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Library of Congress Cataloging‐in‐Publication Data
Names: Rosenkranz, Gerd, 1955‐ author.
Title: Exploratory subgroup analyses in clinical research / Gerd
Rosenkranz.
Other titles: Statistics in practice.
Description: Hoboken, NJ : Wiley, 2020. | Series: Wiley series in
statistics in practice | Includes bibliographical references and index.
Identifiers: LCCN 2019051500 (print) | LCCN 2019051501 (ebook) | ISBN
9781119536970 (hardback) | ISBN 9781119536956 (adobe pdf) | ISBN
9781119537007 (epub)
Subjects: MESH: Cluster Analysis | Clinical Trials as Topic | Models,
Statistical | Precision Medicine
Classification: LCC R853.C55 (print) | LCC R853.C55 (ebook) | NLM WA 950
| DDC 610.72/4–dc23
LC record available at https://lccn.loc.gov/2019051500
LC ebook record available at https://lccn.loc.gov/2019051501
ISBN: 9781119536970
Cover Design: Wiley
Cover Image: Gerd Rosenkranz Figure 7.5
To my parents,
Ruth and Karl
A few years ago I started a book by first writing a fairly extensive preface. I never finished that book and resolved that in the future I would write first the book and then the preface.
LEO BREIMAN (1928–2005)—Preface to “Probability” (Breiman, 1968)
When I eventually agreed to write a book on subgroup analyses I remembered the first paragraph of the preface that the late (and great) probabilist and statistician Leo Breiman added to his book “Probability,” a classic textbook during my study days. I interpreted Leo's words as a warning to all potential authors not to start from the wrong end. Hence I postponed writing this part of the book if not to the very end but to the point when progress looked encouraging.
This book is about a topic of intense research driven on one hand by the promises of precision medicine and on the other by the intention of regulating agencies to obtain information about the consistency of findings from clinical trials in drug applications. It can therefore be at best a snapshot of the state of the art at a given point in time from the author's perspective of the topic.
To whom may the book concern? First, its main parts require a solid knowledge of statistical concepts like random variables, bias, variance, confidence intervals, and statistical tests, but also a background in statistical modeling, re‐sampling, and model selection. Re‐sampling is well presented in “An Introduction to the Bootstrap” (Efron and Tibshirani, 1993) while “Statistical Learning with Sparsity” (Hastie et al., 2015) covers the modern aspects of modeling and model selection.
On the practical side, knowledge about concepts of clinical trials and drug development like efficacy and safety, and randomization and blinding are helpful. “Statistical Issues in Drug Development” (Senn, 2007) covers many of these topics.
Notwithstanding what is said above, parts of the book should be readable by a non‐statistical audience, mainly the chapters on history and to a lesser extent on pitfalls. Chapters digging a bit deeper into methodology (those coming with a heavier load of equations) should be primarily appreciated by statisticians. With this in mind, clinicians and statisticians from the area of clinical development and regulation should benefit most, although the topic of subgroup analysis has a much wider scope.
Lörrach, Germany
April 2019
GERD K. ROSENKRANZ
Part of the work presented here was developed while I was employed with Novartis Pharma AG in Basel, Switzerland, in cooperation with an EFSPI Working Group on subgroup analyses led by Aaron Dane (DaneStat) and later by David Svensson (AstraZeneca). I thank both Aaron and David, as well as Amy Spencer (University of Sheffield) and Ilya Lipkovich (IQVIA, now Lilly) from this group for their cooperation. The results of this group are presented in Dane et al. (2019). I would like to thank specifically Björn Bornkamp (Novartis) for many discussions on subgroup selection and modeling.
The topic was developed further during a two‐year visiting professorship at the Center of Medical Statistics, Informatics and Intelligent Systems at the Medical University of Vienna, for which I am really grateful to Martin Posch, the center director, and to Franz König. The hospitality at the Institute and the cooperation with colleagues, in particular with our then PhD student Nicolas Ballarini, added new motivation to keep working on the topic with new drive and direction. Having had the opportunity to work and live in the city of Vienna was really a privilege. Sincere thanks also to Thomas Jaki (University of Lancaster) for providing funding from the UK Medical Research Council, Project No. MR/M005755/1 during this time.
My involvement in the subgroup topic got on the radar screen of Alison Oliver from John Wiley after a half day seminar I presented at ISCB 2016 in Birmingham, UK. Without her indefatigable reminders to make up my mind and agree on a book project this would have hardly happened.
Last but not least I would like to thank my parents who gave me (and my brother) the opportunity and the support to complete an education of our choice. I also want to thank my wife for accepting the seemingly endless hours I withdrew to work at the laptop in my home office.
GERD K. ROSENKRANZ
This book is accompanied by a companion website:
www.wiley.com/go/rosenkranz/exploratory
The website includes:
Datasets and Programs.
Scan this QR code to visit the companion website.
The promise of precision medicine is to identify subgroups of patients that respond better to treatment than the patient population as a whole. This idea is particularly relevant for new anticancer agents that target specific molecular pathways (Karapetis et al., 2008). Since treatments targeting specific pathways are becoming more prominent in other indications as well, the quest for predictive markers increases (Slager et al., 2012; Buck and Hemmer, 2014).
The topic is also of interest in a broader regulatory context. In a recent guideline, the European Medicines Agency (EMA, 2019) states that investigation into the effects of treatment in well‐defined subsets of the trial population is an integral part of clinical trial planning, analysis, and inference that follows the inspection of the primary outcome of the trial. The intention is to investigate consistency or heterogeneity of the treatment effect across subgroups defined in terms of background characteristics.
As early as 1988 the Food and Drug Administration (FDA) of the United States issued regulations on the content and format of new drug applications (FDA, 1988) that require the presentation of effectiveness and safety data by gender, age, and racial subgroups, and the identification of dosage modifications for specific subgroups. In 2014, the FDA published an action plan to enhance the collection and availability of demographic subgroup data (FDA, 2014).
Subgroup analysis poses issues (Assmann et al., 2000; Senn, 2001; Wang et al., 2007) and can be controversial, in particular in regard to findings after the fact; see debates in Horwitz et al. (1996,1997), Senn and Harrell (1997), Bender et al. (2010), and Hasford et al. (2010,2011). Nevertheless there are good arguments to investigate a potential heterogeneity of treatment effect, for example in relation to pathophysiology (Rothwell, 2005).
The focus of the book is a situation where some, but not too many subgroups like gender, age, region, disease severity, ethnic origin, metabolism etc., have been identified at the trial outset to be examined in an exploratory way when the data are available. Identifying subgroups encompasses searching for a feature that is sticking out, for example an extraordinary treatment or side effect. This entails a two‐fold risk of wrongly selecting subgroups and of overestimating the effect size in the selected subgroup(s). (Adjustment for multiplicity can cope with the risk of too many false positive results, but not automatically with selection bias.) The statistical problem has become known as “selective inference”, the assessment of relevance and effect sizes from a dataset after mining the same data to find associations (Taylor and Tibshirani, 2015).
It has been pointed out by several authors (Assmann et al., 2000; Rothwell, 2005) that the correct criterion to identify subgroups with higher treatment effects is not the significance of the treatment effect in one subgroup or the other, but whether the effect differs between the subgroups defined by a factor, i.e. a treatment by factor or treatment by subgroup interaction. However, a test for this interaction suffers from the fact that it may come out significant for minor interactions when the sample size is large, while it may tend to miss large interactions when the sample size is small. Hence other methods may be required to address subgroup identification.
The book is organized as follows. First we take a guided tour through the history of subgroup analyses and introduce subgroup analyses that actually happened and are each remarkable for a special reason. This part of the book should be readable (and understandable) by a broad audience beyond statisticians.
Next we summarize the objectives of subgroup analyses and present definitions around subgroups. Some of the most prominent pitfalls of subgroup analyses are discussed in Chapter 3 followed by an introduction of different methods to analyze data from subgroups: hierarchical models to reduce variability of estimators (Chapter 5), application of the bootstrap to reduce bias in effect estimators after subgroup selection (Chapter 6), methods to obtain estimates of expected individual treatment effects (Chapter 7) and prediction errors in prediction models (Chapter 8). The presentation of methods for subgroup analyses includes illustrative case studies.