STATISTICAL METHODS FOR ADAPTIVE DESIGNS

Transcription

1 STATISTICAL METHODS FOR ADAPTIVE DESIGNS Workshop on flexible designs for diagnostic studies Göttingen, 6-7 November 2017 Tim Friede Department of Medical Statistics University Medical Center Göttingen Göttingen, Germany

2 ACKNOWLEDGEMENTS Collaborative work with Nigel Stallard, Nick Parsons and Thomas Homburg (Warwick) BIostatistische Methoden zur effizienten Evaluation von Individualisierten Therapien (BIMIT) funded by BMBF WP C: Tim Friede, Marius Placzek, Roland Gera (Göttingen); Heinz Schmidli (Novartis) "Innovative methodology for small populations research" (InSPiRe) funded by EU's FP7 (HEALTH ) WP3 led by Martin Posch (Vienna) Identification und confirmation of biomarker-defined populations in the personalized pharmacotherapy co-funded by BfArM PIs Tim Friede, Jürgen Brockmöller (UMG), Norbert Benda, Julia Stingl (BfArM) 2

3 OUTLINE Motivation Learning and confirming in clinical development Overview of statistical methods for adaptive designs Treatment selection in adaptive designs Comparison of methods Case study in secondary progressive MS Interim decisions and early outcomes Subgroup selection in adaptive designs Motivation: Biomarkers, Personalised medicine Adaptive enrichment designs Internal pilot studies in adaptive enrichment designs 3

4 LEARNING VS. CONFIRMING Drug development process as two learning / confirming cycles (Sheiner, 1997) First learning / confirming cycle (Phase I-IIa) Learning about tolerated dose (Phase I) Then confirming of efficacy of selected dose in selected group of patients (Phase IIa) Second learning / confirming cycle (Phase IIb-III, IV) Learning about optimal use in respresentative patients (Phase IIb) Then confirming of acceptable benefit / risk ratio (Phase III) Traditionally separate studies for learning and confirming 4

5 ADAPTIVE SEAMLESS DESIGNS (ASD) Drug development very expensive and risky with many compounds failing in late development phases Adaptive designs recognized as a way to improve efficiency of drug development FDA Critical Path Initiative Industry led initiatives such as PhARMA working group Combining trials of different phases into one study, e.g. adaptive seamless phase II/III design Adaptations of interest include: treatment (or dose) selection, subgroup selection, sample size reestimation 5

6 ADAPTATIONS IN LATE STAGE CLINICAL TRIALS sample size re-estimation treatment (or dose) selection (combining Ph IIb/ III) subgroup selection (predefined, possibly based on genomic biomarkers) changing objectives, e.g. switching between non-inferiority and superiority change of primary endpoint or analysis,... 6

7 OUTLINE Motivation Learning and confirming in clinical development Overview of statistical methods for adaptive designs Treatment selection in adaptive designs Comparison of methods Case study in secondary progressive MS Interim decisions and early outcomes Subgroup selection in adaptive designs Motivation: Biomarkers, Personalised medicine Adaptive enrichment designs Internal pilot studies in adaptive enrichment designs 7

8 STATISTICAL METHODOLOGY FOR ASD repeated testing classical group sequential designs (e.g. Jennison & Turnbull 1999) combining pre/ post adaptation data (recursive) combination test (Brannath et al, 2002), conditional error function approach (Müller & Schäfer, 2001) multiple hypotheses closed test principle (Marcus et al, 1976), Bonferroni,... combinations of these approaches in ASDs: e.g. weighted inverse normal method and closed test principle 8

9 COMBINATION TEST AND CLOSURE PRINCIPLE Stage 1 data only Stage 2 data only e.g. weighted inverse normal combination function Figure taken from Bretz et al (2006) Biometrical Journal

10 OUTLINE Motivation Learning and confirming in clinical development Overview of statistical methods for adaptive designs Treatment selection in adaptive designs Comparison of methods Case study in secondary progressive MS Interim decisions and early outcomes Subgroup selection in adaptive designs Motivation: Biomarkers, Personalised medicine Adaptive enrichment designs Internal pilot studies in adaptive enrichment designs 10

11 COMPARISON OF METHODS FOR TREATMENT SELECTION IN ADAPTIVE DESIGNS Classical Dunnett Single stage test Combination test (Bretz et al, 2006) Intersection hypotheses tested by Dunnett test Inverse normal combination function Adaptive Dunnett (Koenig et al, 2008) Conditional error function approach based on Dunnett test Group-sequential approach (Stallard & Friede, 2008) Test statistic at the final analysis is the sum of the largest test statistics based on the data from each stage of the trial 11

12 COMPARISON OF METHODS FOR TREATMENT SELECTION IN ADAPTIVE DESIGNS Under the global null hypothesis (Friede & Stallard, 2008) 12

13 COMPARISON OF METHODS FOR TREATMENT SELECTION IN ADAPTIVE DESIGNS Under alternatives (Friede & Stallard, 2008) 13

14 ADAPTIVE SEAMLESS PHASE II/III DESIGN IN SECONDARY PROGRESSIVE MS Chataway et al (2011) MSJ 14

15 ADAPTIVE SEAMLESS PHASE II/III DESIGN IN SECONDARY PROGRESSIVE MS Chataway et al (2011) MSJ 15

16 ADAPTATIONS BASED ON EARLY OUTCOMES Sometimes the primary endpoint only available after longterm follow-up and recruitment relatively fast: Adaptations need to be based on early outcome data Example: PFS and OS in oncology (Jenkins et al, 2011) Complete follow-up Stage 1: Patients recruited before adaptation (regardless whether their follow-up extends beyond the interim analysis) Stage 2: Patients recruited after adaptation Discontinued follow-up Conservative imputation of test statistic Reference: Friede et al (2011) 16

17 ADAPTIVE SEAMLESS PHASE II/III DESIGN IN SECONDARY PROGRESSIVE MS Type I error rate control Sample size savings Friede et al (2011) SiM Chataway et al (2011) MSJ 17

18 INCORPORATING SHORT-TERM ENDPOINTS If for at least some patients early and primary outcomes are available, interim decisions can be improved by integrating the data of those patients from whom only early outcomes are available. Further reading Stallard N (2010). A confirmatory seamless phase II/III clinical trial design incorporating short-term endpoint information. Statistics in Medicine 29: Kunz CU, Friede T, Parsons N, Todd S, Stallard N (2015) A comparison of methods for treatment selection in seamless phase II /III clinical trials incorporating information on short-term endpoints. Journal of Biopharmaceutical Statistics 25: Kunz CU, Friede T, Parsons N, Todd S, Stallard N (2014) Data-driven treatment selection for seamless phase II/III trials incorporating earlyoutcome data. Pharmaceutical Statistics 13:

19 OUTLINE Motivation Learning and confirming in clinical development Overview of statistical methods for adaptive designs Treatment selection in adaptive designs Comparison of methods Case study in secondary progressive MS Interim decisions and early outcomes Subgroup selection in adaptive designs Motivation: Biomarkers, Personalised medicine Adaptive enrichment designs Internal pilot studies in adaptive enrichment designs 19

20 WHAT ARE BIOMARKERS? Definition by the Biomarkers Definitions Working Group (2001) A characteristic that is objectively measured and evaluated as an indicator of normal biological processes, pathogenic processes, or pharmacologic responses to a therapeutic intervention. Very general definition 20

21 WHAT ARE BIOMARKERS USED FOR? Biomarkers are used to diagnose diseases (or certain subtypes) to predict disease course or response to treatment to stratify populations to monitor patients as endpoints in clinical trials 21

22 SUBGROUP IDENTIFICATION For an overview refer to recent systematic literature review by Ondra et al. (2015) on methods for subgroup identification and confirmation in clinical trials Exploratory subgroup identification attracted a lot of attention over the past years several methods proposed Here we assume Biomarker-defined subgroup identified in exploratory study Subgroup to be confirmed by independent data Confirmation of treatment effect in selected population 22

23 STRATIFIED MEDICINE F S Full population Sub-population

24 HYPOTHESES AND TEST STATISTICS Subpopulation with prevalence Denote standardised test statistics for testing, (no effect in full/subpopulation) by and Under (no effect in full and subpopulation):

25 HYPOTHESES AND TEST STATISTICS Extension to several nested subgroups: prevalences, Under (no effect in any population) Note: same structure as in group-sequential designs 25 Spiessens & Debois (2011) CCT

26 NESTED SUBGROUPS: STATISTICAL ANALYSIS In case of normally distributed data Reference distributions for hypothesis tests Variances Equal across subgroups Unequal across subgroups Known Exact MVN Exact MVN Unknown Exact MVT df=n - 2 (k+1) Approx. / asympt. MVT df=n (k) - 2 (k+1) MVN: multivariate normal; MVT: multivariate T distr.; n total sample size; n (k) sample size of smallest subgroup; k subgroups; k+1 hypotheses Placzek & Friede (2017) SMMR 26

27 NESTED SUBGROUPS: TYPE I ERROR RATES Practical applications: unknown and unequal variances most likely Placzek & Friede (2017) SMMR 27

28 ALTERNATIVE APPROACH Pocock (1977) Biometrika and Jennison and Turnbull (2000) propose (for group-sequential designs) to calculate the critical values based on the multivariate normal distribution then to transform critical values to the corresponding boundary of the univariate t-distribution with n (i) 2 degrees of freedom (based on actual sample size) Student s t-tests to account for unknown variance using the critical values above Note: (a) Ease of computation as multivariate normal distribution used (not multivariate t-distribution); (b) degrees of freedom vary across subgroups Graf et al (2017) (submitted) 28

29 INTERIM SELECTION RULES Thresholds for hazard ratios (Jenkins et al., 2011) Table II from Jenkins et al (2011) ε-rule on z-statistics (Friede & Stallard, 2008; Kelly et al, 2005) Bayesian decision tools (Brannath et al., 2009)

30 ADAPTIVE ENRICHMENT DESIGN Interim analysis Stage 1 Stage 2 Option F S Futility stopping / Early success F only S only (Enrichment) F and S 30

31 ENRICHMENT DESIGNS MORE POWERFUL Friede et al. (2012) Stat Med

32 CONDITIONAL ERROR FUNCTION APPROACH WITH CONTINUOUS ENDPOINTS Conditional error function approach by Friede et al (2012) based on (approximate) normal distribution of test statistics Adapted to continuous data with unknown variances that might vary across subgroups using test strategies proposed in Placzek and Friede (2017) and Graf et al (2017) Placzek and Friede (2017) (in preparation) 32

33 CONDITIONAL ERROR FUNCTION APPROACH WITH CONTINUOUS ENDPOINTS Placzek and Friede (2017) (in preparation) 33

34 OPTIMAL TIME POINT FOR INTERIM ANALYSIS Adaptive enrichment design with CEF approach 0.85 tau=0.5 Simulation results for n sim =10,000 replications n=400 subjects per group (treatment/placebo) Under the alternative power 0.75 tau=0.4 Maximum in power after 40-50% of the subjects 0.65 eps=0 eps=1 eps=inf tau= n1/n

35 NESTED SUBGROUPS: INTERNAL PILOT STUDY Power / sample size depend among other quantities on nuisance parameters such as the variances of the outcomes in the subgroups and the prevalences of the subgroups. Knowledge of these nuisance parameters might be very scarce in the planning phase of such a trial resulting in a considerable risk of choosing an inappropriate sample size. These risks can be mitigated in an internal pilot study design 35

36 INTERNAL PILOT STUDY (IPS) DESIGN (Wittes & Brittain,1990) Three step procedure: Initial sample size calculation N 0 based on estimates of the standard deviation from previous studies Sample size review when n 1 =p N 0 (e.g. p=1/2) patients completed the study reestimation of sample size based on estimate of standard deviation from the n 1 patients Final analysis based on all n 1 +n 2 patients 36

37 BLINDED SAMPLE SIZE REESTIMATION (BSSR) IN ADAPTIVE ENRICHMENT DESIGNS Enrichment decision / Futility stopping BSSR Early IA for blinded sample size reestimation Later IA for enrichment decision / futility stopping (unblinding)

38 SOME REFERENCES Bretz F, Schmidli H., König F, Racine A, Maurer W (2006) Confirmatory seamless phase II/III clinical trials with hypotheses selection at interim: General concepts. Biometrical Journal 48: Friede T, Parsons N, Stallard N (2012) A conditional error function approach for subgroup selection in adaptive clinical trials. Statistics in Medicine 31: Friede T, Parsons N, Stallard N, Todd S, Valdés-Márquez E, Chataway J, Nicholas R (2011) Designing a seamless phase II/III clinical trial using early outcomes for treatment selection: An application in multiple sclerosis. Statistics in Medicine 30: Friede T, Stallard N (2008) A comparison of methods for adaptive treatment selection. Biometrical Journal 50: Ondra T, Dmitrienko A, Friede T, Graf A, Miller F, Stallard N, Posch M (2015) Methods for identification and confirmation of targeted subgroups in clinical trials: A systematic review. Journal of Biopharmaceutical Statistics 26: Placzek M, Friede T (2017) Clinical trials with nested subgroups: Analysis, sample size determination and internal pilot studies. Statistical Methods in Medical Research (in press). 38