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Файл:Ординатура / Хирургия / Библиотека им академика М.И. Перельмана / Книга_5431_Библиотеки_им_академика_М_И_Перельмана.pdf
Causal Inference in
Pharmaceutical Statistics
Causal Inference in Pharmaceutical Statistics introduces the basic concepts and fundamen-
tal methods of causal inference relevant to pharmaceutical statistics. is book covers causal
thinking for dierent types of commonly used study designs in the pharmaceutical industry,
including but not limited to randomized controlled clinical trials, longitudinal studies, single-
arm clinical trials with external controls, and real-world evidence studies. e book starts with
the central questions in drug development and licensing, takes the reader through the basic
concepts and methods via dierent study types and through dierent stages, and concludes
with a roadmap to conduct causal inference in clinical studies. e book is intended for clinical
statisticians and epidemiologists working in the pharmaceutical industry. It will also be useful
to graduate students in statistics, biostatistics, and data science looking to pursue a career in the
pharmaceutical industry.
Key Features:
• Causal inference book for clinical statisticians in the pharmaceutical industry
• Introductory level on the most important concepts and methods
• Align with FDA and ICH guidance documents
• Across dierent stages of clinical studies
• Cover a variety of commonly used study designs
Yixin Fang, Ph.D. is Director of Statistics and Research Fellow at AbbVie Inc. He obtained his
Ph.D. in Statistics from Columbia University and is an experienced statistician and data scientist
who has a history of working in both the biopharmaceutical industry and academia.
Chapman & Hall/CRC Biostatistics Series
Series Editors
Shein-Chung Chow, Duke University School of Medicine, USA
Byron Jones, Novartis Pharma AG, Switzerland
Jen-pei Liu, National Taiwan University, Taiwan
Karl E. Peace, Georgia Southern University, USA
Bruce W. Turnbull, Cornell University, USA
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For more information about this series, please visit: https://www.routledge.com/
Chapman--Hall-CRC-Biostatistics-Series/book-series/CHBIOSTATIS
Causal Inference in
Pharmaceutical Statistics
Yixin Fang
Designe d cover image: © Shutters tock Stock Illustration: 197106719, Illust ration Contributor Mopic
First edition published 2024
by CRC Press
2385 NW Executive Center Drive, Suite 320, Boca Raton FL 33431
and by CRC Press
4 Park Square, Milton Park, Abingdon, Oxon, OX14 4RN
CRC Press is an imprint of Taylor & Francis Group, LLC
© 2024 Yixin Fang
Reasonable eorts have been made to publish reliable data and information, but the author and pub-
lisher cannot assume responsibility for the validity of all materials or the consequences of their use.
e authors and publishers have attempted to trace the copyright holders of all material reproduced
in this publication and apologize to copyright holders if permission to publish in this form has not
been obtained. If any copyright material has not been acknowledged please write and let us know so
we may rectify in any future reprint.
Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced,
transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or
hereafter invented, including photocopying, microlming, and recording, or in any information
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Trademark notice: Product or corporate names may be trademarks or registered trademarks and are
used only for identication and explanation without intent to infringe.
ISBN: 978-1-032-56014-4 (hbk)
ISBN: 978-1-032-56015-1 (pbk)
ISBN: 978-1-003-43337-8 (ebk)
DOI: 10.1201/9781003433378
Typeset in CMR10
by KnowledgeWorks Global Ltd.
Publisher’s note: is book has been prepared from camera-ready copy provided by the authors.
To Mandy, Sophie, and Roger
Contents
Preface xiii
1 Introduction 1
1.1 CentralQuestions ......................... 1
1.2 PotentialOutcomes......................... 3
1.3 Estimand .............................. 5
1.3.1 The PROTECT checklist ................. 5
1.3.2 Estimandforagivenpopulation ............. 6
1.3.3 Estimandforagivensuper-population.......... 8
1.3.4 Internalvalidityandexternalvalidity .......... 8
1.4 Probability and Statistics ..................... 10
1.4.1 Probability ......................... 10
1.4.2 Directedacyclicgraphs .................. 13
1.4.3 Statistics .......................... 15
1.5 Exercises .............................. 16
2 Randomized Controlled Clinical Trials 19
2.1 RandomizationandBlinding ................... 19
2.2 Estimand .............................. 21
2.2.1 Causalestimand ...................... 21
2.2.2 Statisticalestimand .................... 22
2.3 Estimator .............................. 24
2.3.1 Expectationoftheestimator ............... 24
2.3.2 Varianceoftheestimator ................. 26
2.3.3 Statisticalinference .................... 29
2.4 CommonTypesofRandomization ................ 30
2.4.1 Simplerandomization ................... 30
2.4.2 Blockrandomization.................... 33
2.4.3 Stratifiedrandomization.................. 34
2.5 Exercises .............................. 38
3 Missing Data Handling 40
3.1 MissingData ............................ 40
3.2 Intent-to-treatEffect........................ 41
3.2.1 Scenarioone ........................ 41
3.2.2 Scenariotwo ........................ 42
vii
viii Contents
3.3 Per-protocolEffect ......................... 45
3.4 SourcesofMissingData ...................... 48
3.4.1 Intercurrentevents..................... 48
3.4.2 MissingdatathatareconsequencesofICEs ....... 49
3.4.3 Missing data that are not consequences of ICEs . . . . . 50
3.5 Appendix .............................. 51
3.6 Exercises .............................. 52
4 Intercurrent Events Handling 54
4.1 FiveStrategies ........................... 54
4.1.1 Thetreatmentpolicystrategy............... 55
4.1.2 Thehypotheticalstrategy................. 57
4.1.3 Thecompositevariablestrategy ............. 59
4.1.4 Thewhileontreatmentstrategy ............. 62
4.1.5 Theprincipalstratumstrategy .............. 63
4.2 CombinationsofStrategies .................... 70
4.3 Time-to-eventOutcome ...................... 72
4.3.1 Censoring.......................... 72
4.3.2 Thetreatmentpolicystrategy............... 73
4.3.3 Thehypotheticalstrategy................. 73
4.3.4 Thecompositevariablestrategy ............. 73
4.3.5 Thewhileontreatmentstrategy ............. 73
4.3.6 Theprincipalstratumstrategy .............. 74
4.3.7 Thecompetingriskstrategy................ 74
4.4 SampleSizeCalculation ...................... 74
4.4.1 Thetreatmentpolicystrategy............... 75
4.4.2 Thehypotheticalstrategy................. 76
4.4.3 Thecompositevariablestrategy ............. 76
4.4.4 Thewhileontreatmentstrategy ............. 76
4.4.5 Theprincipalstratumstrategy .............. 77
4.5 Exercises .............................. 77
5 Longitudinal Studies 79
5.1 ContinuousorBinaryOutcome .................. 79
5.1.1 Theintent-to-treateffect ................. 80
5.1.2 Theper-protocoleffect................... 86
5.2 Time-to-eventOutcome ...................... 89
5.2.1 Theintent-to-treateffect ................. 91
5.2.2 Theper-protocoleffect................... 92
5.3 TreatmentRegimes......................... 92
5.3.1 Dynamictreatmentregimes................ 94
5.3.2 SMARTdesign....................... 95
5.4 Exercises .............................. 97
Contents ix
6 Real-World Evidence Studies 99
6.1 RWEStudies ............................ 99
6.1.1 PragmaticRCTs ...................... 99
6.1.2 Observationalstudies ...................100
6.1.3 Externallycontrolledtrials ................101
6.2 Confounding Bias ..........................101
6.2.1 No unmeasured confounder . ...............102
6.2.2 Unmeasured confounders .................105
6.2.3 Proxyvariables.......................107
6.3 LongitudinalCohortStudies....................109
6.3.1 Causalestimand ......................109
6.3.2 Identifiabilityassumptions.................110
6.3.3 Identification ........................111
6.4 ExternallyControlledTrials....................113
6.4.1 Causalestimand ......................113
6.4.2 Identification ........................114
6.5 Appendix ..............................115
6.6 Exercises ..............................117
7 The Art of Estimation (I): M-estimation 119
7.1 Introduction.............................119
7.2 M-estimation ............................120
7.2.1 M-estimator.........................120
7.2.2 Asymptoticlinearity ....................122
7.2.3 Regularity..........................122
7.3 G-computationEstimator .....................127
7.3.1 Plug-inestimator......................127
7.3.2 MLE.............................128
7.3.3 Asymptoticvariance ....................130
7.3.4 Influence function . . . ..................131
7.4 Inverse Probability Weighted Estimator .............131
7.4.1 IPWestimator .......................131
7.4.2 Asymptoticvariance ....................132
7.4.3 Influence function . . . ..................134
7.5 Augmented Inverse Probability Weighted Estimator ......134
7.5.1 Aclassofestimators....................134
7.5.2 Asymptoticvariances ...................135
7.5.3 AIPWestimator ......................136
7.5.4 Doublerobustness .....................138
7.5.5 Influence function . . . ..................139
7.6 Exercises ..............................140