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- Herausgeber: John Wiley & Sons
- Kategorie: Wissenschaft und neue Technologien
- Serie: Statistics in Practice
- Sprache: Englisch
- Veröffentlichungsjahr: 2020
This essential guide on subgroup analyses in the emerging area of personalized medicine covers the issues of subgroup analyses from a practical and a theoretical/methodological point of view. The practical part introduces the issues using examples from the literature where subgroup analyses led to unexpected or difficult-to-interpret results, which have been interpreted differently by different stakeholders. On the technical side, the book addresses selection and selection bias variance reduction by borrowing information from the full population in estimating a subgroup effect. To this end, subgroup analysis will be linked to statistical modelling, and subgroup selection to model selection. This connection makes the techniques developed for model selection applicable to subgroup analysis. Beginning with a history of subgroup analysis, Exploratory Subgroup Analyses in Clinical Research offers chapters that cover: objectives and current practice of subgroup analyses; pitfalls of subgroup analyses; subgroup analysis and modeling; hierarchical models in subgroup analysis; and selection bias in regression. It also looks at the predicted individual treatment effect and offers an outlook of the topic in its final chapter. * Focuses on the statistical aspects of subgroup analysis * Filled with classroom and conference-workshop tested material * Written by a leading expert in the field of subgroup analysis * Complemented with a companion website featuring downloadable datasets and examples for teaching use Exploratory Subgroup Analyses in Clinical Research is an ideal book for medical statisticians and biostatisticians and will greatly benefit physicians and researchers interested in personalized medicine.
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Table of Contents
Cover
Preface
Acknowledgments
Acronyms
About the Companion Website
Introduction
1 Some History of Subgroup Analysis
1.1 Introduction
1.2 Questionable Subgroup Analyses
1.3 Encouraging Subgroup Analyses
1.4 Subgroups and Drug Approvals
1.5 Concluding Remarks
Notes
2 Objectives and Current Practice of Subgroup Analyses
2.1 Introduction
2.2 Objectives of Subgroup Analyses
2.3 Definitions Around Subgroups
2.4 Confounding
2.5 Two Types of Subgroup Analyses
2.6 Reporting of Subgroups
2.7 Concluding Remarks
3 Pitfalls of Subgroup Analyses
3.1 Introduction
3.2 Extreme Effect Estimates
3.3 Selection Bias
3.4 Reversal of Effects
3.5 Regression to the Mean
3.6 Simpson's Paradox
3.7 Post‐hoc Analyses
3.8 Concluding Remarks
4 Subgroup Analysis and Modeling
4.1 Introduction
4.2 Modeling and Prediction
4.3 Subgroups and Hierarchical Models
4.4 Subgroups and Regression Models
4.5 Variable Selection in Regression
4.6 Concluding Remarks
5 Hierarchical Models in Subgroup Analysis
5.1 Introduction
5.2 A General Hierarchical Model
5.3 Parameter Estimation
5.4 Case Studies
5.5 Concluding Remarks
6 Selection Bias in Regression
6.1 Introduction
6.2 Correction for Selection Bias
6.3 Variance Estimation
6.4 A Case Study
6.5 Concluding Remarks
7 The Predicted Individual Treatment Effect
7.1 Introduction
7.2 Definition of the PITE
7.3 Confidence Intervals of the PITE
7.4 Case Studies
7.5 Concluding Remarks
8 Prediction models
8.1 Introduction
8.2 Prediction Error
8.3 Model Selection or Averaging
8.4 Prediction Error of the PITE
8.5 A Case Study
8.6 Concluding Remarks
9 Outlook
Bibliography
Index
End User License Agreement
List of Tables
Chapter 1
Table 1.1 Approved targeted therapies
Table 1.2 Vascular deaths in the ISIS–2 study
Table 1.3 Results from BHAT by center subgroups and overall
Table 1.4 Results on time to progression and survival from the trastuzumab study...
Table 1.5 PLATO results overall and by region and ASA dose (mg)
Table 1.6 Results for the PLATO trial by ASA dose within region
Table 1.7 Median (progression‐free) survival and hazard ratios
Table 1.8 Relative risk reduction with 95% confidence interval (CI) by subgroup ...
Chapter 2
Table 2.1 Percentage of false positive subgroup findings conditional on overall ...
Table 2.2 Reporting of subgroups as proposed by CONSORT 2010
Chapter 3
Table 3.1 Probability of large effect estimates.
Table 3.2 Probability of observing at least one positive subgroup result when th...
Table 3.3 Results of a fictitious study.
Table 3.4 Results of the fictitious study by gender.
Chapter 4
Table 4.1 Estimates and standard errors of regression coefficients from four dif...
Chapter 5
Table 5.1 Estimates of the model parameters for the toxoplasmosis data
Table 5.2 BCG data
Table 5.3 Estimates of the model parameters for the BCG data
Table 5.4 Estimates of the model parameters for the prostate cancer data
Table 5.5 Estimates and standard error of the gene expression difference by the ...
Chapter 6
Table 6.1 Estimates of treatment by subgroup interaction and model fit statistic...
Table 6.2 Percentage of covariate selection from 2000 bootstrap samples of the p...
Table 6.3 Estimates of treatment effects within and between age groups from 2000...
Chapter 7
Table 7.1 Number of patients with CIN over total number of patients by patient s...
Table 7.2 Odds ratios of the risk of CIN under contrast medium 1 relative to med...
Table 7.3 Predicted odds ratio and proportions of
bootstrap samples leading to ...
Chapter 8
Table 8.1 Parameter estimates of linear predictor for Alzheimer data
Table 8.2 Upper bounds of the prediction error estimate of the PITE for predicto...
Table 8.3 Selection percentage of variables for the Alzheimer data for a predict...
List of Illustrations
Chapter 1
Figure 1.1 Relative risk reduction with 95% confidence intervals by subgroup a...
Chapter 2
Figure 2.1
‐values in subgroups if point estimates in subgroups are identical...
Chapter 3
Figure 3.1 Bias of the estimator of the maximum of two means of standard norma...
Chapter 4
Figure 4.1 No treatment by subgroup interaction: constant difference
between...
Figure 4.2 Example of quantitative treatment by subgroup interaction...
Figure 4.3 Example of qualitative treatment by subgroup interaction: differenc...
Figure 4.4 Subgroups defined by two binary (upper diagram) or two numerical co...
Figure 4.5 Subgroups defined by the individual treatment effect in the case of...
Chapter 5
Figure 5.1 Box plots of the means of the bias estimates from all 10 000 simula...
Figure 5.2 Differences between the posterior means of a model with a single pr...
Figure 5.3 Original estimates (blue) and empirical Bayes estimates for the sin...
Figure 5.4 Original estimates (blue) and empirical Bayes estimates for the sin...
Figure 5.5 Original estimates (dark gray) and empirical Bayes estimates for a ...
Figure 5.6 Standard errors of the original estimates (solid line) and empirica...
Chapter 6
Figure 6.1 Treatment effect estimates in terms of log hazard ratios and standa...
Chapter 7
Figure 7.1 Average coverage of the confidence intervals for the PITE in (A) th...
Figure 7.2 Estimates and confidence intervals for model parameters (A) and fou...
Figure 7.3 Parameter estimates and confidence intervals for the prostate cance...
Figure 7.4 PITE for combinations of levels of age and bone metastases for the ...
Figure 7.5 PITEs and 90% confidence intervals for different subject characteri...
Guide
Cover
Table of Contents
Begin Reading
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Formulas for Dynamics, Acoustics and Vibration Blevins November 2015
Engineering Vibroacoustic Analysis:
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The Effects of Sound on People Cowan May 2016
Exploratory Subgroup Analyses in Clinical Research
Gerd Rosenkranz
Statistical Consultant
Copyright
This edition first published 2020
© 2020 John Wiley & Sons Ltd
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by law. Advice on how to obtain permission to reuse material from this title is available at http://www.wiley.com/go/permissions.
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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
Preface
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.
LEOBREIMAN (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, GermanyApril 2019
GERD K. ROSENKRANZ
Acknowledgments
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
Acronyms
ASA
Acetylsalicylic acid
AIC
Akaike information criterion
ATE
Average treatment effect
BHAT
Beta‐Blocker Heart Attack Trial
BIC
Bayesian information criterion
CAPRIE
Clopidogrel versus aspirin in patients at risk of Ischemic events
cdf
Cumulative distribution function
CONSORT
Consolidated Standards of Reporting Trials
DILI
Drug induced liver injury
EB
Empirical Bayes
EGFR
Epidermal growth factor receptor
EMA
European Medicines Agency
FDA
Food and Drug Administration
Fdr
False discovery rate
GISSI
Gruppo Italiano per lo Studio della Streptochinasi nell'Infarcto Miocardico
GLIM
Generalized linear model
HAMD
Hamilton depression rating scale
HER2
Human epidermal growth factor receptor 2
IPF
Idiopathic pulmonary fibrosis
IQWiQ
Institute for Quality and Efficiency in Healthcare
ITT
Intention to treat
ISIS
International Study of Infarct Survival
KM
Kaplan–Meier
KRAS
Kirsten Rat Sarcoma viral oncogene analog
Lasso
Least absolute shrinkage and selection operator
MARS
Montgomery–Asberg depression rating scale
ME
Model error
MLE
Maximum likelihood estimator
MERIT‐HF
Metoprolol controlled release randomized intervention trial in heart failure
MHLW
Ministry of Health, Labor and Welfare
NICE
National Institute of Health and Clinical Excellence
Probability density function
PE
Prediction error
PEP
Prediction error of the PITE
PITE
Predicted individual treatment effect
PLATO
Platelet Inhibition and Clinical Outcomes Trial
PMDA
Pharmaceuticals and Medical Devices Agency
RSE
Residual squared error
r.v.
Random variable(s)
SE
Standard error
TARGET
Therapeutic Arthritis Research and Gastrointestinal Event Trial
TAYLORx
Trial Assigning Individualized Options for Treatment
TMS
Transcranial magnetic stimulation
About the Companion Website
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.
Introduction
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.
1Some History of Subgroup Analysis
Alvan R Feinstein (1925–2001)
The Problem of Cogent Subgroups: A Clinicostatistical Tragedy.
1.1 Introduction
The history of subgroup analysis is characterized by a strong difference in opinions about its value. One group of scientists has a skeptical attitude towards the topic warning of the risks of subgroup analysis and other attempts to target treatments. For example, Yusuf et al. (1984) stated that “…it would be unfortunate if desire for the perfect (i.e. knowledge of exactly who will benefit from treatment) were to become the enemy of the possible (i.e. knowledge of the direction and approximate size of the effects of treatment of wide categories of patients).” Many clinicians are afraid of applying the overall results of large trials to individual patients without consideration of determinants of individual responses (Rothwell, 2005) while most prominently statisticians have raised concerns (Assmann et al., 2000, Sleight, 2000, Lagakos, 2006, Guillemin, 2007, Lonergan et al., 2017) and requested that:
Investigators should be cautious when undertaking subgroup analyses.
Subgroup findings should be exploratory, and only exceptionally should they affect the conclusions from trials.
Editors and reviewers of journals need to correct any inappropriate, over‐enthusiastic uses of subgroup analyses.
The statement “subgroups kill people” was attributed – rightly or wrongly – to statistician Sir Richard Peto in van Gijn and Algra (1994). In fact, Peto commented on subgroup analyses undertaken on the GISSI1 study (GISSI Study Group, 1986): “The GISSI study…is one of the most important randomized trials ever conducted and when it was published provided the best evidence then available that thrombolytic therapy reduced mortality. But the ability of the GISSI report to save lives could be substantially compromised by misinterpretation by clinicians of some of the data‐dependent subset analyses that it contained.” (Peto, 1990)
A second camp of scientists and pharmaceutical executives is more attracted by the opportunities than by the risks of subgroup analysis driven by the vision of “personalized” medicine. In 1977, Sir Richard Sykes, at the time chief executive officer of Glaxo‐Wellcome, later chairman of GlaxoSmith‐Kline and rector of Imperial College London, wrote:
