Multiple Imputation and its Application. (2023)

• Record Type: Book
• Further Information: Note: James R. Carpenter, Jonathan W. Bartlett, Tim P. Morris, Angela M. Wood, Matteo Quartagno, Michael G. Kenward.
• Authors: Carpenter, James R; Bartlett, Jonathan W; Morris, Tim P; Wood, Angela M; Quartagno, Matteo; Kenward, Michael G
• Contents: Preface Data acknowledgments Glossary I Foundations 1 1 Introduction 2 1.1 Reasons for missing data . . . . . . . . . . . . . . . . . . . . . 5 1.2 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.3 Patterns of missing data . . . . . . . . . . . . . . . . . . . . . 8 1.3.1 Consequences of missing data . . . . . . . . . . . . . . . 10 1.4 Inferential framework and notation . . . . . . . . . . . . . . . . 13 1.4.1 Missing Completely At Random (MCAR) . . . . . . . . 15 1.4.2 Missing At Random (MAR) . . . . . . . . . . . . . . . . 16 1.4.3 Missing Not At Random (MNAR) . . . . . . . . . . . . 22 1.4.4 Ignorability . . . . . . . . . . . . . . . . . . . . . . . . . 27 1.5 Using observed data to inform assumptions about the missingness mechanism . .. . . . . . . 28 1.6 Implications of missing data mechanisms for regression analyses 32 1.6.1 Partially observed response . . . . . . . . . . . . . . . . 33 1.6.2 Missing covariates . . . . . . . . . . . . . . . . . . . . . 37 1.6.3 Missing covariates and response . . . . . . . . . . . . . . 40 1.6.4 Subtle issues I: the odds ratio . . . . . . . . . . . . . . . 40 1.6.5 Implication for linear regression . . . . . . . . . . . . . . 43 1.6.6 Subtle issues II: sub sample ignorability . . . . . . . . . 44 1.6.7 Summary: when restricting to complete records is valid 45 1.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 1.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 2 The Multiple Imputation Procedure and Its Justification 52 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 2.2 Intuitive outline of the MI procedure . . . . . . . . . . . . . . 54 2.3 The generic MI Procedure . . . . . . . . . . . . . . . . . . . . . 61 2.4 Bayesian justification of MI . . . . . . . . . . . . . . . . . . . . 64 2.5 Frequentist Inference . . . . . . . . . . . . . . . . . . . . . . . 66 2.6 Choosing the number of imputations . . . . . . . . . . . . . . . 73 2.7 Some simple examples . . . . . . . . . . . . . . . . . . . . . . . 75 2.8 MI in More General Settings . . . . . . . . . . . . . . . . . . . 84 2.8.1 Proper imputation . . . . . . . . . . . . . . . . . . . . . 84 2.8.2 Congenial imputation and substantive model . . . . . . 85 2.8.3 Uncongenial imputation and substantive models . . . . 87 2.8.4 Survey Sample Settings . . . . . . . . . . . . . . . . . . 94 2.9 Constructing congenial imputation models . . . . . . . . . . . . 95 2.10 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 2.11 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 1.6.3 Missing covariates and response . . . . . . . . . . . . . . 40 1.6.4 Subtle issues I: the odds ratio . . . . . . . . . . . . . . . 40 1.6.5 Implication for linear regression . . . . . . . . . . . . . . 43 1.6.6 Subtle issues II: sub sample ignorability . . . . . . . . . 44 1.6.7 Summary: when restricting to complete records is valid 45 1.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 1.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 2 The Multiple Imputation Procedure and Its Justification 52 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 2.2 Intuitive outline of the MI procedure . . . . . . . . . . . . . . 54 2.3 The generic MI Procedure . . . . . . . . . . . . . . . . . . . . . 61 2.4 Bayesian justification of MI . . . . . . . . . . . . . . . . . . . . 64 2.5 Frequentist Inference . . . . . . . . . . . . . . . . . . . . . . . 66 2.6 Choosing the number of imputations . . . . . . . . . . . . . . . 73 2.7 Some simple examples . . . . . . . . . . . . . . . . . . . . . . . 75 2.8 MI in More General Settings . . . . . . . . . . . . . . . . . . . 84 2.8.1 Proper imputation . . . . . . . . . . . . . . . . . . . . . 84 2.8.2 Congenial imputation and substantive model . . . . . . 85 2.8.3 Uncongenial imputation and substantive models . . . . 87 2.8.4 Survey Sample Settings . . . . . . . . . . . . . . . . . . 94 2.9 Constructing congenial imputation models . . . . . . . . . . . . 95 2.10 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 2.11 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 II Multiple imputation for simple data structures 104 3 Multiple imputation of quantitative data 105 3.1 Regression imputation with a monotone missingness pattern . . 105 3.1.1 MAR mechanisms consistent with a monotone pattern . 107 3.1.2 Justification . . . . . . . . . . . . . . . . . . . . . . . . 109 3.2 Joint modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 3.2.1 Fitting the imputation model . . . . . . . . . . . . . . 111 3.2.2 Adding covariates . . . . . . . . . . . . . . . . . . . . . 115 3.3 Full conditional specification . . . . . . . . . . . . . . . . . . . 118 3.3.1 Justification . . . . . . . . . . . . . . . . . . . . . . . . . 119 3.4 Full conditional specification versus joint modelling . . . . . . . 121 3.5 Software for multivariate normal imputation . . . . . . . . . . . 121 3.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 3.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 4 Multiple imputation of binary and ordinal data 125 4.1 Sequential imputation with monotone missingness pattern . . 125 4.2 Joint modelling with the multivariate normal distribution . . . 127 4.3 Modelling binary data using latent normal variables . . . . . . 130 4.3.1 Latent normal model for ordinal data . . . . . . . . . . 137 4.4 General location model . . . . . . . . . . . . . . . . . . . . . . 141 4.5 Full conditional specification . . . . . . . . . . . . . . . . . . . 142 4.5.1 Justification . . . . . . . . . . . . . . . . . . . . . . . . . 143 4.6 Issues with over-fitting . . . . . . . . . . . . . . . . . . . . . . 144 4.7 Pros and cons of the various approaches . . . . . . . . . . . . . 150 4.8 Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 4.9 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 4.10 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 5 Imputation of unordered categorical data 156 5.1 Monotone missing data . . . . . . . . . . . . . . . . . . . . . . 157 5.2 Multivariate normal imputation for categorical data . . . . . . 158 5.3 Maximum indicant model . . . . . . . . . . . . . . . . . . . . . 159 5.3.1 Continuous and categorical variable . . . . . . . . . . . 162 5.3.2 Imputing missing data . . . . . . . . . . . . . . . . . . . 164 5.4 General location model . . . . . . . . . . . . . . . . . . . . . . 165 5.5 FCS with categorical data . . . . . . . . . . . . . . . . . . . . 169 5.6 Perfect prediction issues with categorical data . . . . . . . . . . 170 5.7 Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 5.8 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 5.9 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173 III Multiple imputation in practice 175 6 Non-linear relationships, interactions, and other derived variables 176 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 6.1.1 Interactions . . . . . . . . . . . . . . . . . . . . . . . . . 178 6.1.2 Squares . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 6.1.3 Ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180 6.1.4 Sum scores . . . . . . . . . . . . . . . . . . . . . . . . . 181 6.1.5 Composite endpoints . . . . . . . . . . . . . . . . . . . . 182 6.2 No missing data in derived variables . . . . . . . . . . . . . . . 184 &
• Edition: 2nd
• Publisher Details: Wiley
• Publication Date: 2023
• Extent: 1 online resource (464 pages)
• Languages: English
• ISBNs: 9781119756101
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.