Issues Generally, not very accurate depiction of true dose-response (or dose-toxicity) curve Require dose levels specified in advance Usually start far from target dose Don’t fully use information from previously treated patients Don’t use information on ordinal response (e.g. graded toxicity) Estimate of MTD is seriously biased or invalid EUGM, Nov 2019 37 (more) limitations of 3+3 Ignores dosage history other than previous cohort 0/3, 0/3, 0/3, 0/3, 0/3, 2/6 provides more information than 0/3, 2/6 • Same action under qualitatively different situations 0/3 and 1/6 lead to same action (escalate to the next provisional dose) • 2/3, 3/3, 2/6, 3/6, and 4/6 lead to same action (de-escalate) • Ignores uncertainty: • If true DLT rate is p=0.5, 11% of the time we will see 0 or 1 DLT in 6 patients • If true DLT rate is p=0.166, 26% of the time we will see at least 2 DLT in 6 patients Cannot re-escalate Fixed cohort sizes (either 3 or 6) Pre-defined dose levels to be potentially tested Low probability of selecting true MTD (e.g. Thall and Lee. 2003) High variability in MTD estimates (Goodman et al. 1995) Alessandro Matano, Novartis, http://www.smi-online.co.uk/pharmaceuticals/archive/4-2013/conference/adaptive-designs EUGM, Nov 2019 38 10/28/19 19
Target Toxicity? Common misconception target toxicity is fixed (eg., 17%, or 33%). He et al. (2006) showed via simulation that the expected toxicity level at the MTD for the 3+3 is between 19-22%. EUGM, Nov 2019 39 Accelerated Titration Simon et al. (1997): "...cohorts of one new patient per dose level. When the first instance of first course DLT is observed,...expand the cohort for current dose level. EUGM, Nov 2019 40 10/28/19 20
Accelerated Titration Similar to traditional design with small cohorts at low doses Attempts to use information in ordinal toxicity responses at lower doses May reduce the number of patients needed to reach MTD EUGM, Nov 2019 41 Regulatory Guidelines FDA Guidance (Clinical Considerations for Therapeutic Cancer Vaccines) EMEA / CHMP Guideline on Clinical Trials in Small Populations Alternative Approach Needed To Meet Design Requirements EUGM, Nov 2019 42 10/28/19 21
Bayesian Framework (Based on Matano. Bayesian Adaptive Designs for Oncology Phase 1 Trials, 2013) EUGM, Nov 2019 43 The Continual Reassessment Method (CRM) Bayesian model-based method (O'Quigley et al. 1990) Uses all available information from doses to guide dose assignment Inputs to specify: • Target toxicity p T (usually at 33%) • A single-parameter (θ) dose-toxicity curve • prior distribution for θ • prior mean probabilities at each dose (“skeleton”) Next recommended : posterior toxicity probability closest to target EUGM, Nov 2019 44 10/28/19 22
CRM: The Process 1. Patient cohorts treated at each dose level 2. Toxicity outcome observed 3. Using Bayes theorem, prior distribution and observed outcomes are used to calculate the posterior mean of the probability of toxicity at each dose level, ̂ 𝑞 # 4. Next cohort of patients assigned to dose level that has its ̂ 𝑞 # closest to target toxicity 5. Repeat 1-4 until termination criteria met EUGM, Nov 2019 45 Modified CRM EUGM, Nov 2019 46 10/28/19 23
Modified CRM Differences: • Can start at lowest dose • Allow multiple patients per cohort • Restrict escalation to one dose (do not allow skipping when escalating) “The unmodified CRM...produces only modest increases in accuracy over the modified CRM, but at the price of greater toxicity, and, most important, clinical acceptability.” EUGM, Nov 2019 47 CRM Simulation Parameters EUGM, Nov 2019 48 10/28/19 24
Uncertainty in toxicity rate CRM relies on point estimate, ignores uncertainty. eg, same posterior mean, but Pr( p > 0.6) = 0.168 vs 0.002 EUGM, Nov 2019 49 Bayesian Logistic Regression Model (BLRM) EUGM, Nov 2019 50 10/28/19 25
Bayesian Logistic Regression Model (BLRM) Two parameter logistic: is the “reference dose” (arbitrary scaling dose) α>0 is the odds of DLT at β>0 is the increase in log-odds of DLT for unit increase in log-dose EUGM, Nov 2019 51 Bayes Risk Choose dose that minimizes posterior expected loss. EUGM, Nov 2019 52 10/28/19 26
Escalation With Overdose Control (EWOC) • Choose dose that maximizes targeted toxicity probability, given not overdosing. EUGM, Nov 2019 53 Prior Specification (Direct vs Indirect) Enter directly bivariate Indirectly: normal for log(α) and log(β) : EUGM, Nov 2019 54 10/28/19 27
Prior Specification (Indirect) Assuming logits of toxicity are linear, calculate prior probabilities of toxicity (predicted median) at each dose level Assign a “minimally informative unimodal” Beta distribution at each dose level (Neuenschwander et al., 2008 Appendix A) Generate n sets of logits from Beta distributions, to obtain n estimates of log(α) and log(β) using least squares Use sample means, variance, correlation for bivariate normal EUGM, Nov 2019 55 Modified Toxicity Probability Interval (Mtpi) mTPI is Bayesian like CRM and BLRM, but rule-based like 3+3 Challenges for model-based methods: complexity (esp for non-statisticians); sensitivity to priors EUGM, Nov 2019 56 10/28/19 28
Modified Toxicity Probability Interval (mTPI) “...almost all phase I oncology trials conducted at Merck in past 2 years have been based on the mTPI design” EUGM, Nov 2019 57 Trial Monitoring Table Yuan Ji, KOL Lecture Oct. 2013 EUGM, Nov 2019 58 10/28/19 29
modified Toxicity Probability Interval (mTPI) Probability of toxicity at each dose modeled by independent Beta distributions Set of decision intervals specified (like in BLRM) Dosing decisions determined by 'normalized' posterior probability in each interval at the current dose d i : • Escalate to d i+1 if d i is 'underdosing' • Stay at d i if 'proper dosing' • De-escalate to d i-1 if d i is 'overdosing' EUGM, Nov 2019 59 mTPI Priors “[W] e believe that for phase I trials with small sample sizes...the dependence introduced by prior models will have a strong influence on the operating characteristics...The independent prior models performs quite well compared to existing approaches.” EUGM, Nov 2019 60 10/28/19 30
Equivalence Intervals The Equivalence Interval (EI) is defined as [ p T -ε 1 ; p T +ε 2 ] p T -ε 1 is the lowest toxicity probability that the physician would be comfortable using to treat future patients without dose escalation p T +ε 2 is the highest toxicity probability that the physician would be comfortable using to treat future patients without dose de-escalation EUGM, Nov 2019 61 Unit Probability Mass UPM (interval) = Post Pr(interval) / length(interval) EUGM, Nov 2019 62 10/28/19 31
mTPI Dose Exclusion / Stopping Rule EUGM, Nov 2019 63 Summary Bayesian? Model dose-toxicity? Probability Intervals? (number of parameters) Single Agent Designs 3+3 No No No CRM Yes Yes (1) No BLRM Yes Yes (2) Yes mTPI Yes No Yes Double Agent Designs comb2BLRM Yes Yes (5) Yes PIPE Yes No No EUGM, Nov 2019 64 10/28/19 32
Case Study (Shaw et al 2014) EUGM, Nov 2019 65 EUGM, Nov 2019 66 10/28/19 33
EUGM, Nov 2019 67 EUGM, Nov 2019 68 10/28/19 34
EUGM, Nov 2019 69 Covariate Model NB: The published protocol uses the following covariate model, which is not currently implemented in East ESCALATE . EUGM, Nov 2019 70 10/28/19 35
EUGM, Nov 2019 71 EUGM, Nov 2019 72 10/28/19 36
EUGM, Nov 2019 73 EUGM, Nov 2019 74 10/28/19 37
EUGM, Nov 2019 75 Option: Copy from Excel EUGM, Nov 2019 76 10/28/19 38
EUGM, Nov 2019 77 EUGM, Nov 2019 78 10/28/19 39
EUGM, Nov 2019 79 Prior Specification Options 1. Use prior calculator (indirect methods) 2. Enter informative prior parameters for bivariate normal. Plot & refine. 3. Enter weakly-informative prior parameters for bivariate normal EUGM, Nov 2019 80 10/28/19 40
Prior calculator EUGM, Nov 2019 81 EUGM, Nov 2019 82 10/28/19 41
Weakly-informative priors EUGM, Nov 2019 83 Stopping Rules EUGM, Nov 2019 84 10/28/19 42
Posterior Sampling Methods EUGM, Nov 2019 85 Simulation Controls EUGM, Nov 2019 86 10/28/19 43
To View Simulation Details: In Output Preview, right-click Sim1, select “Save in Workbook” to save to Library. In Library, right-click Sim1, select “Details”. In Library, select Plots icon EUGM, Nov 2019 87 Interim Monitoring Exercise EUGM, Nov 2019 88 10/28/19 44
EUGM, Nov 2019 89 Use default Stopping Rules (none), and Response Generation. Simulate 1 trial, then save to Library. EUGM, Nov 2019 90 10/28/19 45
Open Interim Monitoring Dashboard. Click “Enter Interim Data”. EUGM, Nov 2019 91 Enter Cohort Data As Below. EUGM, Nov 2019 92 10/28/19 46
Match Results? EUGM, Nov 2019 93 EUGM, Nov 2019 94 10/28/19 47
EUGM, Nov 2019 95 EUGM, Nov 2019 96 10/28/19 48
EUGM, Nov 2019 97 EUGM, Nov 2019 98 10/28/19 49
References 3+3 B.E. Storer. Design and analysis of phase I clinical trials. Biometrics, 45:925-937, 1989. mTPI Y. Ji, P. Liu, Y. Li, and N. Bekele. A modified toxicity probability interval method for dose finding trials. Clinical trials, 7:653-656, 2010. CRM J. O’Quigley, M. Pepe, and L. Fisher. Continual reassessment method: A practical design for phase I clinical trials in cancer. Biometrics, 46:33-48, 1990. S.N. Goodman, M.L. Zahurak, and S Piantadosi. Some practical improvements in the continual reassessment method for phase I studies. Statistics in Medicine, 14:1149-1161, 1995 BLRM B. Neuenschwander, M. Branson, and T. Gsponer. Clinical aspects of the Bayesian approach to phase I cancer trials. Statistics in Medicine, 27:2420-2439, 2008. L. W. Huson and N. Kinnersley. Bayesian fitting of a logistic dose– response curve with numerically derived priors. Pharmaceutical Statistics , 8: 279–286, 2009 Combination B. Neuenschwander, et al. A Bayesian Industry Approach to Phase I Combination Trials in Oncology. Statistical Methods in Drug Combination Studies, 95-135, 2015 A.P. Mander and M.J. Sweeting. A product of independent beta probabilities dose escalation design for dual-agent phase I trials. Statistics in Medicine, 34:1261-1276, 2015 EUGM, Nov 2019 99 Shaping the Future of Drug Development Phase I: Dose Escalation With Cohort Expansion 10/28/19 50
Clinical Trial Simulation Define true underlying scenario(s) for endpoint(s), study design(s), decision rule(s) Generate many repetitions Summarize results Use to choose and justify trial design - Demonstrates design performance for a span of potential true scenarios Widely used in Drug Development EUGM, Nov 2019 101 Drug Program Simulation Define a sequence of clinical trial simulations and decision rules and design options for moving from one trial to the next Aim to optimize the sequence of trials for a particular set of drug program objectives EUGM, Nov 2019 102 10/28/19 51
Program Design Design & Simulate Sequence of Trials Two types planned for 6.5: • Dose Escalation followed by a cohort expansion study o Stage1: Dose escalation design (3+3, mTPI, CRM, BLRM) o Stage2: Single-arm cohort expansion o Frequentist or Bayesian GNG rules • Phase 2 oncology trial followed by Group Sequential o Stage1: Single-arm binomial, Simon’s two-stage, or 2-arm survival o Stage2: A group sequential design EUGM, Nov 2019 103 Example: Dose Escalation with Cohort Expansion Stage 1 Parameters: • Design: mTPI Sample Size: 30 • Cohort Size: 3 • • Target Probability of Toxicity: 30% • No. of Doses: 7 EUGM, Nov 2019 104 10/28/19 52
Stage 2 Parameters • Design: Single Proportion GNG rule • Cohort expansion phase Sample Size: 20\ • Clinically meaningful level (k1): 10% • desired level of clinical activity (k2): 20% • Prior: Beta (1, 1) The true response rate is 0.1 for the three lowest doses below the true MTD, and 0.2 for all • doses at the true MTD and higher. EUGM, Nov 2019 105 Design in East Click Program: Program Simulation on the Design tab, and then click Dose Escalation with Cohort Expansion . EUGM, Nov 2019 106 10/28/19 53
Design in East Right-click the Start node and add an mTPI design with all default inputs. EUGM, Nov 2019 107 Design in East Right-click the mTPI node and add a Single Proportion GNG Rule. EUGM, Nov 2019 108 10/28/19 54
Design in East Right-click the mTPI node and add a Single Proportion GNG Rule . EUGM, Nov 2019 109 Design in East Test Parameters Tab EUGM, Nov 2019 110 10/28/19 55
Design in East Response Generation Tab EUGM, Nov 2019 111 Design in East On the Simulation Controls tab, enter Number of simulations as 10000 trials and click Simulate in the bottom right corner. EUGM, Nov 2019 112 10/28/19 56
Analysis • Dose D4 (25 mg) is the true MTD and Dose D5 (40 mg) had a true DLT rate at the upper limit of the Proper Dosing interval (0.35) • These two doses are selected as MTD the most often - 36% and 18%, respectively EUGM, Nov 2019 113 Analysis When doses D4 and D5 are selected as MTD, a Go decision is made most often, around 70% of the time EUGM, Nov 2019 114 10/28/19 57
Shaping the Future of Drug Development Phase II: MCPMod Agenda Introduction to MCPMod • The traditional approach • Why use MCPMod? • Case study • Questions • EUGM, Nov 2019 116 10/28/19 58
Dose-Response Studies Establish Proof-of-Concept (PoC) • Change in dose desirable change in endpoint of interest Dose finding step • Select one (or more) “good” dose levels for confirmatory Phase III once PoC has been established EUGM, Nov 2019 117 Traditional Approach Proof-of-Concept: Conducted using (multiple) active arms and placebo Selection of Target Dose: 1. statistically significant at the proof-of-concept stage 2. smallest of statistically significant doses but also clinically relevant Dose-Response Modeling: 1. use data from PoC and earlier trials 2. find a statistical model capturing the effects of target dose on dose-response EUGM, Nov 2019 118 10/28/19 59
Traditional Approach Straight-forward approach However: • focuses on narrow dose range where sponsors can have faith that they will establish a clear dose-signal dose-response model should itself play a greater role in choosing the right dose • focuses on modeling at the very end of the process • EUGM, Nov 2019 119 MCP vs Mod MCP: • Dose is a qualitative factor • Inference about target dose restricted to the discrete set of doses used in the trial Mod : Dose Response (parametric functional relationship) • Dose is quantitative • Modeling approach validity depends on pre-specification of appropriate dose-response model EUGM, Nov 2019 120 10/28/19 60
Multiple Comparison Procedures – Modelling MCP-step • Establish a dose-response signal (the dose-response curve is not flat) using multiple comparison procedures Mod-step • Estimate the dose-response curve and target doses of interest (ED50, ED90, MED, etc) using modelling techniques Modelling is pre-specified at the design stage Model uncertainty addressed using • A candidate set of models • A procedure on how to perform model selection EUGM, Nov 2019 121 MCP + Mod = MCPMod Design Stage Trial Design Stage • Pre-specification of candidate dose-response models Analysis Stage (MCP-step) • Statistical test for dose- response signal. Model selection based on significant Trial Analysis Stage dose response models Analysis Stage (Mod-step) • Dose response and target dose estimation based on dose-response modeling EUGM, Nov 2019 122 10/28/19 61
MCP + Mod = MCPMod Design Stage Design Stage Trial • Pre-specification of candidate dose-response models Analysis Stage (MCP-step) Analysis Stage Trial • Statistical test for dose- response signal. Model selection based on significant dose response models Analysis Stage (Mod-step) • Dose response and target dose estimation based on dose-response modeling EUGM, Nov 2019 123 List of dose-response models EUGM, Nov 2019 124 10/28/19 62
MCP-Mod : Scope Development Phase Ph II dose-response studies to support dose selection for Phase III • Response can be continuous, binary, count, time-to-event Number of doses, dose-range • Minimum: 2 active doses (for the MCP-step), 3 active doses (Mod step) • Recommendations (rules of thumb): 4-7 active doses, >10-fold dose range Control • MCP-step makes most sense when there is a placebo control in the trial Bjorn Bornkamp, EFSPI Meeting, Nov 2015 EUGM, Nov 2019 125 Regulatory Opinion CHMP: First opinion issued in 2010, since then 12 qualification opinions (biomarkers, technologies/devices, simulation models) • MCP-Mod first statistical methodology qualified FDA: Issued its Fit-for-Purpose (FFP) designation for guiding dose selection for Phase III testing. • https://www.fda.gov/downloads/Drugs/DevelopmentApprovalProcess/UCM508700.pdf EUGM, Nov 2019 126 10/28/19 63
Example: Continuous Data BIOM study • randomized double-blind parallel group trial with patients being allocated to either placebo or one of four active doses coded as 0.05, 0.20, 0.60, and 1 • Response variable is baseline adjusted abdominal pain score larger values correspond to better treatment effect • EUGM, Nov 2019 127 Example: The Design Part One-sided type I error of 0.05 • Calculate Power for a total sample size of 100 • EUGM, Nov 2019 128 10/28/19 64
Example: The Design Part • Candidate Models: EUGM, Nov 2019 129 Example: Patient Allocation Optimized: Equal: EUGM, Nov 2019 130 10/28/19 65
Example: Output Summary EUGM, Nov 2019 131 Example: Output Details EUGM, Nov 2019 132 10/28/19 66
Example: Power Plot for Mean Power fct EUGM, Nov 2019 133 Example: Sample Size for 90% Mean Power EUGM, Nov 2019 134 10/28/19 67
Example: The Analysis Part The Dataset Consists Of Following Variables: • subjectID - This corresponds to the subject ID in the trial. • dose - The dose values administered to these subjects. • resp - The baseline adjusted abdominal pain score for subjects EUGM, Nov 2019 135 Example: The Analysis Part The Set Of Candidate Models Includes : 1. emax1 : Emax(0.2) 2. linlog1 : Lin in Log Dose 3. linear1 : Linear 4. expn1 : Exponential(1.13) 5. quad1 : Quadratic(-0.7322) 6. beta1 : Beta(2,4) EUGM, Nov 2019 136 10/28/19 68
Example: The Analysis Part Some More About The Options Used: • Significant models will be selected using the pValue method (adjusted p-values). • The adequate model will be selected based on its AIC (default choice). Estimate: Target dose is specified as the dose level that achieves a target effect of • Delta over placebo EUGM, Nov 2019 137 Example: The Analysis Part EUGM, Nov 2019 138 10/28/19 69
Example: Analysis/Candidate Models EUGM, Nov 2019 139 Example: Analysis/Candidate models EUGM, Nov 2019 140 10/28/19 70
Analysis: Output EUGM, Nov 2019 141 Analysis: Output MCP Part: Multiple Contrast test: Observe that the adjusted p-values for all models except • Beta are smaller than 0 . 05 Mod part: Fit the significant models to the data and estimate the target dose. • • Model selection is based on the AIC criterion EUGM, Nov 2019 142 10/28/19 71
Analysis: Output EUGM, Nov 2019 143 Analysis: Output EUGM, Nov 2019 144 10/28/19 72
Analysis: Output Modelling part: • Based on the model selection criteria of minimum AIC, LinLog is the adequate model. • The corresponding target dose is 0.6. • The target doses on continuous scale differ for the different models though. Emax calculates it approximately as 0.289, LinLog as 0.299 and Quadratic as 0.387. EUGM, Nov 2019 145 References Bornkamp, B. et al (2007) Innovative Approaches for Designing and Analyzing Adaptive • Dose-Ranging Trials, Journal of Biopharmaceutical Statistics, 17, 965-995 Bretz, F., Pinheiro, J.C., and Branson, M. (2005) Combining multiple comparisons and • modeling techniques in dose-response studies. Biometrics, 61, 738–748 • EMA (2014) Qualification opinion of MCP-Mod as an efficient statistical methodology for model-based design and analysis of Phase II dose finding studies under model uncertainty, http://goo.gl/imT7IT • Pinheiro, J.C., Bornkamp, B., Glimm, E., and Bretz, F. (2014) Model-based dose finding under model uncertainty using general parametric models. Statistics in Medicine, 33, 1646–1661 EUGM, Nov 2019 146 10/28/19 73
Shaping the Future of Drug Development Phase II/III: Multi-Arm Multi-Stage Designs East MAMS MULTI-STAGE MULTI ARM DESIGNS SUCCESSFUL OUTCOME: Compare Operating Characteristics Of Multi-arm Group Sequential Designs • 2-stage “Treatment Selection” design using p-value combination approach by Posch et. al. (Statistics in Medicine, 2005) Functions: • MAMS design – Extension of GSD to more than 2 arms • Identification of promising therapies and inference on selected treatments performed in two or more stages Benefits: • Multiple treatments to be compared with a control • Allows several primary research questions to be answered in a single trial with increased efficiency compared to separate trials • Binomial multi-stage; Survival p-value combination New in 6.5: EUGM, Nov 2019 148 10/28/19 74
Overview Two-stage Multi-Arm Designs using p-value combination • Multi-stage Multi-Arm Designs (MaMs) • EUGM, Nov 2019 149 Two-Stage Design: Motivation • Identification of promising therapies and inference on selected treatments performed in two stages • Multiple treatments to be compared with a control • After interim analysis in first stage, trial may be terminated or continued with second stage • Set of treatments may be reduced due to lack of efficacy • presence of safety problems with some of the treatments • Highly flexible procedure with possible re-estimation of the sample size for the second stage EUGM, Nov 2019 150 10/28/19 75
Example: Acute Coronary Syndrome • Placebo controlled, double blind, randomized trial to evaluate the efficacy, pharmacokinetics, safety and tolerability of a New Chemical Entity (NCE) given as multiple weekly infusions in subjects with a recent acute coronary syndrome • Four dose regimens to be investigated • Treatment effect is assessed through change in PAV (percent atheroma volume) from baseline to Day 36 2-stage adaptive design • Stage 1: 250 subjects randomized equally to one of four treatment arms and placebo • Stage 2: continue with additional 225 subjects enrolling into 1/2/3 arms or stop due to • toxicity One-sided level 0.025 test • EUGM, Nov 2019 151 Design in East Setting est parameters EUGM, Nov 2019 152 10/28/19 76
Design in East Specifying Stopping Boundaries EUGM, Nov 2019 153 Design in East Specifying response generation EUGM, Nov 2019 154 10/28/19 77
Design in East Treatment selection for stage II EUGM, Nov 2019 155 Keeping Best Two Treatments In Stage II EUGM, Nov 2019 156 10/28/19 78
Keeping All Four Treatments In Stage II EUGM, Nov 2019 157 Keeping Only Treatments Within Ε = 0.05 In Stage II EUGM, Nov 2019 158 10/28/19 79
Maintaining Type I Error EUGM, Nov 2019 159 Design Under Different Alternative Hypotheses EUGM, Nov 2019 160 10/28/19 80
Sample Size Re-Estimation At Interim EUGM, Nov 2019 161 Multi-Stage Design: Motivation • Identification of promising therapies and inference on selected treatments performed in two or more stages • Multiple treatments to be compared with a control • Allows several primary research questions to be answered in a single trial with increased efficiency compared to separate trials Various modifications lead to distinct MaMs designs • group-sequential MaMs designs • drop-the-loser(s) designs • EUGM, Nov 2019 162 10/28/19 81
MaMs in EAST • Generalization of group sequential design to more than two arms • An alternative to the combination function approach of Posch et. al. (SiM, 2005) • Current implementation: trial stops if any arm crosses efficacy boundary • • trial stops if all arms cross futility boundary drop the losers at each interim look • Under development: dose selection and adaptive SSR • EUGM, Nov 2019 163 Mathematical Framework K-look GSD • Only 1 comparison to a control, made K times - K i 1 å [ ] ! é ù P ( W < e and W ³ e ) = a ë û 0 j j i i i 1 = = j 1 K-look MAMS: • D comparisons to common control, made K times • Generalization of Dunnett’s test K i 1 - å [ ] ! ( é < ù ³ = a P max{W ...W } e and max{W ...W } e ) ë û 0 j1 jD j i1 iD i = i 1 j 1 = 10/28/19 82
Boundary Computations Two Arm Tria l: • W j , j=1,2,3, are scalars. Trial stops if W 1 ≥e 1 or W 2 ≥e 2 or W 3 ≥e 3 • We want P 0 (W 1 ≥e 1 or W 2 ≥e 2 or W 3 ≥e 3 )=α • Computations are simplified because W j and (W j -W j-1 ) are independent EUGM, Nov 2019 165 Boundary Computations Multi-Arm Trial: • W j =(W j1 ,W j2 ,...W jD ) are vectors. Trial stops if max(W 11 ,W 12 ,...W 1D )≥e 1 or max(W 21 ,W 22 ,...W 2D )≥e 2 or max(W 31 ,W 32 ,...W 3D )≥e 3 • Want P 0 {max(W 11 ,W 12 ,...W 1D )≥e 1 or max(W 21 ,W 22 ,...W 2D )≥e 2 or max(W 31 ,W 32 ,...W 3D )≥e 3 }= α • Computations are complex because the components (W j1 ,W j2 ,...W jD ) are correlated whereas W j and (W j -W j-1 ) are independent EUGM, Nov 2019 166 10/28/19 83
Inhance Trial: Chronic Obstructive Pulmonary Disease Once daily bronchodilators for COPD (Am. J. Respiratory & Critical Care, vol 182, 2010) Compare three doses (150 mg, 300 mg, 500 mg) of Indacaterol to Placebo Endpoint: Week 12 change from baseline in 24 hour trough FEV1 Expect differences from placebo of between 0.14 and 0.18 liters with standard deviation s =0.5 Design for 90% power at one-sided a =0.025 Two-Arm, Three-look GSD Requires 165 patients/arm for d =0.18, s =0.5 Expected sample size under H 1 is 132/arm 10/28/19 84
Four-Arm, Three-look MAMS Requires 130 patients/arm for d =0.18, s =0. Expected sample size under H 1 is 105/arm EUGM, Nov 2019 169 Compare the 2 Arm & 4-Arm Boundaries 2-arm Boundaries On Z-scale 4-arm boundaries on Z-scale EUGM, Nov 2019 170 10/28/19 85
Higher Hurdle With 4-arm Trial Table of Boundary Comparisons Plot of Boundary Comparisons Info Two Four Look Fraction Arm Arm 1 0.333 3.704 3.976 2 0.667 2.514 2.856 3 1.0 1.992 2.391 EUGM, Nov 2019 171 Boundary and Sample Size Comparison The boundaries for the 4-arm trial are higher than for the 2 arm trial This compensates for the greater probability of boundary crossing under H 0 But the sample size/arm is lower for 4-arm trial. (More chances to exit under H 1 ) What would happen if the value of d was not the same for each treatment 10/28/19 86
4-arm Design With Different D Values • Same boundaries, but requires commitment of 169/arm • Expected sample size under H 1 is 136/arm • Here 4-arm design requires more patients/arm than 2-arm design • The higher efficacy boundary hurdle is not offset by extra opportunities to cross the efficacy boundary because only one dose has a strong effect EUGM, Nov 2019 173 Introduce A Futility Boundary For 676 Patient Trial With D =(0.18, .14, .14) EUGM, Nov 2019 174 10/28/19 87
Impact of futility boundary; 2% power drop • Power dropped to 88% due to introduction of a futility boundary • The efficacy boundary is unchanged since futility boundary is non-binding • Trial stops for futility only if ALL the arms cross the futility boundary • But individual arms that cross the futility boundary will be dropped EUGM, Nov 2019 175 Simulate Trial For Additional Insight EUGM, Nov 2019 176 10/28/19 88
More Simulation Details EUGM, Nov 2019 177 Marginal & Detailed Outcome Tables EUGM, Nov 2019 178 10/28/19 89
What If Two Treatments Were Ineffective EUGM, Nov 2019 179 More Simulation Details EUGM, Nov 2019 180 10/28/19 90
Marginal & Detailed Outcome Tables EUGM, Nov 2019 181 Simulation under the global null EUGM, Nov 2019 182 10/28/19 91
Shaping the Future of Drug Development Phase III: Group Sequential Designs -- Survival East SEQUENTIAL SUCCESSFUL OUTCOME: Compare operating characteristics of group sequential designs Pre-Requisites: East BASE • Extensive selection families of stopping rules for efficacy and futility • Display boundaries on multiple scales. Functions: • Optimize trial design for savings in sample size, study duration, & cost • Conditional and Predictive Power calculations for interim decisions • Equivalence Group Sequential Designs New in 6.5: EUGM, Nov 2019 184 10/28/19 92
East SURVIVAL Test Survival Endpoints In Superiority & Non-inferiority Studies Compute Events, Sample Size, Study Duration, For SUCCESSFUL OUTCOME: Complex Survival Designs Pre-Requisites: East SEQUENTIAL • Variable & fixed subject follow-up • Piecewise hazard rates, accruals, & dropouts Functions: • Charts for predicting events/sample size, accrual & study duration • Simulate non-proportional hazards • Go-No-Go Based on Surrogate Endpoints New in 6.5: EUGM, Nov 2019 185 Survival Studies For studies with survival or time-to-event endpoints, the asymptotic distribution theory and the derivation of stopping boundaries remains the same There are however some special considerations The information is directly proportional to the number of events • Thus the number of events, not the number of patients, determines the power of the study • If study duration is not fixed, there is a trade-off between sample size and study duration. • EUGM, Nov 2019 186 10/28/19 93
Survival Studies If we recruit more patients to the study, we obtain the required number of events sooner and the total study duration is reduced EUGM, Nov 2019 187 Example: The JUPITER Study • Justification for the Use of Statins in Prevention: an Intervention Trial Evaluating Rosuvastatin (JUPITER) examined the question of whether treatment with 20 mg of rosuvastatin daily, as compared with placebo, would reduce the rate of first major cardiovascular events (Ridker et al., 2008) EUGM, Nov 2019 188 10/28/19 94
Example: The JUPITER study (cont.) • JUPITER was a randomized, double-blind, placebo-controlled, multicenter trial conducted between 2003 and 2008 by AstraZeneca at 1315 sites in 26 countries Composite primary endpoint: occurrence of a first major cardiovascular event, • defined as nonfatal myocardial infarction, nonfatal stroke, hospitalization for unstable angina, an arterial revascularization procedure, or confirmed death from cardiovascular causes EUGM, Nov 2019 189 Example: The JUPITER study (cont.) • Designed for statistical power of 90% to detect a 25% reduction in the rate of the primary end point, with a two-sided significance level of 0.05 We are interested in a 25% reduction in the rate of the primary endpoint, • i.e. a hazard ratio λ t = λ c = 0.75; the effect size is thus δ = -ln(λ t /λ c ) = 0.2877 • Baseline hazard rate in placebo arm of 0.0077 • Study to complete in 7.5 years, with 4 years accrual and 3.5 years of follow-up • Two interim analyses are planned with LD(OF) spending function defined boundaries at 37.5% and 75% of the information • How do we design such a trial? EUGM, Nov 2019 190 10/28/19 95
JUPITER Study Design in East We can use the Logrank Test Given Accrual Duration and Study Duration design in • East to obtain a 3-look GSD for the JUPITER trial East tells us that the required number of events is Dmax = 517 as previously • determined, and that we will require 14,229 subjects accrued over 4 years EUGM, Nov 2019 191 Planning for DMC Meetings The Events vs. Time Chart is useful in planning for interim analyses & DMC meetings; • eg., after the second look, 389 events should occur roughly 6.1 years into the study assuming the treatment effect is δ 1 EUGM, Nov 2019 192 10/28/19 96
JUPITER Design Dropouts Dropouts: 5% per year in both the treatment and placebo arms • • Like events: Dropouts assumed exponential, with corresponding hazard rates Like Cumulative % survival: Cumulative % dropout calculated for patient • time (from study entry), not calendar time (from study start) EUGM, Nov 2019 193 JUPITER Design Accruals • Non constant accrual (piece-wise linear): 15% by end of year 1; 35% by end of year 2; 65% by end of year 3 EUGM, Nov 2019 194 10/28/19 97
Revisited JUPITER Design in East Note that since we have not changed the effect size δ 1 that we are powering the trial for, Dmax = 517 has not changed. However, the dropouts and slow starting accrual means we now need 17,344 patients if we want to finish the study within 7.5 years EUGM, Nov 2019 195 Surrogate Endpoints in Survival Studies EUGM, Nov 2019 196 10/28/19 98
Background Most time to event endpoint requires longer follow-up. • Any early stopping (futility) decision using primary endpoint only be performed at late time • point trial. • Secondary endpoint (PFS, DFS, ORR) can be used to make Go-No Go decision about the trial without inflating type I error. EUGM, Nov 2019 197 Example : Malignant Mesothelioma Available treatments are macroscopic complete resection or systemic chemotherapy • Median survival time is 1.5 years in average. • • Recently a newer type of treatment being tested on mesothelioma is gene therapy. • Consider a study to evaluate a new gene therapy treatment compared against placebo in patients with MPM after completing surgery + chemotherapy EUGM, Nov 2019 198 10/28/19 99
2 Stage GSD Based on OS Primary Endpoint: Overall survival (OS) • 2-stage GSD at 0.025 alpha (1-sided); LD(OF) spending function efficacy; Median OS of 16 • months in the placebo group vs a 24 months on the new treatment. • 30 months Accrual Duration and final analysis will be taken at month 48. • Detecting 90% power required 257 events and sample size 192 on each arm (total 382). EUGM, Nov 2019 199 Interim Analysis • IA at 28 months(129 OS events). • 90% of total population will be enrolled by 28 months and therefore stopping for futility at IA only saves 8% resources.\ • Stopping for futility earlier will force us to stop without seeing 50% of planned number of events. Should consider secondary endpoint like PFS, ORR. • Each patient will have regular PFS assessment in every 3 months for at least 3 years o Median PFS is 8 months in the placebo and 11 months o Correlation between OS and PFS is 0.75 o EUGM, Nov 2019 200 10/28/19 100
Recommend
More recommend
