# Designing and analysing multi-arm multi-stage clinical trials with one or more endpoints

Department Name: Mathematics and Statistics

### Abstract

In the early stages of drug development there is often uncertainty about the most promising among a set of different treatments. In order to ensure the best use of resources in such situations it is important to decide which, if any, of the treatments should be taken forward for further testing. An efficient solution to this problem are multi-arm clinical trials in which several active treatments are compared to a common control group. By comparing several treatments within one trial the sample size and duration required tends to be markedly smaller than if each treatment would have been evaluated separately. For added efficiency it is desirable to monitor the trial at a series of interim analyses in order to allow early stopping if efficacy is quickly established and similarly to eliminate ineffective treatments early. In confirmatory studies these designs are also useful as it has been shown that using two doses instead of a single dose can markedly improve the study's success probability.

This proposal aims to develop statistical methods to investigate how these, so called multi-arm multi-stage trials, can best be designed and analysed. The work will utilize three recently finished or currently ongoing studies in three important medical areas: HIV/AIDS, leukemia and metastatic prostate cancer. The multidisciplinary research team includes experienced clinical specialists and clinical trialists for each study from the clinical trials research unit in Leeds, the University of Liverpool and the MRC clinical trials unit as well as statisticians with experience in statistical methods for clinical trials from the University of Bremen and the Warwick medical school.

### Technical Summary

Multi-arm multi-stage designs are a broad class of designs in which several active treatment arms are compared to a common control. Their advantage over traditional 2-armed studies is that, on the one hand, a common control group is used yielding smaller expected sample sizes compared to multiple 2-armed trials and allowing direct comparisons of all active arms under the same study conditions and, on the other hand, that decisions about effective and ineffective treatments can be made at early interim analyses. Although some work on designing these trials in simple situations (e.g. play-the-winner designs) is available no adequate methods are available for many situations of practical interest (e.g. multiple endpoints). Moreover methods for adequately estimating the treatment effect and finding the corresponding confidence intervals in such trials are not available beyond two stages.

This proposal aims to
1. develop statistical designs for multi-arm multi-stage designs that use intermediate endpoints for treatment selection;
2. develop and evaluate methods for estimating the treatment effect and corresponding confidence intervals in multi-arm multi-stage designs with treatment selection and obtain their confidence intervals;
3. develop statistical methods for multi-arm multi-stage designs with multiple endpoints;
4. develop an open-source software package and associated training tailored to clinical trialists and applied statisticians working on clinical trials.

### Planned Impact

In addition to academic beneficiaries, the work proposed in this grant will have great impact on others. By extending methodology for multi-arm multi-stage clinical trials (MAMS) to allow for differing endpoints at each stage, we shall be able to apply the theory of optimal design to a broader range of MAMS trials. This is of great benefit to patients recruited to such trials - stopping boundaries can be specified that reduce the average number of patients recruited to poor treatments, but keep effective treatments in the trial. Use of such designs will mean fewer patients are exposed to poor treatments. This will also be of interest to clinicians running and supporting the trial, who are naturally interested in ensuring their patients do not receive ineffective treatments. Funders of trials would also benefit, since fewer patients would be required on average, thus reducing the average cost. Because MAMS trials are high cost trials, even relatively small improvements in the design can lead to large savings in costs. Since this is a design issue, the benefit from this work will come in the medium-term future, when actual trials using the methodology start recruiting. In addition to the immediate benefit to patients on the trial the number of patients in the trial and hence the duration of the trial is reduced resulting in effective treatments to be put into clinical practice sooner.

Reducing bias in the estimation of treatment effects after a MAMS trial will be of great interest to those using results from a clinical trial. Those planning future trials will be able to use results to inform the design of their trial with the knowledge that the bias is minimised. Regulatory organisations such as the European Medicines Agency or the National Institute for Clinical Excellence will be able to judge the cost-effectiveness of a drug using reliable data. This area of research will have a more immediate impact since it can be applied to data from a MAMS trial designed prior to this work.

Through the extension of methodology to the exact and optimal design of MAMS trials with multiple endpoints, we shall make a greater range of efficient trials possible. This would be of interest to organisations that design and run trials, such as clinical trial units (CTUs) and pharmaceutical companies, or those who support the design of trials, such as research design services (RDSs). In addition, patients recruited to such trials will benefit because there will be clear, statistically sound, rules as to when to drop a treatment which is potentially dangerous. Since this is a design issue, the impact of this work would be in the medium-term future.

### Publications

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Davies GR (2015) Adaptive clinical trials in tuberculosis: applications, challenges and solutions. in The international journal of tuberculosis and lung disease : the official journal of the International Union against Tuberculosis and Lung Disease

Jaki T (2019) The R Package MAMS for Designing Multi-Arm Multi-Stage Clinical Trials in Journal of Statistical Software

Description Short-course Oxford
Geographic Reach National
Policy Influence Type Influenced training of practitioners or researchers
Impact Improved understanding of available tools for more efficient clinical trials

Description A Practical Adaptive and Novel Designs Toolkit
Amount £100,000 (GBP)
Organisation National Institute for Health Research
Sector Public
Country United Kingdom
Start 07/2019
End 06/2020

Description Developing efficient perpetual platform trials to study multiple treatments and multiple biomarkers
Amount £228,041 (GBP)
Funding ID MR/N028171/1
Organisation Medical Research Council (MRC)
Sector Public
Country United Kingdom
Start 02/2017
End 01/2020

Description Marie Curie ITN
Amount € 3,639,394 (EUR)
Funding ID 633567
Organisation European Commission
Sector Public
Country European Union (EU)
Start 01/2015
End 12/2018

Description Methodology Research Panel - Estimation project
Amount £345,000 (GBP)
Funding ID MR/M005755/1
Organisation Medical Research Council (MRC)
Sector Public
Country United Kingdom
Start 01/2015
End 12/2017

Description NIHR Senior Research Fellowship
Amount £653,526 (GBP)
Funding ID SRF-2015-08-001
Organisation National Institute for Health Research
Sector Public
Country United Kingdom
Start 01/2016
End 12/2020

Organisation Medical University of Vienna
Department Centre for Medical Statistics, Informatics and Intelligent Systems
Country Austria
PI Contribution Joint research
Collaborator Contribution Joint research
Impact Publications.
Start Year 2011

Description NWHTMR
Organisation University of Liverpool
Department Department of Biostatistics
Country United Kingdom
PI Contribution Joint research and support in implementation of methods
Collaborator Contribution Joint research and implementation of methods
Impact Joint papers, funding applications
Start Year 2009

Title MAMS package
Description Software to design multi-arm multi-stage designs in the statistical software R
Type Of Technology Software
Year Produced 2013
Impact Increased uptake of the methodology
URL http://cran.r-project.org/web/packages/MAMS/index.html

Description 8th International Conference on Multiple Comparison Procedures, Southampton, UK, Sept 2013
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Invited presentation at 8th International Conference on Multiple Comparison Procedures, Southampton, UK, Sept 2013
Year(s) Of Engagement Activity 2013

Description Adaptive and Bayesian Methods Course
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Annual Short course on adaptive and Bayesian methods
Year(s) Of Engagement Activity 2015,2016,2017,2018

Description Conference of the Austro-Swiss Region of the International Biometric Society
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Invited presentation at Conference of the Austro-Swiss Region of the International Biometric Society
Year(s) Of Engagement Activity 2013

Description Design of Experiments in Drug Development open for business
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Discussion event around improving drug development through adaptive designs.
Year(s) Of Engagement Activity 2015

Description International Biometric Conference, Florence, Italy
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Invited conference presentation at International Biometric Conference
Year(s) Of Engagement Activity 2014

Description International Conference on Simultaneous Inference
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Invited presentation at International Conference on Simultaneous Inference
Year(s) Of Engagement Activity 2013

Description NCRI CTU annual meeting 2015
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Professional Practitioners
Results and Impact Workshop on "Novel trial designs for phase II oncology" at NCRI CTU annual meeting 2015
Year(s) Of Engagement Activity 2015

Description SCT Conference
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Invited Conference talk at the Society for Clinical Trials conference
Year(s) Of Engagement Activity 2015

Description Short courses
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International
Primary Audience Professional Practitioners
Results and Impact Several short-course for professionals and students that are based on the undertaken research

Wider uptake of methods
Year(s) Of Engagement Activity 2011,2012,2013,2014,2015

Description Statistical Innovations in Clinical Trials Workshop 2015
Form Of Engagement Activity Participation in an activity, workshop or similar
Part Of Official Scheme? No
Geographic Reach International