgroup interaction). Ineither case, primary interest may be in both subgroups, andthe design should enroll patients in both subgroups intoa single trial. Such a design could allow or prospectiveplanning o a design to identiy predictive markers. Forexample, KRAS mutations were identied in a retrospectiveanalysis to be predictive or overall survival response tocetuximab in colon cancer []. We could imagine havinginstead proposed a prospective phase II direct assignmentdesignenrollingtwosubgroupstoenabletheKRASdiscovery in phase II. Alternatively in some settings, primary interestmay only be in one o the subgroups. However, there may
Hindawi Publishing CorporationComputational and Mathematical Methods in MedicineVolume 2015, Article ID 210817, 6 pageshttp://dx.doi.org/10.1155/2015/210817
Computational and Mathematical Methods in Medicinebesecondaryinterestinthesecondsubgroup,anddependingon available resources and the clinical setting, one may wishto enroll the second subgroup as well. One design option orthis setting is a stratied balanced randomized design. Tisdesign could be readily modied to incorporate and enjoy thebenetsothedirectassignmentoptionintroducedinAnet al. [].In this paper thereore, we consider a design with directassignment option or the setting o two predened sub-groups o patients. Te proposed design is a -subgroupdirect assignment design with IA (DAD-), enrolling thesubgroupsinparallel,eachusingaDAD-withtheoptionstostop early or utility, continue with randomization, continuewith direct assignment, or stop early or eﬃcacy at IA(able ). We power the design to test or separate subgrouptreatment eﬀects, where the direction o treatment eﬀect isprespecied,andalsoincludeapost-hocassessmentopowerto detect a treatment-subgroup interaction. We compare the-subgroup DAD- with a -subgroup balanced randomizeddesign with IA (BRD-), with options to stop early or util-ity, continue with randomization, or stop early or eﬃcacy atIA. We perorm a simulation study to examine the statisticalproperties o the designs, under a variety o response ratesettings. Finally, we discuss a planning exercise or enrollinga second subgroup, when primary interest is only in onesubgroup.
2. Methods
.. When Both Subgroups Are of Primary Interest.
Weconsider a binary outcome, such as response, as the trialendpoint, and two patient subgroups, which we call M+ andM
−
. Since we are interested in separate treatment eﬀects inthe two subgroups, we consider two independent primary hypotheses. Let
Δ
+
and
Δ
−
denote the ratio o response ratesor treated versus control groups (i.e., treatment eﬀect) inthe M+ and M
−
subgroups, respectively. We assume that
Δ
+
is positive (i.e., treatment is benecial) and assume that
Δ
−
is specied a priori as either positive or negative by theinvestigator based on expert knowledge. Tus in the M+subgroup, we are interested in the one-sided test H
0+
:
Δ
+
=1
versus H
1+
:
Δ
+
> 1
; in the M
−
subgroup, we are alsointerestedinaone-sidedtestH
0−
:
Δ
−
= 1
versusH
1−
:
Δ
−
> 1
or H
0−
:
Δ
−
= 1
versus H
1−
:
Δ
−
< 1
, depending on whether
Δ
−
isspeciedaprioritobegreaterorlessthan.Wemakenoassumption on the relationship o treatment eﬀect betweenthe two subgroups. Specically, we do not assume that thetreatment will be benecial in the M
−
subgroup only i it isrst benecial in the M+ subgroup. Since this is the phaseII setting, a treatment-subgroup interaction is typically noto primary interest. However, we include an assessment o power to detect a treatment-subgroup interaction in a post-hoc test: H
0,
Int
:
Δ
+
/Δ
−
= 1
versus H
0,
Int
:
Δ
+
/Δ
−
̸= 1
.We speciy a desired treatment eﬀect size
Δ
, (
= +
or
−
) or each subgroup, an acceptable type I error rate(
; the probability o rejecting the subgroup-specic null,when the null is true), and the desired power to detect thetreatmenteﬀect size
Δ
(i.e.,
1−
,theprobabilityorejectingthe subgroup-specic null, when the alternative
Δ
is true).We assume common
and
, but possibly diﬀerent
Δ
, orthe two subgroups. Sample sizes are calculated separately ineachsubgroup.Specically,wecalculatesamplesizebasedonaone-sided-sampletestorproportionsora-stagedesignwith : randomization, interim analysis, and O’Brien-Fleming stopping rules using EAS sofware, as in theoriginaldesignwithdirectassignmentoption(ordetails,see[]).
Simulation Study
. o understand the statistical properties o the -subgroup direct assignment option design with -IA(DAD-), we conducted a simulation study. For testing thesubgroup main eﬀects, we specied
1 − = 0.80
and
=0.20
, corresponding to widely recommended and acceptedstandards in the phase II setting []. In the M+ subgroup,we considered a control arm response rate o . versusa treatment arm response rate o .. Tat is, we assumethat the treatment is eﬀective in the M+ subgroup (
Δ
+
=2.0
), based on preliminary studies. In the M
−
subgroup, weconsider a control arm response rate o . versus treatmentarm response rates o ., ., and ., reecting possiblescenarios:areversetreatmenteﬀect
(Δ
−
= 0.5
),notreatmenteﬀect (
Δ
−
= 1
), and a treatment benet (
Δ
−
= 2.0
),respectively. Note that, here, a treatment arm response ratein the M
−
subgroup o either . or . corresponds to atreatment-subgroup interaction. Te resulting sample sizecalculations are summarized in able .Wesimulatedtrialsoreachothetwocases(able ).In Case I (no interaction), we consider a treatment eﬀect inboth subgroups (i.e., treatment versus control response rates:. versus ., in both M+ and M
−
); in Case II (interaction),we consider a treatment eﬀect in M+ (treatment versuscontrolresponserates:.versus.)andareversetreatmenteﬀect in M
−
(treatment versus control response rates: . versus .). For each trial, we tested main eﬀects separately in each subgroup and an interaction eﬀect and recorded theresults or testing each o the three independent hypotheses:one-sided tests or main eﬀects—H
0+
:
Δ
+
= 1
versus H
1+
:
Δ
+
> 1
; H
0−
:
Δ
−
= 1
versus H
1−
:
Δ
−
> 1
or H
1−
:
Δ
−
< 1
(depending on the a priori hypothesized treatmenteﬀect)andthetwo-sidedtestoraninteractioneﬀect—H
0,
Int
:
Δ
+
/Δ
−
= 1
versusH
0,
Int
:
Δ
+
/Δ
−
̸= 1
.Forthepost-hoctestorinteraction,weusedaconservative
-levelo.(two-sided)or rejecting the null hypothesis o no interaction. Averagingthese outcomes over the simulated trials, we obtainedestimates o type I error rate and power or each hypothesis.For comparison, we also studied the outcomes under a -subgroupbalancedrandomized(:)designwithIAandnooption or direct assignment (BRD-), based on the O’Brien-Fleming stopping rules.
.. When One Subgroup Is of Primary Interest: ProspectivePlanning Exercise for Enrolling a Second Subgroup.
In somesettings, interest may be only in one subgroup, say M+.However, instead o altogether excluding the other subgroup,M
−
, i resources are available, a design could include the M
−
subgroup (as long as there are no saety or eﬃcacy concerns)by accruing to the M
−
subgroup while the M+ subgroup isaccruing. An exploratory analysis in the M
−
subgroup could
Computational and Mathematical Methods in Medicine
: Options available at interim analysis (IA) in a -subgroup direct assignment design with IA (DAD-) versus a -subgroup balancedrandomized design with IA (BRD-). Te decisions are independently made in each subgroup at the time o IA. Some cells in the BRD-table are intentionally lef blank, to highlight the missing option o direct assignment in this design. Te options in bold are those that areavailable only in the design with direct assignment option.Options at interim analysis (IA)-subgroup direct assignment design with IA (DAD-) -subgroup balanced randomized design with IA (BRD-)M
−
M+ M
−
M+Stop, utility Stop, utility Stop, utility Stop, utility Continue, randomize Continue, randomize
Continue, direct
Stop, eﬃcacy Stop, eﬃcacy Continue, randomizeStop, utility Continue, randomizeStop, utility Continue, randomize Continue, randomize
Continue, direct
Stop, eﬃcacy Stop, eﬃcacy
Continue, directStop, futility Continue, randomizeContinue, directStop, eﬃcacy
Stop, eﬃcacy Stop, utility Stop, eﬃcacy Stop, utility Continue, randomize Continue, randomize
Continue, direct
Stop, eﬃcacy Stop, eﬃcacy : Sample size calculations or -sided
= 0.20
and
1 − = 0.80
, or diﬀerent treatment eﬀects in the two subgroups. RR
trt
is theresponse rate in the treatment group, RR
control
is the response rate in the control group, and RRR
trt
:
control
is the ratio o response rates in thetreatment versus control groups (i.e., treatment eﬀect).Case M+ subgroup M
−
subgroupreatment eﬀect, RRR
trt
:
control
RR
trt
/RR
control
reatment eﬀect, RRR
trt
:
control
RR
trt
/RR
control
I (no interaction) ./. ./. II (interaction) ./. . (i.e., reverse benet) ./.
then yield preliminary indication o treatment eﬀect in theM
−
subgroup.o decide between enrolling M+ patients only andadditionally enrolling the M
−
subgroup as an exploratory companiongroup,aprospectiveplanningsimulationexercisecould be conducted. Since the M
−
subgroup is not o primary interest, it is likely that there is no precise prelimi-nary inormation about the treatment eﬀect in the M
−
sub-group. Instead, one might speciy in the M
−
subgroup theresponse rate in the control arm (RR
control
) to be uniormly distributed over some interval [RR
,
control
,
RR
,
control
] andthe response rate ratio comparing treated versus controlarms (RRR
trt
:
control
) to be uniormly distributed over anotherinterval [RRR
,
trt
:
control
,
RRR
,
trt
:
control
]. I the interval or theRRR
trt
:
control
includes,thensuchaspecicationwouldallow or the treatment to have a negative (RRR
trt
:
control
< 0
),neutral (RRR
trt
:
control
= 0
), or positive (RRR
trt
:
control
> 0
)eﬀect in the M
−
subgroup, thus reecting vague knowledgeaboutthetreatmentactivityintheM
−
subgroup.Itispossiblethen to simulate a trial and record the observed diﬀerencein response rates. Averaging across the simulated trials, onecan obtain a probability o observing a diﬀerence in responserates that exceeds some threshold, say
, that is o clinicalinterest. O course this probability will depend on the samplesize. Since accrual to M
−
will occur while accrual to M+ isopen,thesamplesizeorM
−
willdependontheaccrualratesto both M+ and M
−
and the prevalence o the subgroupsand may not be known in advance. Probabilities that thediﬀerence exceeds
can be generated, under a variety o plausible settings. Te investigator can use the probability distributions as a guide to decide whether to enroll the M
−
subgroup as an exploratory companion group, depending onwhether he or she believes the probability to be suﬃciently high to make enrollment into M
−
worthwhile.As an example o the prospective planning exercise, weconsidered
= 0.15
. Tat is, an observed diﬀerence inresponseratescomparingtreatedversuscontrolo%wouldbe considered clinically relevant. We urther specied thecontrol group response rate to be uniormly distributed over
[0.1,0.3]
and RRR
trt
:
control
to be uniormly distributed over
[0.5,1.5]
. We considered sample sizes o
1,−
= 6
, ,and patients or the rst stage in the M
−
group. Tesecorrespond to M+/M
−
prevalence o
1,+
/6
,
1,+
/16
, and
1,+
/48
, assuming a sample size o
1,+
in the rst stage or
Computational and Mathematical Methods in Medicine
:Simulationstudyresultsbasedonsimulatedtrials.Samplesizeandtreatmenteﬀectsasspeciedin able .Statisticalpropertiesothe-subgroupdirectassignmentoptiondesignwithIA(DAD-)versusa-subgroupbalancedrandomizeddesignwithinterimanalysis(BRD-). One-sided
= 0.20
and
1 − = 0.80
or the subgroup main eﬀects; two-sided
int
= 0.10
or the post-hoc test or an interactioneﬀect.
(a)
Separate subgroup main eﬀectsCaseM+ subgroup M
−
subgroupPower ype I error rate Power ype I error rateDAD- BRD- DAD- BRD- DAD- BRD- DAD- BRD-I (no interaction) . . . . . . . .II (interaction) . . . . . . . .
(b)
Subgroup-treatment interaction eﬀectCase Power ype I error rateDAD- BRD- DAD- BRD-I (no interaction) — — . .II (interaction) . . — —
the M+ group. For each sample size, we simulated trials.We created histograms o the observed treatment diﬀerencesand recorded the proportion o trials where the absoluteobservedtreatmentdiﬀerenceinresponseratesexceeded
=0.15
.
3. Results
.. When Both Subgroups Are of Primary Interest.
Tenominal power and type I error rate are preserved in the -subgroup DAD-, relative to a -subgroup BRD- (able ).In particular, or the M+ group, the power to detect aRRR
trt
:
control
oorDAD-is.%(versus.%oraBRD-), and the type I error rate is .% (versus .% or a BRD-).FortheM
−
group,thepowertodetectaRRR
trt
:
control
o.or the DAD- is .% (versus .% or a BRD-), and thetype I error rate is .% (versus .% or a BRD-).We were also interested in the properties o a post-hoctest or an interaction eﬀect. ype I error rate is preservedat the nominal rate, and power decreases slightly relative tothe nominal rate. Specically, or Case I (no interaction), thetype I error rate is .% or the DAD-, compared with .%or a BRD-. For Case II (interaction), the power to detect aninteractioneﬀectatatwo-sidedalphalevelo.orversus.is.%ortheDAD-,comparedwith.%oraBRD-.
.. When One Subgroup Is of Primary Interest: ProspectivePlanning Exercise for Enrolling a Second Subgroup.
Fromthe simulated trials, when
[
RR
,
control
,
RR
,
control
] =[0.1,0.3]
and
[
RRR
,
trt
:
control
,
RRR
,
trt
:
control
] = [0.5,1.5]
, theprobability o the absolute observed diﬀerence exceeding
=0.15
is % or
= 6
patients per treatment arm in therst stage (Figure ). In contrast, using
= 16
() patientsper arm in the rst stage, the probability o the observeddiﬀerence exceeding
= 0.15
is .% (%).
F r e q u e n c y F r e q u e n c y F r e q u e n c y
0.00.51.00.00.51.00.00.51.0
N
1
= 6
;mean
= 0.011
;SD
= 0.5486
; pr (diﬀ
≥ 0.15) = 0.67N
1
= 16
;mean
= 0.0018
;SD
= 0.5582
; pr (diﬀ
≥ 0.15) = 0.328250150500150100500100500P
trt
− P
control
P
trt
− P
control
P
trt
− P
control
−1.0 −0.5−1.0 −0.5−1.0 −0.5N
1
= 48
;mean
= 8e − 04
;SD
= 0.5632
; pr (diﬀ
≥ 0.15) = 0.13
F : Distributions o observed treatment diﬀerences in theM
−
subgroup at interim analysis, across simulated trials,using control response rate uniormly distributed over
[0.1,0.3]
and response rate ratio or treated versus control arms uniormly distributed over
[0.5,1.5]
. Sample sizes in the rst stage,
1
= 6
,, and . Proportion o trials where observed treatment diﬀerenceexceeds
= 0.15
in absolute value is %, .%, and %,respectively.
4. Discussion
Te direct assignment option design was rst proposed asa design enrolling a single cohort []. We have applied thedesign in the -subgroup setting. Te -subgroup DAD- preserves power and type I error rates at their nominal
Computational and Mathematical Methods in Medicine levels.Further,thisdesignhasreasonablepowerorplanningpurposes or a post-hoc test or detecting a treatment-subgroup interaction. Te rst nding is to be expected sincethe -subgroup DAD- applies the direct assignment optiondesign in parallel to each subgroup. However, the secondresult that there is reasonable (post-hoc) power to detect atreatment-subgroupinteractionispreviouslyunexploredandis o potential interest.Te assessment o power to detect an interaction in apost-hoc test using the -subgroup DAD- and an
-level o . suggests reasonable power (.% to detect a responserate o . in M+ versus response rate o . in M
−
). Werecognize that this
-level is conservative or an interactiontest when the main eﬀects use a one-sided
-level o ..Te sample size that was used to detect the interaction waslarger than that o a typical phase II trial ( patients inM+ and patients in M
−
). However, the reality is that nophase II trial can reliably detect interaction eﬀects o the sizeexplored in this simulation study using small sample sizes. Inact, an alternative strategy o prospectively planning or aninteraction test would have similarly yielded a large samplesize ( total patients, based on a balanced randomizeddesign with no IA). Our strategy thereorehas no sample sizedisadvantage in detecting an interaction eﬀect relative to onethatprospectivelyplansorasimilarlysizedinteractioneﬀectin a phase II setting.Te -subgroup DAD- could be applied in any settingwhere there are two subpopulations o interest. A naturalsetting is that o targeted, biomarker-based therapies. Otherso-called integrated biomarker designs have previously beenproposed.Wehighlightacoupleosuchdesigns;comprehen-sive reviews o such designs are available elsewhere (e.g., [,]). Te parallel subgroup-specic design [] evaluates treat-
menteﬀectsseparatelyintwosubgroups.Whenthetreatmenteﬀect is homogeneous across subgroups, this design has lesspowerordetectingatreatmentbenet,comparedtoadesignthat tests or an overall treatment eﬀect. In an attempt toaddress the lack o power in a homogeneous treatment set-ting, other designs have adopted a sequential testing strategy.Specically, the Marker Sequential est (MaS) design rsttests or a treatment eﬀect in the M+ subgroup []. I thistestisstatisticallysignicant,thentheM
−
subgroupistested.However, i the test is not statistically signicant, then anoverall population is tested. MaS increases power to detecttreatment benet when the treatment eﬀect is homogeneousacross subgroups and preserves power when the treatment iseﬀective in the M+ subgroup but not the M
−
subgroup, ascompared to a parallel subgroup-specic design.At rst glance, the proposed design resembles a parallelsubgroup-specic design in spirit. As noted in Freidlin etal. [], under the case o homogeneous treatment eﬀect, theparallelsubgroup-specicdesignlackspowerrelativetoatestor overall treatment eﬀect and the MaS design. However,the proposed design diﬀers rom the setting consideredby Freidlin et al. [] in two important ways. First, theproposed design is or the phase II setting and not the phaseIII setting. At this early exploratory stage, it is importantto rst understand the treatment eﬀect in each subgroupseparately without necessarily examining overall treatmenteﬀects.Tatis,althoughatestoroveralltreatmenteﬀectmay be more powerul than separate tests or subgroup-specictreatment benet when the treatment eﬀect is homogeneousacross subgroups, an overall treatment eﬀect would not be o primary interest in the phase II setting. Second, the MaSdesign’s property o improving power in the homogeneoustreatment setting rests on a key assumption: i the treatmentdoes not work in the M+ subgroup, then it cannot work in the M
−
subgroup. We reer to this as the
treatment monotonicity
assumption and do not invoke this assumptionor the proposed design setting. Rather, we allow or thesubgroup-specictreatmenteﬀectstobeindependentoeachother.It is not always the case that primary interest is in twosubgroups. However, even i primary interest is only in onesubgroup, it may be inormative to enroll a second subgroupas an exploratory companion group (i ethical) in early phase trials. Te decision to enroll a second subgroup willdependonthetradeoﬀamongavailableresources,theclinicalimportance o the diﬀerence in response rates
, and theestimated probability o the observed diﬀerence exceeding
.Teresultsromtheprospectiveplanningexercise, thereore,could aid the study design team in this decision.
5. Conclusion
In summary, we have illustrated at a practical level a -subgroup design with direct assignment option or the phaseII setting where primary interest is in separate subgrouptreatment eﬀects. Such a design not only preserves thenominal type I error rate and power or testing or separatesubgroup treatment eﬀects but also enjoys reasonable post-hoc power to detect a treatment-subgroup interaction, i oneexists, as well as clinical appeal and logistical simplicity. Inthe case where primary interest is only in one subgroup butresources may be available to enroll the second subgroup, wehaveproposedaplanningexerciseoraidingthestudydesignteam in deciding to enroll the second subgroup, using theramework o the direct assignment option design.
Conflict of Interests
Te authors declare that there is no conict o interestsregarding the publication o this paper.
Acknowledgment
Sumithra J. Mandrekar and Daniel J. Sargent are supportedin part by the National Cancer Institute Grant no. CA-(Mayo Clinic Cancer Center).
References
[] M.-W. An, S. J. Mandrekar, and D. J. Sargent, “A -stage phaseII design with direct assignment option in stage II or initialmarker validation,”
Clinical Cancer Research
, vol. , no. , pp.–, .[] A. Li`evre, J.-B. Bachet, V. Boige et al., “KRAS mutations asan independent prognostic actor in patients with advanced

Search

Similar documents

Tags

Related Search

The Kingdom of Two SiciliesA Portrait Of The Artist As A Young ManDrawing as a tool for designMinimalism as a Sole Legitimate Design IdiomTHE USE OF GLASS AS A BUILDING MATERIALAbraham as a Victim of PTSD as seen in the BiBathing as a technology of the body ( Marcel Interior Design as the Making of MetaphorsThe role of skills as a constraint and enableLanguage as a complex, dynamic system; the re

We Need Your Support

Thank you for visiting our website and your interest in our free products and services. We are nonprofit website to share and download documents. To the running of this website, we need your help to support us.

Thanks to everyone for your continued support.

No, Thanks