Self-controlled case series studies : a modelling guide with R

377 Pages·2018·30.716 MB·English

by  Farrington, Paddy, Ghebremichael Weldeselassie, Yonas, Whitaker, Heather

Self-Controlled Case
Series Studies
A Modelling Guide with R
Chapman & Hall/CRC Biostatistics Series
Shein-Chung Chow, Duke University of Medicine
Byron Jones, Novartis Pharma AG
Jen-pei Liu, National Taiwan University
Karl E. Peace, Georgia Southern University
Bruce W. Turnbull, Cornell University
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Self-Controlled Case
Series Studies
A Modelling Guide with R
By
Paddy Farrington
School of Mathematics and Statistics, The Open University, UK
Heather Whitaker
School of Mathematics and Statistics, The Open University, UK
Yonas Ghebremichael Weldeselassie
University of Warwick Medical School, UK
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Library of Congress Cataloging-in-Publication Data
Names: Farrington, Paddy, author. | Whitaker, Heather, author. |
Ghebremichael Weldeselassie, Yonas, author.
Title: Self-controlled case series studies : a modelling guide with R / Paddy
Farrington, Heather Whitaker, Yonas Ghebremichael Weldeselassie.
Description: Boca Raton, Florida : CRC Press, 2018. | Includes
bibliographical references and index.
Identifiers: LCCN 2018002262| ISBN 9781498781596 (hardback : alk. paper) |
ISBN 9780429491313 (e-book)
Subjects: LCSH: Medicine--Research--Methodology. | Clinical
trials--Methodology.
Classification: LCC R850 .F37 2018 | DDC 610.72/4--dc23
LC record available at https://lccn.loc.gov/2018002262
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Contents
Note: Starred (*) sections may be skipped.
Preface xiii
1 Introduction 1
1.1 Control and self-control in epidemiology . . . . . . . . . . . . 1
1.2 Self-controlled methods . . . . . . . . . . . . . . . . . . . . . 2
1.3 Guide to contents . . . . . . . . . . . . . . . . . . . . . . . . 4
1.4 Computer package and data . . . . . . . . . . . . . . . . . . 4
2 Epidemiological overview 7
2.1 Genesis of the SCCS method . . . . . . . . . . . . . . . . . . 7
2.2 Rationale for the SCCS method . . . . . . . . . . . . . . . . 9
2.2.1 Case series . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2.2 Self-control . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2.3 Data requirements . . . . . . . . . . . . . . . . . . . . 11
2.3 Some illustrations . . . . . . . . . . . . . . . . . . . . . . . . 13
2.3.1 Using only cases . . . . . . . . . . . . . . . . . . . . . 13
2.3.2 Controlling confounding . . . . . . . . . . . . . . . . . 16
2.4 Assumptions and alternatives . . . . . . . . . . . . . . . . . . 18
2.4.1 Assumptions of the SCCS method . . . . . . . . . . . 18
2.4.2 What if the assumptions are not satisfied? . . . . . . . 19
2.5 Bibliographical notes and further material . . . . . . . . . . 20
3 The SCCS likelihood 21
3.1 Why start with the likelihood? . . . . . . . . . . . . . . . . . 21
3.2 Likelihood for the standard SCCS model . . . . . . . . . . . 22
3.3 Properties of the SCCS likelihood . . . . . . . . . . . . . . . 26
3.4 Example: MMR vaccine and aseptic meningitis . . . . . . . . 27
3.5 The general SCCS likelihood . . . . . . . . . . . . . . . . . . 32
3.6 MMR vaccine and aseptic meningitis: derivation of the
SCCS likelihood . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.7 Assumptions of the SCCS method . . . . . . . . . . . . . . . 36
3.7.1 Assumption 1: Poisson or rare events . . . . . . . . . . 36
3.7.2 A counter-example: negative binomial events* . . . . . 37
3.7.3 Assumptions 2 and 3: validity of conditioning . . . . . 37
3.7.4 A more formal demonstration* . . . . . . . . . . . . . 39
vii
viii Contents
3.7.5 Assumption 4: independent ascertainment . . . . . . . 40
3.8 Derivation of the SCCS likelihood* . . . . . . . . . . . . . . 41
3.9 Bibliographical notes and further material . . . . . . . . . . 45
4 The standard SCCS model 47
4.1 Proportional incidence models . . . . . . . . . . . . . . . . . 47
4.2 Fitting the standard SCCS model . . . . . . . . . . . . . . . 49
4.3 The R package SCCS: standard SCCS model . . . . . . . . . 51
4.3.1 A single point exposure: MMR vaccine and ITP . . . 51
4.3.2 Reshaping the MMR vaccine and ITP data . . . . . . 55
4.3.3 Extended exposures: antidepressants and
hip fracture . . . . . . . . . . . . . . . . . . . . . . . . 57
4.4 Data formats for repeated exposures . . . . . . . . . . . . . . 59
4.4.1 Intermittent treatments: NSAIDs and GI bleeds . . . 60
4.4.2 Multiple vaccine doses: convulsions and
DTP vaccine . . . . . . . . . . . . . . . . . . . . . . . 62
4.5 Multiple exposure types . . . . . . . . . . . . . . . . . . . . . 65
4.5.1 Exposures of several types: convulsions, Hib
and MMR vaccines . . . . . . . . . . . . . . . . . . . . 66
4.5.2 Multiple exposures of several types: NSAIDs,
antidepressants and GI bleeds . . . . . . . . . . . . . . 68
4.5.3 Multiple doses of different vaccines: convulsions,
DTP and Hib vaccines . . . . . . . . . . . . . . . . . . 70
4.5.4 Overlapping risk periods: convulsions and DTP . . . . 73
4.6 Comparing models: likelihood ratio tests . . . . . . . . . . . 74
4.6.1 Comparing models: ITP and MMR vaccine . . . . . . 75
4.6.2 Combining multinomial categories* . . . . . . . . . . . 76
4.7 Interactions: effect modification and stratification . . . . . . 77
4.7.1 Interactions: sex, ITP and MMR vaccine. . . . . . . . 78
4.7.2 Interactions between exposures: GI bleeds, NSAIDs
and antidepressants . . . . . . . . . . . . . . . . . . . 81
4.8 Indefinite and extremal risk periods . . . . . . . . . . . . . . 83
4.8.1 Curtailed observation: antidiabetics and fractures . . . 84
4.8.2 Indefinite risk periods: MMR vaccine and autism . . . 87
4.8.3 Initial risk periods: NRT and MI . . . . . . . . . . . . 90
4.9 SCCS analyses with temporal effects . . . . . . . . . . . . . . 92
4.9.1 Calendar time: GBS and influenza vaccine . . . . . . . 93
4.9.2 Seasonal SCCS model: OPV and intussusception . . . 95
4.10 Parameterisation of the standard SCCS model* . . . . . . . 100
4.11 Bibliographical notes and further material . . . . . . . . . . 101
5 Checking model assumptions 103
5.1 Rare disease assumption for non-recurrent events . . . . . . . 104
5.1.1 Evaluation of absolute risks: convulsions
and stroke . . . . . . . . . . . . . . . . . . . . . . . . . 105
Contents ix
5.1.2 Quantifying the bias for non-recurrent events* . . . . 106
5.2 Poisson assumption for potentially recurrent events . . . . . 107
5.2.1 Investigating recurrences. . . . . . . . . . . . . . . . . 107
5.2.2 Recurrences for MMR and ITP data . . . . . . . . . . 109
5.2.3 Recurrent convulsions and MMR vaccine . . . . . . . 111
5.3 Event-dependent observation periods . . . . . . . . . . . . . 114
5.3.1 Investigating event-dependent observation periods . . 115
5.3.2 Planned and actual observation periods:
NRT and MI . . . . . . . . . . . . . . . . . . . . . . . 117
5.3.3 Heavy censoring: antipsychotics and stroke . . . . . . 119
5.3.4 Censoring of observation periods* . . . . . . . . . . . 125
5.4 Event-dependent exposures . . . . . . . . . . . . . . . . . . . 127
5.4.1 Investigating event-dependent exposures . . . . . . . . 128
5.4.2 Event-dependence of exposures: ITP and MMR . . . . 130
5.4.3 Event-dependence with multiple exposures:
NSAIDs, antidepressants and GI bleeds . . . . . . . . 134
5.4.4 Long-term dependence: influenza vaccine and GBS . . 137
5.4.5 Interpretation of pre-exposure risk period* . . . . . . 140
5.5 Modelling assumptions . . . . . . . . . . . . . . . . . . . . . 143
5.5.1 Checking the model . . . . . . . . . . . . . . . . . . . 143
5.5.2 Risk periods and age groups: MMR and convulsions . 144
5.5.3 Homogeneity of effect: MMR and convulsions . . . . . 147
5.6 Asymptotic assumptions . . . . . . . . . . . . . . . . . . . . 149
5.6.1 Permutation test for the aseptic meningitis data . . . 150
5.6.2 Permutation test for the ITP data . . . . . . . . . . . 151
5.7 Bibliographical notes and further material . . . . . . . . . . 154
6 Further SCCS models 157
6.1 Semiparametric SCCS model . . . . . . . . . . . . . . . . . . 157
6.1.1 Formulation of the semiparametric model . . . . . . . 158
6.1.2 Semiparametric model for the MMR and ITP data . . 160
6.1.3 Semiparametric model for the MMR and
autism data . . . . . . . . . . . . . . . . . . . . . . . . 162
6.1.4 Further details of the semiparametric model* . . . . . 163
6.2 SCCS model with spline-based age effect . . . . . . . . . . . 166
6.2.1 Splines for the relative age effect . . . . . . . . . . . . 167
6.2.2 Spline model for age: MMR vaccine and ITP . . . . . 170
6.2.3 Spline model for age: antidepressants and
hip fracture . . . . . . . . . . . . . . . . . . . . . . . . 173
6.2.4 Precision of estimators: MMR and autism . . . . . . . 176
6.2.5 Modelling with M-splines* . . . . . . . . . . . . . . . . 179
6.3 SCCS models with spline-based exposure effect . . . . . . . . 181
6.3.1 Splines for exposure effects . . . . . . . . . . . . . . . 182
6.3.2 Spline model for exposure: MMR and autism . . . . . 185