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STATISTICAL THINKING FOR NON-STATISTICIANS IN DRUG REGULATION

Statistical methods in the pharmaceutical industry are accepted as a key element in the design and analysis of clinical studies. Increasingly, the medical and scientific community are aligning with the regulatory authorities and recognizing that correct statistical methodology is essential as the basis for valid conclusions. In order for those correct and robust methods to be successfully employed there needs to be effective communication across disciplines at all stages of the planning, conducting, analyzing and reporting of clinical studies associated with the development and evaluation of new drugs and devices.

Statistical Thinking for Non-Statisticians in Drug Regulation provides a comprehensive in-depth guide to statistical methodology for pharmaceutical industry professionals, including physicians, investigators, medical science liaisons, clinical research scientists, medical writers, regulatory personnel, statistical programmers, senior data managers and those working in pharmacovigilance. The author’s years of experience and up-to-date familiarity with pharmaceutical regulations and statistical practice within the wider clinical community make this an essential guide for the those working in and with the industry.

The third edition of Statistical Thinking for Non-Statisticians in Drug Regulation includes:

  • A detailed new chapter on Estimands in line with the 2019 Addendum to ICH E9
  • Major new sections on topics including Combining Hierarchical Testing and Alpha Adjustment, Biosimilars, Restricted Mean Survival Time, Composite Endpoints and Cumulative Incidence Functions, Adjusting for Cross-Over in Oncology, Inverse Propensity Score Weighting, and Network Meta-Analysis
  • Updated coverage of many existing topics to reflect new and revised guidance from regulatory authorities and author experience

Statistical Thinking for Non-Statisticians in Drug Regulation is a valuable guide for pharmaceutical and medical device industry professionals, as well as statisticians joining the pharmaceutical industry and students and teachers of drug development.

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Statistical Thinking for Non‐Statisticians in Drug Regulation

THIRD EDITION

Richard Kay, PhD

Statistical Consultant, RK Statistics Ltd

Honorary Visiting Professor, School of Pharmacy, Cardiff University, UK

This edition first published 2023© 2023 John Wiley & Sons Ltd

Edition HistoryFirst edition John Wiley & Sons, Ltd. (2007); Second edition John Wiley & Sons, Ltd. (2015)

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The right of Richard Kay to be identified as the author of this work has been asserted in accordance with law.

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Library of Congress Cataloging‐in‐Publication DataNames: Kay, Richard, 1949– author.Title: Statistical thinking for non‐statisticians in drug regulation / Richard Kay.Description: Third edition. | Hoboken, NJ : Wiley‐Blackwell, 2023. | Includes bibliographical references and index.Identifiers: LCCN 2022032464 (print) | LCCN 2022032465 (ebook) | ISBN 9781119867388 (hardback) | ISBN 9781119867395 (adobe pdf) | ISBN 9781119867401 (epub)Subjects: MESH: Clinical Trials as Topic–methods | Drug Approval | Statistics as Topic | Drug IndustryClassification: LCC RM301.27 (print) | LCC RM301.27 (ebook) | NLM QV 771.4 | DDC 615.1072/4–dc23/eng/20220916LC record available at https://lccn.loc.gov/2022032464LC ebook record available at https://lccn.loc.gov/2022032465

Cover Design: WileyCover Image: © WHYFRAME/Shutterstock

Preface to the third edition

There have been numerous regulatory guidelines issued since the publication of the second edition of this book, and many of these impact the application of statistics to our clinical investigations and the development of new medicines and devices. Outside of the regulatory arena, the introduction of new methodologies also feeds through to affect the application of statistics in pharmaceutical medicine. The key milestone from a regulatory guideline perspective has been the publication of the ICH E9 Addendum on Estimands. The need for this guideline has grown out of concerns from regulators and the statistical community more widely regarding several elements of the way we design our trials and analyse our data. Primarily, these concerns have been driven by the developing sophistication and availability of methods for dealing with missing data and the use of these methods without really understanding their purpose or properties in relation to the clinical question being addressed. In addition, there have been concerns regarding how we use data collected following events such as withdrawal of consent, taking rescue medication, withdrawal from trial medication due to serious adverse events and also the role of sensitivity analyses, which have often been seen as simply a tick‐box exercise that we undertake without really understanding what questions they are addressing. The estimand framework starts with the clinical question(s) of interest and sets down methods of statistical analysis that address those questions in a systematic and structured way – and this leads to a more considered position on the aspects that I have mentioned. A new chapter (Chapter 8) in this third edition covers estimands.

Both the EMA and the FDA have revised (in the case of EMA) and introduced (in the case of the FDA) guidelines on multiplicity. Multiple testing remains a major concern within the regulatory framework, and these guidelines provide additional insight into the issues and methodologies for dealing with the problems. We have also seen a shift in the way journal editors view the issues associated with multiplicity, with tighter control on the reporting of p‐values. The chapter on multiplicity (Chapter 10) has been revised to incorporate developments in this area. We have also seen the publication by CPMP of a guideline on the evaluation of subgroups. Multiplicity plays a role in the way we consider subgroups, and discussions that relate to this topic are also included in the revised Chapter 10.

In 2016, the FDA updated their guideline on non‐inferiority, and some of the points raised in that revision have been incorporated in Chapter 12. I have also introduced a specific section on biosimilars (Section 12.11). This in part is reflective of my own experience in that area, which to a large extent is a consequence of the increasing development of biosimilars.

Three new sections in the chapter on the analysis of survival data (Chapter 13) cover restricted mean survival time, cross‐over in oncology studies and cumulative incidence functions. The restricted mean survival time is an additional summary measure calculated from the Kaplan‐Meier curve and can be the basis for a comparison of those curves when the assumption of proportional hazards is violated. This topic is covered in Section 13.5. Cross‐over occurs in patients who progress in the control arm and are offered a switch to the experimental treatment. If the experimental treatment has efficacy, this switch will likely impact overall survival in the context of comparing the pure effect of the experimental treatment. This topic is covered in Section 13.8. Cumulative incidence functions, now discussed in Section 13.9, are used for composite time‐to‐event endpoints and allow the evaluation of the separate components of the composite.

The use of network meta‐analysis for incorporating indirect non‐randomised evidence in treatment comparisons has increased in recent years. This is not primarily in regulatory submissions but more in the context of health technology assessment and promotional activities. This topic is introduced and discussed in Chapter 18.

I would like to thank readers who have provided feedback to the first two editions of this book. Please do continue to give your feedback and pull me up on inconsistencies, mistakes and, indeed, areas where you disagree with the position I have taken. I very much learn from these interactions.

Richard Kay

Bakewell

May 2022

Preface to the second edition

The first edition of this book was submitted for publication over seven years ago. As predicted, there have been numerous developments, both in the world of pharmaceutical statistics and within the regulatory environment, which need to be presented and explained. In the intervening years, the FDA has published guidelines on Adaptive Designs and on Non‐Inferiority Trials. The CHMP have updated their guidance on Missing Data, produced a guideline on the Clinical Evaluation of Diagnostic Agents and have undertaken a major exercise on the evaluation of the benefit–risk balance. In recent years, we have seen greater application of the use of observational studies within regulatory applications, particularly when dealing with orphan drugs, and also a willingness to consider the use of Bayesian methods. Although there is still considerable concern expressed about various elements of adaptive designs, we are beginning to understand where the boundaries are and what can be done without compromising the scientific integrity of the study. All of these aspects and more have led to me write this new edition.

There are five new chapters and several other chapters have been restructured. Chapter 15 looks at Bayesian Statistics, contrasting the Bayesian methodology with classical methods, presenting the advantages and concerns and discussing the use of these methods in pharmaceutical applications. Adaptive designs are discussed in Chapter 16 with sections on minimising bias and covering various types of adaptations. Some practicalities and recommendations regarding the circumstances under which such designs can be considered are also presented. We all recognise that the randomised controlled trial is the gold standard in terms of evaluating the efficacy and also the safety of a new medicine, but in some settings running such trials is not possible. Observational studies offer an alternative, but their ability to provide valid conclusions is heavily dependent on good design and conduct and careful analysis. Such designs are discussed in Chapter 17. In recent years, we have become much more formal in the statistical evaluation of safety data. Chapter 19 covers various aspects of safety data analysis, including the use of graphical methods, and goes on to detail potential approaches to the quantification of the benefit–risk balance both inside and outside of the regulatory submission. This chapter concludes with a discussion on methods for post‐approval safety monitoring. Statistical methods for the evaluation of diagnostic methods and method comparison are discussed in Chapter 20.

Chapter 5 in the first edition of the book was entitled ‘Multi‐Centre Trials’. This chapter has been restructured and is now entitled ‘Adjusting the Analysis’. This restructuring is based on my recent teaching experiences in explaining the rationale around adjusting the statistical analysis for baseline factors in a general way. Several other chapters contain sections similarly restructured as a result of my teaching experience. I hope that these changes make things clearer than maybe they were before. Chapter 18 entitled ‘Meta‐Analysis’ is a major restructuring of the initial chapter on this topic and reflects the current uses of this methodology within the pharmaceutical industry.

I have received many encouraging comments on the first edition of this book and I would like to thank everyone who has given feedback. I hope that this revision is also well‐received. My aim is to make statistical thinking and methods used within the pharmaceutical industry accessible to non‐statisticians so that they are better able to communicate using statistical language, better able to understand statistical methods used in reports and publications and what can and cannot be concluded from the resulting analyses, and are better equipped to contribute to statistical arguments used within regulatory submissions and beyond. I continue to teach courses on statistics for non‐statisticians, and many of the changes and additions that I make to my teaching materials and have made to this book have come out of my experiences on those courses. I would like to thank my students for their challenging questions; they make me think about better ways to explain things. Finally I would like to thank all of those who got in touch to point out mistakes in the first edition. I have corrected those but some may remain and indeed the new material may contain some more. I encourage the reader to provide feedback for this second edition and please do not hesitate to point out any mistakes, for which I am solely responsible.

Richard Kay

Great Longstone

March 2014

Preface to the first edition

This book is primarily concerned with clinical trials planned and conducted within the pharmaceutical industry. Much of the methodology presented is in fact applicable on a broader basis and can be used in observational studies and in clinical trials outside of the pharmaceutical sector; nonetheless, the primary context is clinical trials and pharmaceuticals. The development is aimed at non‐statisticians and will be suitable for physicians, investigators, clinical research scientists, medical writers, regulatory personnel, statistical programmers, senior data managers and those working in quality assurance. Statisticians moving from other areas of application outside of pharmaceuticals may also find the book useful in that it places the methods that they are familiar with, in context in their new environment. There is substantial coverage of regulatory aspects of drug registration that impact on statistical issues. Those of us working within the pharmaceutical industry recognise the importance of being familiar with the rules and regulations that govern our activities, and statistics is a key aspect of this.

The aim of the book is not to turn non‐statisticians into statisticians. I do not want you to go away from this book and ‘do’ statistics. It is the job of the statistician to provide statistical input to the development plan, to individual protocols, to write the statistical analysis plan, to analyse the data and to work with medical writing in producing the clinical report, and also to support the company in its interactions with regulators on statistical issues.

The aims of the book are really threefold. Firstly, to aid communication between statisticians and non‐statisticians; secondly, to help in the critical review of reports and publications; and finally, to enable the more effective use of statistical arguments within the regulatory process. We will take each of these points in turn.

In many situations, the interaction between a statistician and a non‐statistician is not a particularly successful one. The statistician uses terms such as power, odds ratio, p‐value, full analysis set, hazard ratio, non‐inferiority, type II error, geometric mean, last observation carried forward and so on, of which the non‐statistician has a vague understanding, but maybe not a good enough understanding to be able to get an awful lot out of such interactions. Of course, it is always the job of a statistician to educate and every opportunity should be taken for imparting knowledge about statistics, but in a specific context, there may not be time for that. Hopefully this book will explain, in ways that are understandable, just what these terms mean and provide some insight into their interpretation and the context in which they are used. There is also a lot of confusion between what on the surface appear to be the same or similar things: significance level and p‐value, equivalence and non‐inferiority, odds ratio and relative risk, relative risk and hazard ratio (by the way this is a minefield!) and meta‐analysis and pooling to name just a few. This book will clarify these important distinctions.

It is unfortunately the case that many publications, including some in leading journals, contain mistakes with regard to statistics. Things have improved over the years with the standardisation of the ways in which publications are put together and reviewed. For example, the CONSORT statement (see Section 16.5 [this is Section 21.5 in the 2nd edition]) has led to a distinct improvement in the quality of reporting. Nonetheless mistakes do slip through, in terms of poor design, incorrect analysis, incomplete reporting and inappropriate interpretation – hopefully not all at once! It is important therefore when reading an article that the non‐statistical reader is able to make a judgement regarding the quality of the statistics and to notice any obvious flaws that may undermine the conclusions that have been drawn. Ideally, the non‐statistician should involve their statistical colleagues in evaluating their concerns, but keeping a keen eye on statistical arguments within the publication may help to alert the non‐statistician to a potential problem. The same applies to presentations at conferences, posters, advertising materials and so on.

Finally, the basis of many concerns raised by regulators, when they are reviewing a proposed development plan or assessing an application for regulatory approval, is statistical. It is important that non‐statisticians are able to work with their statistical colleagues in correcting mistakes, changing aspects of the design, responding to questions about the data to hopefully overcome those concerns.

In writing this book, I have made the assumption that the reader is familiar with the general aspects of the drug development process. I have assumed knowledge of the phase I to phase IV framework, of placebos, control groups, and double‐dummy together with other fundamental elements of the nuts and bolts of clinical trials. I have assumed however no knowledge of statistics! This may or may not be the correct assumption in individual cases, but it is the common denominator that we must start from, and also it is actually not a bad thing to refresh on the basics. The book starts with some basic issues in trial design in Chapter 1, and I guess most people picking up this book will be familiar with many of the topics covered there. But don’t be tempted to skip this chapter; there are still certain issues, raised in this first chapter, that will be new and important for understanding arguments put forward in subsequent chapters. Chapter 2 looks at sampling and inferential statistics. In this chapter, we look at the interplay between the population and the sample, basic thoughts on measuring average and variability and then explore the process of sampling leading to the concept of the standard error as a way of capturing precision/reliability of the sampling process. The construction and interpretation of confidence intervals are covered in Chapter 3 together with testing hypotheses and the (dreaded!) p‐value. Common statistical tests for various data types are developed in Chapter 4 which also covers different ways of measuring treatment effect for binary data, such as the odds ratio and relative risk.

Many clinical trials that we conduct are multi‐centre and Chapter 5 looks at how we extend our simple statistical comparisons to this more complex structure. These ideas lead naturally to the topics in Chapter 6 which include the concepts of adjusted analyses, and more generally, analysis of covariance which allows adjustment for many baseline factors, not just centre. Chapters 2–6 follow a logical development sequence in which the basic building blocks are initially put in place and then used to deal with more and more complex data structures. Chapter 7 moves a little away from this development path and covers the important topic of ‘intention‐to‐treat’ and aspects of conforming with that principle through the definition of different analysis sets and dealing with missing data. In Chapter 8, we cover the very important design topics of power and the sample size calculation which then leads naturally to a discussion about the distinction between statistical significance and clinical importance in Chapter 9.

The regulatory authorities, in my experience, tend to dig their heels in on certain issues and one such issue is multiplicity. This topic, which has many facets, is discussed in detail in Chapter 10. Non‐parametric and related methods are covered in Chapter 11. In Chapter 12, we develop the concepts behind the establishment of equivalence and non‐inferiority. This is an area where many mistakes are made in applications, and in many cases, these slip through into published articles. It is a source of great concern to many statisticians that there is widespread misunderstanding of how to deal with equivalence and non‐inferiority. I hope that this chapter helps to develop a better understanding of the methods and the issues. If you have survived so far, then Chapter 13 covers the analysis of survival data. When an endpoint is time to some event, for example, death, the data are inevitably subject to what we call censoring and it is this aspect of so‐called survival data that has led to the development of a completely separate set of statistical methods. Chapter 14 builds on the earlier discussion on multiplicity to cover one particular manifestation of that, the interim analysis. This chapter also looks at the management of these interim looks at the data through data monitoring committees. Meta‐analysis and its role in clinical development is covered in Chapter 15, and the book finishes with a general Chapter 16 on the role of statistics and statisticians in terms of the various aspects of design and analysis and statistical thinking more generally.

It should be clear from the last few paragraphs that the book is organised in a logical way; it is a book for learning rather than a reference book for dipping into. The development in later chapters will build on the development in earlier chapters. I strongly recommend, therefore, that you start on page 1 and work through. I have tried to keep the discussion away from formal mathematics. There are formulas in the book but I have only included these where I think this will enhance understanding; there are no formulas for formulas sake! There are some sections that are more challenging than others and I have marked with an asterisk those sections that can be safely sidestepped on a first (or even a second) run through the book.

The world of statistics is ever changing. New methods are being developed by theoreticians within university departments, and ultimately some of these will find their way into mainstream methods for design and statistical analysis within our industry. The regulatory environment is ever changing as regulators respond to increasing demands for new and more effective medicines. This book in one sense represents a snapshot in time in terms of what statistical methods are employed within the pharmaceutical industry and also in relation to current regulatory requirements. Two statistical topics that are not included in this book are Bayesian Methods and Adaptive (Flexible) Designs (although some brief mention is made of this latter topic in Section 14.5.2). Both areas are receiving considerable attention at the moment, and I am sure that within a fairly short period of time, there will be much to say about them in terms of the methodological thinking, examples of their application and possibly with regard to their regulatory acceptance but for the moment they are excluded from our discussions.

The book has largely come out of courses that I have been running under the general heading of ‘Statistical Thinking for Non‐Statisticians’ for a number of years. There have been several people who have contributed from time to time and I would like to thank them for their input and support: Werner Wierich, Mike Bradburn and in particular Ann Gibb who gave these courses with me over a period of several years and enhanced my understanding through lively discussion and asking many challenging questions. I would also like to thank Simon Gillis who contributed to Chapter 16 [this is Chapter 21 in the 2nd edition] with his much deeper knowledge of the processes that go on within a pharmaceutical company in relation to the analysis and reporting of a clinical trial.

Richard Kay

Great Longstone

January 2007

Abbreviations

6MWD

Six minute walking distance

ADR

adverse drug reaction

AE

adverse event

AFT

accelerated failure time

AIDAC

Anti‐Infective Drugs Advisory Committee

ALKPH

alkaline phosphatase

ALT

alanine transaminase

AMD

age‐related macular degeneration

ANCOVA

analysis of covariance

ANOVA

analysis of variance

ARR

absolute risk reduction

AST

asparate transaminase

AUC

area under the curve

BILTOT

total bilirubin

BMD

bone mineral density

BSC

best supportive care

CDER

Center for Drug Evaluation and Research

CFC

Chlorofluorocarbon

CHMP

Committee for Medicinal Products for Human Use

CI

confidence interval

CIF

cumulative incidence function

CMAX

maximum concentration

CMH

Cochran‐Mantel‐Haenszel

CNS

central nervous system

COPD

chronic obstructive pulmonary disease

CPMP

Committee for Proprietary Medicinal Products

CR

complete response

crd

clinically relevant difference

CRF

Case Report Form

CRO

clinical research organisation

CSR

Clinical Study Report

CTC(AE)

Common Terminology Criteria (for Adverse Events)

dBP

diastolic blood pressure

df

degrees of freedom

DILI

drug‐induced liver injury

DLQI

dermatology life quality index

DMC

Data Monitoring Committee

DSMB

Data and Safety Monitoring Board

DSMC

Data and Safety Monitoring Committee

EBGM

empirical Bayes geometric mean

ECG

Electrocardiogram

ECOG

Eastern Cooperative Oncology Group

EMEA

European Medicines Evaluation Agency

ESRD

end‐stage renal disease

FAS

full analysis set

FDA

Food and Drug Administration

FEV

1

forced expiratory volume in one second

FN(R)

false negative (rate)

FP(R)

false positive (rate)

FWER

family‐wise error rate

GP

General Practitioner

HAMA

Hamilton Anxiety Scale

HAMD

Hamilton Depression Scale

HER2

human epidermal growth factor receptor‐2

HIV

human immunodeficiency virus

HR

Hazard Ratio

HTA

health technology assessment

IC

information component

ICE

intercurrent event

ICH

International Committee on Harmonisation

ICU

intensive care unit

IPSW

inverse propensity score weighting

ISPOR

International Society for Pharmacoeconomics and Outcomes Research

ITT

intention‐to‐treat

IVRS

Interactive Voice Response System

IWRS

Interactive Web Response System

KM

Kaplan‐Meier

LLN

lower limit of normal

LOCF

last observation carried forward

LR

likelihood ratio

MACE

major cardiovascular event(s)

MAR

missing at random

MCAR

missing completely at random

MCDA

multi‐criteria decision analysis

mCRC

metastatic colorectal cancer

MedDRA

Medical Dictionary for Regulatory Activities

MFS

metastases‐free survival

MH

Mantel‐Haenszel

MI

myocardial infarction

mITT

modified intention‐to‐treat

MNAR

missing not at random

NICE

National Institute for Health and Care Excellence

NMA

network meta‐analysis

NNH

number needed to harm

NNT

number needed to treat

NOAC

non‐vitamin K antagonist oral anticoagulants

NPS

nasopharyngeal cancer

NPV

negative predictive value

NS

not statistically significant

OAB

overactive bladder syndrome

OR

odds ratio

ORR

objective response rate

OS

overall survival

PA

predictive accuracy

PASI

psoriasis area and severity index

PD

progressive disease

PEF

peak expiratory flow

PFS

progression‐free survival

PGA

physician's global assessment

PHN

post‐hepatic neuralgia

PHS

public health service

PPS

per‐protocol set

PPV

positive predictive value

PR

partial response

PRR

proportional reporting ratio

PT

preferred term

QoL

quality of life

RECIST

Response Evaluation Criteria in Solid Tumours

RENAAL

Reduction of Endpoints in NIDDM with the Angiotensin II Antagonist Losartan Study

RMST

restricted mean survival time

RPSFTM

rank preserving structural failure time model

RR

relative risk

RRR

relative risk reduction

RT

radiotherapy

RTC

radiotherapy plus chemotherapy

SAE

serious adverse event

SAP

Statistical Analysis Plan

sBP

systolic blood pressure

SD

stable disease

sd

standard deviation

se

standard error

SFE

summary of favourable effects

SOC

system organ class

SRC

safety review committee

SUCRA

surface under the cumulative ranking curve

SUFE

summary of unfavourable effects

TLFs

tables, listings and figures

TN

true negative

TP

true positive

ULN

upper limit of normal

VAS

visual analogue scale

WHO

World Health Organization