Multiple Imputation and its Application by James Carpenter

TABLE OF CONTENTS
Preface xi

Data acknowledgements xiii

Acknowledgements xv

Glossary xvii

PART I FOUNDATIONS 1

1 Introduction 3

1.1 Reasons for missing data 4

1.2 Examples 6

1.3 Patterns of missing data 7

1.3.1 Consequences of missing data 9

1.4 Inferential framework and notation 10

1.4.1 Missing Completely At Random (MCAR) 11

1.4.2 Missing At Random (MAR) 12

1.4.3 Missing Not At Random (MNAR) 17

1.4.4 Ignorability 21

1.5 Using observed data to inform assumptions about the missingness mechanism 21

1.6 Implications of missing data mechanisms for regression analyses 24

1.6.1 Partially observed response 24

1.6.2 Missing covariates 28

1.6.3 Missing covariates and response 30

1.6.4 Subtle issues I: The odds ratio 30

1.6.5 Implication for linear regression 32

1.6.6 Subtle issues II: Subsample ignorability 33

1.6.7 Summary: When restricting to complete records is valid 34

1.7 Summary 35

2 The multiple imputation procedure and its justification 37

2.1 Introduction 37

2.2 Intuitive outline of the MI procedure 38

2.3 The generic MI procedure 44

2.4 Bayesian justification of MI 46

2.5 Frequentist inference 48

2.5.1 Large number of imputations 49

2.5.2 Small number of imputations 49

2.6 Choosing the number of imputations 54

2.7 Some simple examples 55

2.8 MI in more general settings 62

2.8.1 Survey sample settings 70

2.9 Constructing congenial imputation models 70

2.10 Practical considerations for choosing imputation models 71

2.11 Discussion 73

Collecting, analysing and drawing inferences from data is central to research in the medical and social sciences. Unfortunately, it is rarely possible to collect all the intended data. The literature on inference from the resulting incomplete data is now huge, and continues to grow both as methods are developed for large and complex data structures, and as increasing computer power and suitable software enable researchers to apply these methods.

This book focuses on a particular statistical method for analysing and drawing inferences from incomplete data, called Multiple Imputation (MI). MI is attractive because it is both practical and widely applicable. The authors aim is to clarify the issues raised by missing data, describing the rationale for MI, the relationship between the various imputation models and associated algorithms and its application to increasingly ...