monotherapy trials: sequential design

Epilepsy Research 45 (2001) 81–87

Monotherapy trials: sequential design

John Whitehead *Medical and Pharmaceutical Statistics Research Unit, The Uni�ersity of Reading, PO Box 240, Earley Gate,

Reading RG6 6FN, UK

Abstract

In a sequential clinical trial, the accumulating data are subjected to a series of interim analyses, each of whichinvolves a comparison of the treatments under study in respect of the primary efficacy criterion. The trial is stoppedas soon as it is evident that one treatment is superior to the other, or that no such difference is going to be found.The stopping rule is devised to ensure that the required significance level and power are achieved and that validstatistical inference can be drawn at the end of the study. The methodology will be presented by means of a casestudy. This is the SEReNE study, which was completed last year and compared remacemide with carbamazepine inthe treatment of newly diagnosed epilepsy. The study employed a double triangular test : an efficient form of sequentialdesign for the comparison of two active treatments. The primary efficacy response was time from randomisation tothe first seizure following dose titration. Details will be given of the stopping rule employed, the number of patientsforecasted, the progress of the trial and its final analysis. The procedure adopted will be reviewed, and its suitabilityfor future trials assessed. © 2001 Elsevier Science B.V. All rights reserved.

Keywords: Clinical trials; Group sequential methods; Interim analysis; Sequential methods; Trial design

www.elsevier.com/locate/epilepsyres

1. Introduction

A sequential design for a clinical trial allows aseries of interim analyses of the emerging data tobe conducted, and specifies the circumstances un-der which the trial will stop or continue at eachone. Such designs are likely (but not certain) torequire fewer patients than traditional designs of

equal power, and in particular can avoid continu-ation when one treatment is already evidentlyinferior to the other. Valid methods for analysingdata collected using a sequential design have beendeveloped, and software is available for their im-plementation. Such designs are receiving increas-ing use in a wide variety of therapeutic areas.

The purpose of this paper is to illustrate theutility of sequential designs in epilepsy research bydescribing a recently completed sequential clinicaltrial. After presenting this case study, alternativesequential approaches, that may be useful in othersituations, will be discussed.

* Corresponding author. Tel.: +44-118-9318027; fax: +44-118-9753169.

E-mail address: [email protected] (J. Whitehead).

0920-1211/01/$ - see front matter © 2001 Elsevier Science B.V. All rights reserved.

PII: S 0920 -1211 (01 )00224 -8

J. Whitehead / Epilepsy Research 45 (2001) 81–8782

2. Specification for SEReNE study

The SEReNE study was a randomised compari-son of remacemide with carbamazepine in thetreatment of newly diagnosed epilepsy, sponsoredby Astra and conducted between April 1998 andNovember 1999. The primary endpoint was timefrom randomisation to the first seizure followingcompletion of a 42-day titration phase. Prognosticfactors identified as influencing this endpoint werethe seizure type (classified at time of randomisa-tion) and the number of seizures during the 12months prior to randomisation. It was anticipatedthat eight patients would be recruited to the studyeach week.

Prior to starting the study, the probabilities ofno study event occurring on carbamazepine be-fore 6, 12, 18, 30, 42 and 54 weeks were predictedto be 1, 0.72, 0.63, 0.58, 0.54 and 0.50, respec-tively. The first of these is certain to be true as thestudy event is the first seizure following the sixweeks titration phase, the others were derivedfrom past experience. These values give the event-free survival pattern represented by the solid linein Fig. 1.

It was regarded as possible that remacemidewould improve the probability of surviving with-out a study event for 54 weeks from 0.5 to 0.6,and felt that such an improvement would beclinically significant. The broken line in Fig. 1represents a survival pattern achieving this im-provement, and satisfying the theoretical consid-eration of proportional hazards. The powerrequirement for the study was as follows. If thesurvival patterns in the two treatment groups areas shown in Fig. 1, then a significant treatmentdifference (at the 5% level for a two-sided alterna-tive) should be detected with probability 0.90.

3. The design of the SEReNE study

The design chosen for the SEReNE study wasthe double triangular test. The first interim analy-sis was scheduled to take place 48 weeks after thestart of the study, or after 100 study events hadoccurred, whichever occurred second. Subsequentinterim analyses were planned to take place every12 weeks, with 48 new study events anticipated tobe available for each. The interval before the first

Fig. 1. Anticipated event-free survival probabilities for the control (carbamazepine) group and target event-free-survival probabilitiesfor the experimental (remacemide) group.

J. Whitehead / Epilepsy Research 45 (2001) 81–87 83

Fig. 2. The double triangular design for the SEReNE study. The logrank statistic is denoted by Z and its null variance by V.

interim analysis was deliberately chosen to begreater than subsequent intervals to ensure thatany early conclusions would be based on an ade-quate sample size.

Each interim analysis comprised a comparisonof the survival rate on remacemide with that oncarbamazepine by means of Cox’s proportionalhazards regression adjusting for seizure type andfor the number of seizures during the 12 monthsprior to randomisation. The statistic assessing theadvantage of remacemide is denoted by Z, techni-cally it is a ‘score statistic’, and it generalises thebetter known logrank statistic to allow for anyimbalance in prognostic factors. Also calculated isa measure of information, denoted by V, andapproximately equal to one quarter of the numberof events. At each interim analysis, Z and V werecomputed, and then plotted on the graph shownin Fig. 2. This continues until one of theboundaries shown is crossed.

If the sample path formed by the plotted pointscrosses the upper boundary, then significant evi-dence that remacemide is superior to carba-mazepine will have been observed (P�0.05). Ifboth of the inner broken boundaries are crossed,

then the trial stops with no significant treatmentdifference having been observed. Crossing of thelower boundary constitutes significant evidencethat remacemide is worse than carbamazepine.

The statistical model behind this design is basedon the assumption of proportional hazards, mean-ing that the better treatment will reduce the eventrate early after randomisation, in the mediumterm and in the long-term too, according to aspecific relationship. The advantage ofremacemide over carbamazepine can be expressedas the log-hazard ratio, denoted by �, and definedas minus the natural logarithm of the hazard onremacemide over the hazard on carbamazepine.Thus � is positive when the hazard onremacemide is small, that is when remacemide isthe better treatment. The quantities �, Z and Vare related: the expected value of Z is �V and thevariance of Z is V. Thus the plot of Z against Vwill have gradient approximately equal to �, andthe greater the advantage of remacemide, thequicker will the plot advance towards the upperboundary.

Fig. 3 shows a graph of the median and 90thpercentile of sample size, plotted against �. (The


90th percentile will be exceeded with probability0.10.) This shows median sample sizes of 450 or550 when the treatment difference is large (�=−0.5 or 0.5), of just over 700 when there is notreatment difference (�=0) and reaching a maxi-mum of about 850 when there is a modest advan-tage of remacemide (�=0.2). To place thesevalues in context, the treatment advantage por-trayed on Fig. 1 for which power was set to 0.90corresponds to �=0.3, and the fixed sample de-sign of equal power would need to recruit about1000 patients. The 90th percentile of sample sizerises over 1200 when �=0.2, warning that areduction in sample size relative to the traditionalapproach, while likely, is not inevitable.

The double triangular test was chosen becauseit will stop soon if remacemide is advantageous,and yet will distinguish between no difference andinferiority of remacemide. The latter feature wasimportant in this trial, because in the absence ofsignificant evidence that remacemide was worsethan carbamazepine in terms of seizure rates,

certain secondary advantages might have beenworthy of consideration.

The interim analyses were overseen by a Dataand Safety Monitoring Board, comprising astatistician and two clinicians who were indepen-dent of the sponsor and of the study. They hadthe power to overrule the formal conclusion con-cerning stopping if they felt that safety demandedit, or that the assumptions underlying the designwere suspect. They also reviewed substantial setsof safety data prior to and at the time of interimanalyses.

4. Conduct and analysis of the SEReNE study

Recruitment to the study began in April 1998.Initial recruitment was slow, and the first interimanalysis was not conducted until August 1999, bywhich time 134 events had occurred. The secondinterim analysis was conducted in November1999. The sample path at that time is shown inFig. 4.

Fig. 3. Median and 90th percentile of sample size plotted against log-hazard ratio � (theta).


Fig. 4. The final sample path for the SEReNE study. The logrank statistic is denoted by Z and its null variance by V.

The Christmas tree-shaped feature within thelower triangle of the test is a boundary adjustmentto allow for the actual increase in informationbetween interim analyses: the greater the increase,the larger the adjustment and the easier it is to stop.Thus the first plotted point was very close toreaching the stopping criterion. The DSMB feltthat it was important that the study reach adefinitive conclusion, and confirmed the formalinterim verdict that the study continue. The secondplotted point fell below the Christmas treeboundary, and the DSMB recommended that thesponsor stop the study, which was immediatelydone.

As the lower boundary has been crossed, theconclusion was that remacemide was significantlyworse that carbamazepine in terms of shorter timesto first seizure following titration. At the secondinterim analysis, data were available from 449patients, 382 of whom had entered the post-titra-tion phase and 181 of whom had experienced studyevents. Final test statistics were Z= −20.92 and

V=44.35, and model checking revealed no causeto doubt the pre-trial assumption of proportionalhazards. The final Kaplan–Meier estimates ofsurvival are shown in Fig. 5.

Using an analysis that is specific to the sequentialdesign used, the 2-sided P-value is P=0.003. Thelog-hazard ratio � has a median unbiased estimateof −0.46, with a 95% confidence interval of(−0.76, −0.16). Recall again that power was setto detect �=0.3.

5. Discussion

The SEReNE study demonstrated that the con-duct of sequential clinical trials is logistically feasi-ble. The trial resulted in a clear conclusion, and theDSMB had no hesitation in continuing the studyas recommended at the first interim, nor stoppingas recommended at the second. Model assumptionswere not counter-indicated by the data collected.An analysis valid for the design used was presented.


Fig. 5. Kaplan–Meier estimates of event-free-survival probabilities from the final interim analysis of the SEReNE study.

When designing the trial, the study team had avariety of designs to choose from. The doubletriangular test results in smaller samples when thetreatments are clearly different or when the arethe same, and larger samples when treatmentdifferences are moderate (see Fig. 3). The testseeks significant evidence either that experimentalis better than control or that experimental isworse than control. Alternative designs includethe restricted procedure and the triangular test.The restricted procedure does not reduce samplesize when there is no treatment difference, so as toaccrue a large sample on secondary treatmentcharacteristics. The triangular test does not seekto distinguish between experimental being worsethan control or no different, thereby reducingsample size whenever the experimental is actuallyworse. Such asymmetry is especially appropriatewhen a novel experimental treatment is eitherexpensive or toxic, and thus only of interest if it issuperior to control.

Sequential clinical trials are described in detailsin the books by Whitehead (1997) and Jennison

and Turnbull (2000). The triangular test is de-scribed in detail by Whitehead (2001), where otherexamples of its use can be found. Survivalmethodology, including the model of Cox (1972)is presented in Collett (1994). The SEReNE studywas designed and analysed using the softwarepackage PEST 4 (MPS Research Unit, 2000).

Acknowledgements

The author is grateful to all of the members ofthe SEReNE project team at Astra Charnwood(now AstraZeneca R & D Charnwood), especiallyJohn Stevens who selected and computed thisdesign, and to the DSMB of the trial.

References

Collett, D., 1994. Modelling Survival Data in Medical Re-search. Chapman and Hall, London.

Cox, D.R., 1972. Regression models and life-tables. J. Roy.Statist. Soc. Ser. B 34, 187–202.


Jennison, C., Turnbull, B.W., 2000. Group Sequential Meth-ods with Application to Clinical Trials. Chapman andHall/CRC, Boca Raton, USA.

MPS Research Unit 2000. PEST 4: Operating Manual. TheUniversity of Reading.

Whitehead, J., 1997. The Design and Analysis of SequentialClinical Trials, 2nd Edition. Wiley, Chichester.

Whitehead, J., 2001. Use of the triangular test in sequentialclinical trials. In: Crowley, J. (Ed.), Handbook of Statisticsin Clinical Oncology. Dekker, New York To appear.

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monotherapy trials: sequential design

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