East Training EUGM Day 2 Pantelis Vlachos - - PDF document

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Shaping the Future

• f Drug Development

East Training EUGM Day 2

Pantelis Vlachos Pantelis.Vlachos@cytel.com

Agenda

• Cytel Software map
• East Overview/Introduction
• Phase I: Dose Escalation with cohort expansion (ESCALATE + PROGRAM)
• Phase II: Model-based dose finding (MCPMod)
• Phase II/III: Multi-Arm Multi-Stage designs (MAMS)
• Phase III: Group Sequential designs for TTE (SURVIVAL)
• Phase III: Unblinded Sample-Size Re-estimation (SURVADAPT)
• Phase III: Adaptive Population Enrichment (ENRICH)
• Q/A

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Software Solutions

DATA ANALYSIS CLINICAL TRIAL DESIGN CLINICAL OPERATIONS EUGM, Nov 2019 3

Cytel Software Solutions

COMMERCIA L PROPRIETARY TOOLS EUGM, Nov 2019 4

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Shaping the Future

• f Drug Development

East overview

1994 2000 2010

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Broad coverage of designs for biostatisticians One integrated tool for all types of designs: fixed sample, group sequential or adaptive Superior User Interface

• Multiple windows with graphs and tables
• Organized storage of designs in workbooks

Rapid creation, viewing and filtering of multiple scenarios for design parameters Commitment to continuous improvement and expansion of features

What Is Special About The New East?

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East 6.5 (Three New Modules)

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East BASE

Complete package for fixed-sample clinical trial designs

Functions:

• Wide variety of fixed sample options (Normal, Binomial, Survival endpoints)
• Multiple scenarios in one go
• Complex patterns of accruals, dropouts and response lag
• Run R functions
• Bayesian probability of success (Normal / Binomial/Survival)

New in 6.5:

• Super Superiority designs

SUCCESSFUL OUTCOME:

Test variety of superiority, non-inferiority, equivalence, and confidence-interval based designs

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Intro To East

• Introduction to the new East on the Architect platform
• A Normal-Endpoint Example to Illustrate New Features of East

Schizophrenia Trial: illustrates more flexible boundaries; delayed response; incorporating Bayesian priors into design

• Q & A

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Two arm trial: asenapine vs. olanzapine (control) Primary endpoint is negative symptoms assessment (NSA) on 24-point scale observed at week 26 Design for d = 2 and s = 7.5 with two sided a=0.05 and 80% power But d could be as small as 1.6 so examine a range of sample size requirements Enrollment ramps up to 8 patients/week Up to 8% drop-outs anticipated

Example 1: Schizophrenia Trial Input Window

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Inputs With Output Preview

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Use Of Filter To Eliminate Designs

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Convert Single Look Design into GSD

First save the selected design(s) to the library for further editing Then change number of looks and boundary information

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View the Boundaries & Compute

With futility boundary, sample size has increased to 625 patients

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Bayesian Probability of Success (Assurance)

Assign a prior distribution to d to capture the uncertainty associated with it

The “Assurarce” of success is only 0.685 due to uncertainty about d In this case the “Assurance is 0.798 due to less uncertainty about d

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Compare Design Summaries

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Incorporate Delayed Response & Dropouts

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Compare Designs With & Without Lag

• Notice that, due to

the 26 week response lag, there is very little saving in expected sample size.

• Maximum study

duration is 110 weeks

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Reason for lack of sample size saving in GSD when there is a long delay in the primary response

• The is a large gap (> 208 patients) between sample size and completers
• By the time 669 completers for IA 3 the total enrollment is over. Hence

no saving of sample size if trial stops at look 3

• But, there is a saving of time; trial stops 20 weeks earlier if stopped at look

3

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Examine Final Design in Detail

Icons for viewing design details, graphs, tables and summaries

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Shaping the Future

• f Drug Development

Phase I: Dose Escalation East ESCALATE

ADAPTIVE PHASE 1 DOSE-ESCALATION STUDIES

Description:

• Simulate dose-toxicity profiles and designs
• Dose recommendations for next cohort of patients
• Methods include: 3+3, Continual Reassessment Method, Bayesian

Logistic Regression Model, and modified Toxicity Probability Interval

• Dual-agent dose combination designs (BLRM, PIPE)

Benefits:

• Better characterization of the MTD
• Clearly communicate critical information to clinicians
• Improve screening and selection of active agents to carry forward

New in 6.5: • mTPI-2

Pre-Requisites: East BASE

SUCCESSFUL OUTCOME: IDENTIFICATION OF THE MAXIMUM TOLERATED DOSE (MTD)

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Phase I Dose-Escalation Trials

• Assess dose-toxicity relationship
• First-in-human (FIH) studies – single agent
• Determine maximum tolerated dose (MTD) or recommended phase II dose (RP2D)
• Observe Dose limiting toxicities (DLTs)
• Combination dose finding studies (Phase Ib)
• Same primary objective as FIH studies
• Combination of two (or more) drugs
• Addition of a new drug to a registered treatment to increase efficacy

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East ESCALATE (Summary)

Bayesian? Model dose-toxicity? (number of parameters) Probability Intervals? 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

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Single-Agent Dose Escalation

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Phase I dose-escalation (general frame)

Only consider trials with fixed doses. A sequence of K doses, d1,d2,…,dK, as candidates. Dose i has a toxicity probability of pi (unknown). Monotonicity : pi < pi+1 Goal: to find the MTD , defined as the highest dose with toxicity rate lower (or close to) a fixed rate, pT, e.g., pT = 0.30.

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Ethical Requirement

“The major difficulty in phase I trial design and conduct is the ethical requirement that the number of patients in the trial who experiencetoxicity must be limited.”

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Other Challenges and Design Requirements

Alessandro Matano, Novartis, http://www.smi-online.co.uk/pharmaceuticals/archive/4-2013/conference/adaptive-designs

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Rule-based vs Model-based

Rule-based Model-based

Applicability Easy More complex due to statistical component (e.g. evidence-based prior derivation) Flexibility Not very flexible

• Fixed cohort size
• Fixed doses

Flexible: allows for

• Different cohort sizes
• Intermediate doses

Extensibility Rather difficult Easily extendable

• 2 or more treatment arms
• combinations

Inference for true DLT rates Observed DLT rates

• nly

Full inference, uncertainty assessed for true DLT rates Statistical requirements None “reasonable” model, “good” statistics Decisions Algorithm decides Clinically-driven recommendations

(Based on Matano. Bayesian Adaptive Designs for Oncology Phase 1 Trials, 2013)

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The “standard” design

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3+3 (Prevalence)

Over 98% of published Phase 1 trials (1991-2006) use variations of 3+3

(Rotgako et al., 2007)

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94% In Trials Until 2014

The 3+3 design

Rule Based Design Start by allocating lowest dose level to first cohort Adaptively Escalate/De-escalate based on observed DLTs Maximum tolerated dose (MTD) is considered highest dose at which 1 or 0 out of six patients experiences DLT. Doses need to be pre-specified Different versions: 3+3L, 3+3Lmod and 3+3H

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The 3+3 Design (Schematic)

Yuan Ji, KOL Lecture Oct. 2013

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Advantages

Simplicity Of Design, Execution, Inference Meet Ethical Needs Of Exploring Low Doses First Provide Simple, Operational Definition Of The Target Dose Considerable Clinical Experience And Comfort With Their Use They Can Be Easily Studied Quantitatively And Possibly Improved

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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

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(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

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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%.

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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.

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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

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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

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Bayesian Framework

(Based on Matano. Bayesian Adaptive Designs for Oncology Phase 1 Trials, 2013)

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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 pT (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

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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

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Modified CRM

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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.”

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CRM Simulation Parameters

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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

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Bayesian Logistic Regression Model (BLRM)

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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

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Bayesian Logistic Regression Model (BLRM) Bayes Risk

Choose dose that minimizes posterior expected loss.

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Escalation With Overdose Control (EWOC)

• Choose dose that maximizes targeted toxicity probability, given not overdosing.

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Prior Specification (Direct vs Indirect)

Enter directly bivariate normal for log(α) and log(β):

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Indirectly:

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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

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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

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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”

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Trial Monitoring Table

Yuan Ji, KOL Lecture Oct. 2013

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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 di :

• Escalate to di+1 if di is 'underdosing'
• Stay at di if 'proper dosing'
• De-escalate to di-1 if di is 'overdosing'

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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.”

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Equivalence Intervals

The Equivalence Interval (EI) is defined as [pT-ε1; pT +ε2] pT-ε1 is the lowest toxicity probability that the physician would be comfortable using to treat future patients without dose escalation pT +ε2 is the highest toxicity probability that the physician would be comfortable using to treat future patients without dose de-escalation

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Unit Probability Mass

UPM (interval) = Post Pr(interval) / length(interval)

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mTPI Dose Exclusion / Stopping Rule

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Summary

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Bayesian? Model dose-toxicity? (number of parameters) Probability Intervals? 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

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Case Study (Shaw et al 2014)

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NB: The published protocol uses the following covariate model, which is not currently implemented in East ESCALATE.

Covariate Model

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Option: Copy from Excel

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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

Prior Specification Options

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Prior calculator

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Weakly-informative priors

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Stopping Rules

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Posterior Sampling Methods

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Simulation Controls

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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

To View Simulation Details:

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Interim Monitoring Exercise

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Use default Stopping Rules (none), and Response Generation. Simulate 1 trial, then save to Library.

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Open Interim Monitoring Dashboard.

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Click “Enter Interim Data”.

Enter Cohort Data As Below.

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Match Results?

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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

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Shaping the Future

• f Drug Development

Phase I: Dose Escalation With Cohort Expansion

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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

Clinical Trial Simulation

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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

Drug Program Simulation

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Program Design

Design & Simulate Sequence of Trials Two types planned for 6.5:

• Dose Escalation followed by a cohort expansion study
• Stage1: Dose escalation design (3+3, mTPI, CRM, BLRM)
• Stage2: Single-arm cohort expansion
• Frequentist or Bayesian GNG rules
• Phase 2 oncology trial followed by Group Sequential
• Stage1: Single-arm binomial, Simon’s two-stage, or 2-arm survival
• Stage2: A group sequential design

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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

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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.

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Design in East

Click Program: Program Simulation on the Design tab, and then click Dose Escalation with Cohort Expansion.

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Design in East

Right-click the Start node and add an mTPI design with all default inputs.

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Design in East

Right-click the mTPI node and add a Single Proportion GNG Rule.

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Design in East

Right-click the mTPI node and add a Single Proportion GNG Rule.

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Design in East

Test Parameters Tab

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Design in East

Response Generation Tab

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Design in East

On the Simulation Controls tab, enter Number of simulations as 10000 trials and click Simulate in the bottom right corner.

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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

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Analysis

When doses D4 and D5 are selected as MTD, a Go decision is made most

• ften, around 70% of the time

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Shaping the Future

• f Drug Development

Phase II: MCPMod

Agenda

• Introduction to MCPMod
• The traditional approach
• Why use MCPMod?
• Case study
• Questions

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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

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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

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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

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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

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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

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MCP + Mod = MCPMod

Design Stage

• Pre-specification of candidate

dose-response models Analysis Stage (MCP-step)

• 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

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Trial Design Stage Trial Analysis Stage

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MCP + Mod = MCPMod

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Trial Design Stage Trial Analysis Stage

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Design Stage

• Pre-specification of candidate

dose-response models Analysis Stage (MCP-step)

• 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

List of dose-response models

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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

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Bjorn Bornkamp, EFSPI Meeting, Nov 2015

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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

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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

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Example: The Design Part

• One-sided type I error of 0.05
• Calculate Power for a total sample size of 100

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Example: The Design Part

• Candidate Models:

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Example: Patient Allocation

Optimized: Equal:

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Example: Output Summary

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Example: Output Details

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Example: Power Plot for Mean Power fct

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Example: Sample Size for 90% Mean Power

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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

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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)

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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

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Example: The Analysis Part

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Example: Analysis/Candidate Models

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Example: Analysis/Candidate models

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Analysis: Output

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Analysis: Output

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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

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Analysis: Output

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Analysis: Output

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Analysis: Output

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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.

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References

146

• 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

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Shaping the Future

• f Drug Development

Phase II/III: Multi-Arm Multi-Stage Designs

East MAMS

MULTI-STAGE MULTI ARM DESIGNS

Functions:

• 2-stage “Treatment Selection” design using p-value combination approach by Posch et. al.

(Statistics in Medicine, 2005)

• MAMS design – Extension of GSD to more than 2 arms

Benefits:

• 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

New in 6.5:

• Binomial multi-stage; Survival p-value combination

SUCCESSFUL OUTCOME: Compare Operating Characteristics Of Multi-arm Group Sequential Designs

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Overview

• Two-stage Multi-Arm Designs using p-value combination
• Multi-stage Multi-Arm Designs (MaMs)

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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

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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

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Design in East

Setting est parameters

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Design in East

Specifying Stopping Boundaries

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Design in East

Specifying response generation

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Design in East

Treatment selection for stage II

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Keeping Best Two Treatments In Stage II

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Keeping All Four Treatments In Stage II

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Keeping Only Treatments Within Ε = 0.05 In Stage II

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Maintaining Type I Error

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Design Under Different Alternative Hypotheses

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Sample Size Re-Estimation At Interim

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Multi-Stage Design: Motivation

• Identification of promising therapies and inference on selected treatments performed in two
• r 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

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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

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K-look GSD

• Only 1 comparison to a control, made K times

K-look MAMS:

• D comparisons to common control, made K times
• Generalization of Dunnett’s test

Mathematical Framework

[ ]

i 1 K j1 jD j i1 iD i i 1 j 1

P max{W ...W } e and max{W ...W } e )

• =

=

é ù ( < ³ = a ë û

å !

[ ]

i 1 K j j i i i 1 j 1

P W e and W e )

• =

=

é ù ( < ³ = a ë û

å !

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Boundary Computations

165

Two Arm Trial:

• Wj, j=1,2,3, are scalars. Trial stops if

W1≥e1 or W2≥e2 or W3≥e3

• We want P0(W1≥e1 or W2≥e2 or W3≥e3)=α
• Computations are simplified because Wj and (Wj-Wj-1) are independent

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Boundary Computations

166

Multi-Arm Trial:

• Wj=(Wj1,Wj2,...WjD) are vectors. Trial stops if

max(W11,W12,...W1D)≥e1 or max(W21,W22,...W2D)≥e2 or max(W31,W32,...W3D)≥e3

• Want P0{max(W11,W12,...W1D)≥e1 or max(W21,W22,...W2D)≥e2 or

max(W31,W32,...W3D)≥e3}= α

• Computations are complex because the components (Wj1,Wj2,...WjD) are

correlated whereas Wj and (Wj-Wj-1) are independent

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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

Inhance Trial: Chronic Obstructive Pulmonary Disease

Requires 165 patients/arm for d=0.18, s=0.5 Expected sample size under H1 is 132/arm

Two-Arm, Three-look GSD

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Four-Arm, Three-look MAMS

Requires 130 patients/arm for d=0.18, s=0. Expected sample size under H1 is 105/arm

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Compare the 2 Arm & 4-Arm Boundaries

2-arm Boundaries On Z-scale 4-arm boundaries on Z-scale

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Table of Boundary Comparisons

Look Info Fraction Two Arm Four Arm 1 0.333 3.704 3.976 2 0.667 2.514 2.856 3 1.0 1.992 2.391

Plot of Boundary Comparisons

Higher Hurdle With 4-arm Trial

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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 H0 But the sample size/arm is lower for 4-arm trial. (More chances to exit under H1) What would happen if the value of d was not the same for each treatment

Boundary and Sample Size Comparison

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4-arm Design With Different D Values

• Same boundaries, but requires commitment of 169/arm
• Expected sample size under H1 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

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Introduce A Futility Boundary For 676 Patient Trial With D=(0.18, .14, .14)

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Impact of futility boundary; 2% power drop

175

• 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

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Simulate Trial For Additional Insight

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More Simulation Details

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Marginal & Detailed Outcome Tables

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What If Two Treatments Were Ineffective

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More Simulation Details

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Marginal & Detailed Outcome Tables

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Simulation under the global null

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Shaping the Future

• f Drug Development

Phase III: Group Sequential Designs -- Survival

East SEQUENTIAL

Functions:

• Extensive selection families of stopping rules for efficacy and futility
• Display boundaries on multiple scales.
• Optimize trial design for savings in sample size, study duration, & cost
• Conditional and Predictive Power calculations for interim decisions

New in 6.5:

• Equivalence Group Sequential Designs

Pre-Requisites: East BASE

SUCCESSFUL OUTCOME: Compare operating characteristics of group sequential designs

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East SURVIVAL

Test Survival Endpoints In Superiority & Non-inferiority Studies

Functions:

• Variable & fixed subject follow-up
• Piecewise hazard rates, accruals, & dropouts
• Charts for predicting events/sample size, accrual & study duration
• Simulate non-proportional hazards

New in 6.5:

• Go-No-Go Based on Surrogate Endpoints

Pre-Requisites: East SEQUENTIAL

SUCCESSFUL OUTCOME:

Compute Events, Sample Size, Study Duration, For Complex Survival Designs

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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.

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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

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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

• f rosuvastatin daily, as compared with placebo, would reduce the rate of first

major cardiovascular events (Ridker et al., 2008)

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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

189 EUGM, Nov 2019

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 λt= λc = 0.75; the effect size is thus δ = -ln(λt /λc ) = 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?

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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

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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 δ1

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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)

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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

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Revisited JUPITER Design in East

Note that since we have not changed the effect size δ1 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

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Surrogate Endpoints in Survival Studies

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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.

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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

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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).

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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
• Median PFS is 8 months in the placebo and 11 months
• Correlation between OS and PFS is 0.75

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Event vs Time Chart

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Simulation Results

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Shaping the Future

• f Drug Development

Phase III: Sample Size Re-Estimation East ADAPT / SURVADAPT

Incorporate Unblinded Sample Size Re-estimation Rules

Functions:

• Adaptive rules for increasing sample size, or other possibilities
• Methods include CHW, CDL, Müller-Schäfer
• Specific adaptive tools for survival (eg., adapt sample size and events)
• Müller-Schäfer Method for Interim Monitoring
• Unique to East:
• Promising Zone Design based on unblinded interim data
• Adjusted unbiased point estimates, confidence Intervals, and p-values

New in 6.5:

• SSR for Non-Inferiority designs

SUCCESSFUL OUTCOME: Improve statistical power when results are ‘promising’

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Adaptive SSR

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We don't know what δ and σ to power the study for

• Prior experience limited to small pilot studies
• Improved standard of care dilutes treatment effect
• Powering for smallest clinically important effect expensive
• Better safety profile at interim might justify smaller δ
• Opportunity to combine internal and external data

If only σ is unknown, blinded SSR is recommended by FDA

Motivation for Mid-Course Sample Size Correction in Pivotal Trials

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Large effects are uncommon, but designing for very small clinically meaningful effects requires huge up- front investments that management will not approve. A strategy of staged investment is more practical

• Unreliability of Pilot Studies: Most large treatment effects emerge from small studies, and when

additional trials are performed, the effect sizes typically become much smaller. Well-validated large eff ects are uncommon and pertain to nonfatal outcomes. Pereira et. al., JAMA. 2012; 308(16): 1676-1684

• Milestone-Driven Investment: Sunesis Pharmaceuticals to Implement One-Time Sample Size

Increase to Phase 3 VALOR Trial in AML. DSMB Recommends Increase Following Single, Pre- Planned Interim Efficacy and Safety Analysis of VALOR; DSMB Recommendation Triggers $25.0 Million Investment in Sunesis from Royalty Pharma. Press Release, September 11, 2012. Sunesis Pharma, South San Francisco

Why Not Design For The Smallest Clinically Meaningful Treatment Effect?

207

Two arm, multicenter trial with second line therapy for metastatic non-small cell lung cancer Primary endpoint is overall survival (OS) Median for control arm is 8 months Require 90% power to detect HR = 0.7 (median = 11.4 months on experimental arm) One-sided level 0.025 test with one interim look for early efficacy or futility stopping Design 24 month enrollment and 12 months additional follow-up

Example: Metastatic Lung Cancer

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Group Sequential Design

• Uncertainty about

HR=0.7;

• HR = 0.77 is still

clinically meaningful but requires 760 patients and 618 events.

• Up-front commitment is

impossible

209

Design optimistically (HR=0.7; 332 events; 416 subjects) One interim analysis after 50% information

• Stop if overwhelming evidence of efficacy ( $

𝐼𝑆 ≤ 0.63)

• Stop if overwhelming evidence of futility ( $

𝐼𝑆 > 1.02)

• Increase number of events and sample size at the interim if interim results fall in a

promising zone Can define promising zone in terms of conditional power, or HR, or Z-statistic Special CP calculator available in East

Adaptive Strategy

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Partition the interim outcome into three zones based on the estimated conditional power. For example:

• Unfavorable: 𝐷𝑄 < 35% ; no change in design
• Promising: 35% ≤ 𝐷𝑄 < 90% ; increase resources
• Favorable: 𝐷𝑄 ≥ 90%; no change in design

Use simulation to experiment with promising zones Use simulation to experiment with sample size re-estimation rules Use Cui, Hung, Wang (CHW), Chen, DeMets & Lan (CDL) or Mueller and Shaeffer (MS) methods to control type-1 error

The Promising Zone Design

211

Conditional Power Calculator

35% CP corresponds to $ 𝐼𝑆 = 0.83 at the interim analysis 90% CP corresponds to $ 𝐼𝑆 = 0.73 at the interim analysis

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Schema of Adaptive Design

213

Primary driver of power is number of events FDA guidance recommends increase only, not decrease Increase events by amount needed to achieve some target conditional power, subject to a cap Compute sample size increase necessary to achieve the desired increase in events without undue prolongation of the trial Complex relationship exists between increase in events, increase in sample size and study

• duration. Best evaluated by simulation

Adaptation Principles

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Adaptive Simulation Worksheet

215

Operating Characteristics

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It is believed that true HR is between 0.7 and 0.77 Option 1: Power the trial for HR=0.77 with aggressive early stopping boundaries

• Large up-front commitment is often an obstacle
• Aggressive stopping boundaries require spending more alpha at the interim
• Stopping a trial prematurely with aggressive boundaries is unlikely to alter medical practice
• Overruns can be problematic

Option 2: Power the trial for HR=0.7 and increase resources in promising zone

• Requires a lower up-front commitment
• Additional commitment only called forth if it is needed
• Compromise design: Better than non-adaptive trial powered at HR=0.7 but not as

powerful (unconditionally) as the non-adaptive design powered at HR=0.77.

Concluding Observations

217

Shaping the Future

• f Drug Development

Phase III: Adaptive Population Enrichment

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Extending SURVAdapt

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Overview

• Background
• Method and Assumptions
• Software
• Case study in AS
• Q&A

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Background

Population Enrichment (PE): prospective use of any patient characteristic to obtain a study population in which detection is more likely than in unselected population Types of PE:

• Prognostic: identify high risk patients based on biomarkers
• Predictive: identify patients more likely to respond

Issues:

• Cost of clinical trials increasing
• Discovery of blockbuster drugs on the decline; move away from “one size-fits-all idea”

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Background (cont)

Importance:

• Help identify high responsive group, detect treatment effect with smaller sample size
• Failed molecules from one study, may succeed in a different group

Examples:

• BMS immunotherapy Opdivo failed in lung cancer study whereas Merck competitor

Keytruda succeeded: In later case study population was enriched by including only subjects with high level of PD-L1

• ISPY2 identifies different combination therapies across different biomarker subgroups

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Method & Assumptions

Based on Predictive Enrichment Study population: divided in two groups based on a predefined biomarker Study will materialize into two independent cohorts

• First cohort recruits from full population
• Second cohort recruitment depends on an interim analysis based on the first cohort data only

At interim:

• Continue with full population
• Continue with sub-population
• Stop the trial for futility

Subpopulation prevalence will be user-specified

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Angiosarcoma is an ultraorphan disease Poorly addressed by current treatments

• Pazopanib a VEGF inhibitor shows modest benefit
• TRC105 can compliment Pazopanib by inhibiting endoglin, a different angiogenic target

Adaptive trial considered optimal due to:

• Small population (1800 cases/year)
• Limited prior data
• Subgroup interaction. Greater benefit possible with TRC105 for cutaneous vs visceral tumors

Case study: The TAPPAS trial

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The TAPPAS Trial: Objective

Demonstrate superior PFS of the combination of TRC105 + pazopanib vs single agent pazopanib

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Advanced cutaneous and non-cutaneous AS not amenable to curative intent surgery Measurable disease by RECIST 1.1 No prior treatment with a VEGF inhibitor 0,1 or 2 prior lines of therapy ECOG ≤ 1

Eligibility

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p1: p-value for data from cohort 1 p2: p-value for data from cohort 2

2-Stage Design with SSR & Enrichment

ALL COMERS Interim Analysis

Favorable: Continue As Planned Promising: Increase Sample Size Unfavorable Continue As Planned Enrich With Cutaneous Subgroup TRC105 +Pazopanib

Pazopanib

Stop For Futility

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Let 𝐼9

:and 𝐼9 ; denote the null hypotheses for the full population and the

cutaneous group respectively Let 𝐼9

:; = 𝐼9 :⋂𝐼9 ; denote the global null hypothesis

Closed testing principle states that type I error is strongly controlled as long as

• Each of the hypotheses in the closed family is tested at local level-α
• 𝐼9

: significant only if both tests for 𝐼9 : and 𝐼9 :;are significant at local level-α

• 𝐼9

; significant only if both tests for 𝐼9 ; and 𝐼9 :;are significant at local level-α

Preserving type I error

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In case of no enrichment, declare significance on Full population if

𝑥>Φ@> 𝑞>

:; + 𝑥BΦ@> 𝑞B :;

> 𝑨D 𝑥>Φ@> 𝑞>

: + 𝑥BΦ@> 𝑞B :

> 𝑨D

In case of enrichment, declare significance on cutaneous subgroup if

𝑥>Φ@> 𝑞>

:; + 𝑥BΦ@> 𝑞B ;

> 𝑨D 𝑥>Φ@> 𝑞>

; + 𝑥BΦ@> 𝑞B ;

> 𝑨D

Closed Testing With Combination Of P-values

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Independence of p1 and p2 essential for valid level-a test Use of auxiliary data in the censored observations of cohort 1 that become completers in cohort 2 is forbidden

• ORR data, lab values, toxicities of patients censored for PFS in cohort 1 can provide insights

about their eventual PFS result in cohort 2. Type I error could be inflated Use of auxiliary data to decide on enrichment destroys independence of p1 and p2 (Jenkins, Stone and Jennison, Pharmaceutical Statistics, 2011)

Special Considerations for Event-Driven Trials

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Do not choose the interim analysis time point to split data into cohort 1 and cohort 2 Instead, pre-specify allocation of events and sample size to each cohort before taking the interim analysis

• 70 patients and 60 events for cohort 1
• 54 patients and 35 events for cohort 2
• Interim analysis after 40 events have arrived

That will permit full inspection of all cohort 1 data at interim analysis, including censored data

How to permit use of auxiliary data

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Unfavorable Enrichment Cohort 1 Promising Favorable

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Control arm (Pazopanib): median time to progression = 4 months HR expected to be 0.55 Accruals: 8 pts/month Power: 83%

The TAPPAS trial: non-adaptive case

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The TAPPAS trial: Design parameters

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The TAPPAS Trial: Adaptation Parameters Tab

(No Adaptation)

No sample size increase in full population Disable Enrichment and Futility stopping

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The TAPPAS Trial: Adaptation Parameters Tab

(No Adaptation)

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The TAPPAS Trial: Simulation Results (No Adaptation)

Design has 74% power (compared to 83% for fixed design) An adaptive population enrichment should only be considered if there is a possibility that there is a strong treatment effect in the subpopulation, but NOT its complement

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The TAPPAS trial: Design Parameters

When 40 events have arrived, cohort 1 will have met its sample size quota (62 pts) while the total sample size from cohort 1 plus cohort 2 will be 98 patients. Data from half of these extra 36 pts assigned to cohort 2 will NOT be used if there is enrichment Should increase n and events for cohort 1

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The TAPPAS Trial: Design Parameters

16 pts have been assigned to cohort 2 at the time of the interim analysis If interim results fall in the enrichment zone, data from at most 8 cohort 2 patients will be useable

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The TAPPAS trial: Adaptation Parameters

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The TAPPAS trial: Simulation results (with adaptation)

Design has 64% overall power Power conditional on falling in Enrichment zone is 75% Power conditional on falling in promising zone is 81% Power conditional on falling in favourable zone is 83%

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Simulation Outputs

HR(C,NC) Zone P(Zone) Power E(Dur) E(N) 0.55,0.55 Unfavorable 15 45 21 124 Enrich 5 81 35 163 Promising 38 93 30 198 Favorable 42 92 22 124 Total 100 80(97) 25(25) 149(200) 0.55,0.70 Unfavorable 20 32 21 124 Enrich 11 78 34 160 Promising 41 83 30 198 Favorable 28 87 21 124 Total 100 70(86) 25(25) 151(200) 0.55,0.85 Unfavorable 25 23 20 124 Enrich 19 76 33 158 Promising 37 79 30 198 Favorable 19 83 20 124 Total 100 62(66) 25(25) 150(200) 0.55,1.00 Unfavorable 28 18 20 124 Enrich 27 75 32 156 Promising 33 76 29 198 Favorable 12 79 20 124 Total 100 57(43) 25(25) 148(200)

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Compared to fix design of n=200, adaptive design provides

• Greater power
• Smaller sample size
• Shorter duration

Adaptive design maintains 80% power in favorable, promising and enrichment zones for HR=0.55 (cutaneous) even with larger HRs in the non-cutaneous subgroup

Results

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Shaping the Future

• f Drug Development

Q&A Session

Shaping the Future

• f Drug Development

Backup Slides

10/28/19 124

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