Adaptive Clinical Trials Incorporating Treatment Selection and Evaluation: Methodology and Applications in Multiple Sclerosis

Transcription

1 Adaptve Clncal Trals Incorporatng Treatment electon and Evaluaton: Methodology and Applcatons n Multple cleross usan Todd, Tm Frede, Ngel tallard, Ncholas Parsons, Elsa Valdés-Márquez, Jeremy Chataway 3 and Rchard Ncholas 4 Appled tatstcs, Unversty of Readng, Phlp Lyle Buldng, Readng, RG6 6BX, UK (e-mal of correspondng author: s.c.todd@readng.ac.uk) Warwck Medcal chool, Unversty of Warwck, Coventry, CV4 7AL, UK 3 Imperal College Healthcare NH Trust / Natonal Hosptal for Neurology & Neurosurgery, Department of Neurology, t Mary s Hosptal, Praed treet, London, W NY, UK 4 Imperal College Healthcare NH Trust, Department of Cellular & Molecular Neuroscences, Charng Cross Hosptal, Fulham Palace Road, London, W6 8RF, UK Abstract. Recent advances n statstcal methodology for clncal trals have led to the development of seamless adaptve desgns. These allow a number of expermental treatments to be compared wth a control n the same tral, wth less promsng treatments dropped from the study early, whlst mantanng control of type I error rate. From a statstcal vewpont, the treatment selecton may be made n any way wthout compromsng the type I error rate control. From a practcal aspect, however, the treatment selecton rule must be chosen carefully; too strngent a rule ncreases the rsk of erroneously droppng effectve treatments, whereas too lax a rule leads to neffectve treatments remanng n the tral, less effcent use of resources and a reducton n power. In ths paper we explore the mplementaton of a seamless adaptve desgn n the settng of multple scleross. The objectve s to llustrate how the statstcal aspects of the tral desgn are brought together wth the practcal consderatons of runnng a tral. tatstcal smulaton studes are a powerful tool for explorng the propertes of dfferent treatment selecton rules and a key objectve s to explore ther use n ths settng. Conclusons focus on the mportant aspects whch need to be consdered when plannng the actual tral. Keywords. Adaptve desgns, nterm analyses, phase II/III clncal trals, smulaton study. Introducton The clncal evaluaton of new drugs s generally dvded nto three phases (Chow and Lu, 004). The frst two phases may be consdered exploratory, and allow drug tolerablty to be explored and ntal assessment of effcacy to be made, often on the bass of short-term endponts. Phase III clncal trals are confrmatory and provde defntve evdence of treatment effect. Ths s usually va a comparson wth a randomsed placebo control group usng long-term endponts and a clncally realstc patent populaton. The assessment of new treatments for multple scleross (M) presents a number of features that mean that the common phase I-II-III paradgm for clncal tral desgn may not be the most approprate. The smultaneous avalablty of a number of drugs for evaluaton means that t s desrable to compare several actve treatments n the same tral rather than conductng trals wth a sngle new treatment compared wth a placebo. Furthermore, relatvely long follow-up tmes are requred to assess the clncal effcacy of new treatments n ths ndcaton (CHMP, 005). In these crcumstances small scale Phase II trals of ndvdual drugs have to rely on early outcomes and mght be neffcent. Recently, advances n statstcal methodology for clncal trals have led to the development of seamless adaptve desgns (Maca et al, 006; Bretz et al, 006). These allow a number of expermental treatments to be compared wth a control n the same tral, wth less promsng treatments dropped from the tral early. Ths paper explores the applcablty of adaptve methodology n the settng of clncal trals for M, and presents an approach for determnng an effcent clncal tral desgn for the selecton and evaluaton of potental new M therapes. In ecton the methodology wll be presented brefly. In ecton 3 an explanaton s gven of how smulatons, based on a realstc model constructed from analyss of data from prevous trals n M, can be used pror to the commencement of an actual clncal tral to ensure that treatments wll be dropped approprately. ecton 4 presents an llustratve example. The paper concludes wth a bref dscusson n ecton 5.

2 Todd et al. Adaptve desgns n M Adaptve desgn methodology appled to M A partcularly mportant type of adaptaton n the settng of clncal trals n multple scleross as descrbed above s the ablty to select promsng treatments durng the tral or to stop the tral early. It s assumed that the tral s conducted n two stages, and nvolves at least two expermental treatments and a sngle control treatment. In the frst stage, patents are randomsed to receve one of the expermental treatments or the control treatment. The treatments are then compared at the end of stage one usng one of a number of possble selecton rules based on an early outcome measure. Based on ths early outcome measure, ether the tral s stopped for futlty or one or more of the expermental treatments are selected to contnue nto stage two of the tral. The tral then contnues wth randomsaton between the control treatment and the remanng expermental treatments. At the end of the second stage, the remanng expermental treatments are compared, usng a clncally meanngful outcome measure, wth the control treatment n a seres of formal hypothess tests based on data from both desgn stages. The hypothess testng s carred out n such a way that the famlywse type I error rate s strongly controlled, allowng both for the multple comparsons and for the treatment selecton. At the outset of the tral assume that there are k expermental treatments and a sngle control treatment. On completon of the frst stage of the tral some expermental treatments mght be dropped based upon observaton of the early outcome measure, and a non-empty subset of k treatment arms ( 0 k k) together wth the control are contnued nto stage two. In what follows, denote by,,, k the treatment effects of the k expermental treatments each compared to the control. Furthermore, let, and, denote standardsed test statstcs n the frst and second stage, respectvely, where, s based on the data of the second stage only and not on the accumulated data. The : null hypotheses of nterest are denoted by H 0. These are tested aganst the one-sded alternatve hypotheses H : 0. The sample szes per group n stages one and two are denoted by n and n respectvely and the, j follow Normal dstrbutons wth expectatons n j and varance. The standardsed test statstc based on the accumulated data at the end of the second stage s denoted by. It holds that n n, n n, for a total sample sze per group of n n n. Dunnett's test (955) can be used to compare the test treatments to the control treatment based on the late outcome measure at stage one and stage two. The test s a test for many-to-one comparsons testng the null hypothess that all are equal to 0 aganst the alternatve hypothess that at least one s larger than 0. The test statstc s gven by. On observng a z a p- value s calculated as F ( z) where {,, k } k F ( z) [ ( z x)] ( x dx. () ) Ths expresson s the cumulatve dstrbuton functon of wth (.) and (.) denotng the cumulatve dstrbuton functon and the densty functon of the standard normal dstrbuton, respectvely. An objectve of the adaptve desgn s to control the famlywse type I error rate n the strong sense at a pre-specfed level. In order to do ths, the closure test prncple s appled (Marcus et al., 976). Ths means that an ndvdual null hypothess H s rejected only f all ntersecton hypotheses H H (,, k }) wth ndex sets that nclude are rejected at level. Consderng { the case of a tral wth two test treatments, the ntersecton hypothess H {,} s the null hypothess that 0 ;.e. that nether treatment s effectve. An ntersecton hypothess H s tested usng

3 Todd et al. Adaptve desgns n M 3 a Dunnett test whch ncludes all treatments n. The null hypothess H s rejected f ds where the crtcal value d s ( s : number of elements n ) s the soluton of equaton () set to wth k s. The test procedure s modfed to allow for dropped treatments by settng test statstcs, comparng dropped treatments to the control, to (Koeng et al., 008). Inferences can be made usng the late outcome measure, by combnng stagewse p-values from stages one and two of the tral; the combnaton test approach. Bauer and Keser (999) descrbe the fundamental deas of the combnaton test approach referrng to the combnaton functon descrbed by Bauer and Köhne (994) to combne stagewse p-values whch allows for nterm adaptatons and the applcaton of the closed test prncple to control the overall sze of the test across multple hypotheses. The method for combnng p-values that s used here s the weghted nverse normal method as descrbed by Lehmacher and Wassmer (999). Denotng the two p-values from the dfferent stages of the tral by p and p, the weghted nverse normal combnaton functon for these p-values s gven by C p, p ) ( w ( p ) w ( )) () ( p where w j, j, are pre-specfed weghts wth w and w. The most wdely used 0 j w opton for the weghts s wj n j n. If C ( p, p) then the null hypothess s rejected. When a sngle hypothess s tested, the nverse normal method wth the weghts descrbed above s equvalent to a classcal group-sequental test. The stagewse Dunnett p-values for hypothess H are calculated for the test statstcs of the frst stage, and second stage, accordng to equaton () and these are then combned usng equaton (). Three dstnct types of selecton rules have been consdered. These are all based on an early outcome measure. The treatment effects of the early outcome measure for the k expermental treatments are denoted by,,, k and assumed to follow a Normal dstrbuton wth mean and varance. The three selecton rules are as follows; () A fxed selecton rule, selected the m largest values of for m, m and m k. () A varable (epslon) selecton rule, contnued wth all treatments wth an early outcome measure where. Ths ncludes the extremes of selectng exactly one treatment ( 0 ) and selectng all treatments ( ). () A futlty selecton rule, selected only those treatments where C. C, for threshold value 3 trategy for smulatons A general framework for the comprehensve evaluaton of competng optons for clncal programs, tral desgns and analyss methods, as a bass for decson makng has been proposed by Benda et al. (009). They ntroduced key termnology and defntons, and descrbed the overall process as Clncal cenaro Evaluaton (CE); shown n Fgure. tatstcal models that descrbe the data generaton process n a clncal tral and the specfcaton of parameters such as treatment effects, correlatons and standard devatons are called assumptons. The range of assumptons under consderaton are referred to as the assumpton set. Partcular clncal tral desgns and varants of such are called optons. Agan the range of optons relevant to the comparson at hand are referred to as the opton set. The combnaton of the assumpton set and the opton set are the clncal scenaros. In order to judge whether a desgn s effcent or robust we need to defne crtera by whch we judge the desgns. These crtera are referred to as metrcs. In the context of clncal trals metrcs of nterest are for example

4 Todd et al. Adaptve desgns n M 4 statstcal power and selecton probabltes of partcular treatments at nterm. The combnaton of metrcs to be used s called metrcs set. Fnally, clncal scenaro evaluaton s defned as the comparson of the metrcs of alternatve clncal tral desgn optons for a partcular assumpton set. We adopt and use ths convenent CE framework and termnology throughout ths paper. For any clncal scenaro, the methods descrbed n ecton can be mplemented as follows. For gven treatment means for the early outcome, a selecton rule s used at the end of stage one to choose a number of treatments to progress to stage two. Late outcome data from stages one and two are combned together usng Dunnett s test, for a many-to-one comparson aganst the control treatment, usng the weghted nverse normal method Hypothess testng proceeds usng a closed test procedure, such that for elementary hypotheses H for,,, k and ntersecton hypotheses H H for {,, k}, H s rejected f all ntersecton hypotheses H wth are rejected at level. Ths closed testng procedure controls the famlywse error rate n the strong sense. Fg.. Clncal cenaro Evaluaton Programs were wrtten n R ( to mplement the methodologes descrbed above. Followng the CE framework, four desgn optons for the M scenaro were dentfed. These are (a) Number of expermental treatments (b) Total number of patents n the tral (c) Patent numbers at stages and (d) electon rule at the nterm analyss (see above) In order to determne sutable assumptons to be used n the CE framework, three key sources of nformaton were used. Frst, the results from a comprehensve lterature revew of the M lterature; second, detaled analyss of clncal datasets suppled to the project team and thrd, consultaton wth experts n the feld. The followng four assumptons were dentfed (a) tandardsed treatment effect sze (b) Treatment effect type (c) Early and fnal treatment effect szes (d) Correlaton between early and fnal outcomes

5 = 0.5 and one treatment effectve Todd et al. Adaptve desgns n M 5 A varety of settngs were made for each of the optons and assumptons n order to evaluate a range of potental desgn scenaros. Partcular combnatons of the optons and assumptons make up clncal scenaros for evaluaton. The performance of each of the clncal scenaros was assessed by the power to reject at least one false hypothess, based on repeated smulatons of Normally dstrbuted standardzed treatment effects. Ths s the key metrc of nterest. Two thousand smulatons were used for each of clncal scenaros descrbed; ths was chosen manly for practcal reasons, based on the avalable computng resources. 4 Example In ths secton a number of clncal scenaros are selected from the avalable matrx of optons and assumptons n order to llustrate a range of potental tral desgns. The power to reject at least one false hypothess s plotted aganst the total tral sze (between 750 and 000 patents n total) for the followng set of assumptons/optons () four expermental treatments (plus a sngle control) () a standardzed treatment effect sze of = 0.5 () a correlaton between the early and late outcome measures of = 0. (v) a rato between the early and the late outcome measures (F) of.5 (v) a treatment effect type scenaro where only one of the expermental treatments s effectve Three selecton rules are compared, for desgns that allocate patents n the rato : and the rato :3, for the two stages of the tral. The three chosen selecton rules are () a fxed rule selectng one test treatment only at the nterm, () a varable selecton rule where = 0.5 and () a futlty selecton rule determned by F =.5. Plots of power to reject at least one false hypothess are shown n Fgure for these clncal scenaros. tage to rato: : tage to rato: :3 Fg.. Power to reject at least one false hypothess aganst total tral sample sze (patents) for four test treatments, for a fxed selecton rule (select ), a varable selecton rule ( = 0.5) and a futlty rule

6 Todd et al. Adaptve desgns n M 6 5 Conclusons The am of ths work has been to descrbe an applcaton of adaptve desgns for a clncal tral n M. The methodology has been presented brefly, together wth an explanaton of how smulatons, based on a realstc model constructed from analyss of data from prevous trals n M, relevant lterature and expert opnon, can be used pror to the commencement of the actual clncal tral to ensure that treatments wll be dropped approprately. Much of the challenge of mplementaton of a treatment selecton desgn as descrbed above arses exactly because of ts flexblty. It s mportant to consder carefully the range of optons and assumptons lkely to arse and then to use these n a range of smulaton evaluatons. Our work has brought together statstcans and clncans, all of whom, as a result of the process descrbed n ths paper, now have a greater understandng of the mportant factors mpactng the desgn of trals n ths therapeutc area. However, t s only when defntve statements can be made on the number of test treatments and the lkely treatment effect types that a more defntve statement ndcatng the optmal settngs of the desgn parameters for a future study be made. Acknowledgements Ths work was supported by a grant from the Multple cleross (M) ocety of Great Brtan and Northern Ireland. References Bauer, P. and Keser M. (999). Combnng dfferent phases n the development of medcal treatments wthn a sngle tral. tatstcs n Medcne, 8, Bauer, P. and Köhne, K. (994). Evaluaton of experments wth adaptve nterm analyses. Bometrcs, 50, Benda N, Branson M, Maurer W, Frede T. (009). Aspects of modernzng drug development usng clncal scenaro plannng and evaluaton. ubmtted. Bretz F, chmdl H, Koeng F, Racne A, Maurer W. (006). Confrmatory seamless phase II/III clncal trals wth hypotheses selecton at nterm: General concepts. Bometrcal Journal, 48, Commttee for Medcnal Products for Human Use (CHMP). Gudelne on clncal nvestgaton of medcnal products for the treatment of multple scleross. 005, London. Doc. Ref. EMEA/CHMP/EWP/56/98 Rev. Chow,.-C. and Lu, J.-P. (004). Desgn and Analyss of Clncal Trals: Concepts and Methodologes. Wley, Hoboken. econd Edton. Dunnett, C.W. (955). A multple comparson procedure for comparng several treatments wth a control. Journal of the Amercan tatstcal Assocaton, 50, Koeng F, Brannath W, Bretz F, Posch M (008) Adaptve Dunnett tests for treatment selecton. tatstcs n Medcne 7, Lehmacher, W. and Wassmer, G. (999). Adaptve sample sze calculatons n group sequental trals. Bometrcs, 55, Maca J., Bhattacharya., Dragaln V., Gallo P., Krams M. (006) Adaptve seamless phase II/III desgns: Background, operatonal aspects, and examples. Drug Informaton Journal, 40, Marcus, R., Pertz, E., Gabrel, K.R. (976). On closed testng procedures wth specal reference to ordered analyss of varance. Bometrka, 63,