Multiple Imputation and its Application

A practical guide to analysing partially observed
data.

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 complex data
structures.

Multiple Imputation and its Application:

• Discusses the issues raised by the analysis of partially
  observed data, and the assumptions on which analyses rest.

• Presents a practical guide to the issues to consider when
  analysing incomplete data from both observational studies and
  randomized trials.

• Provides a detailed discussion of the practical use of MI with
  real-world examples drawn from medical and social statistics.

• Explores handling non-linear relationships and interactions
  with multiple imputation, survival analysis, multilevel multiple
  imputation, sensitivity analysis via multiple imputation, using
  non-response weights with multiple imputation and doubly robust
  multiple imputation.

Multiple Imputation and its Application is aimed at
quantitative researchers and students in the medical and social
sciences with the aim of clarifying the issues raised by the
analysis of incomplete data data, outlining the rationale for MI
and describing how to consider and address the issues that arise in
its application.

Auteur

James Carpenter, Medical Statistics Unit, London School of Hygiene and Tropical Medicine, UK.

Michael G. Kenward, Medical Statistics Unit, London School of Hygiene and Tropical Medicine, UK
Amongst other areas Professor Kenward has worked in pre-clinical and clinical medicine and epidemiology for over twenty years, holding a number of international positions. He has also been a statistical consultant for over twenty years, predominantly in medical research. He has taught over 80 short courses in biostatistics throughout the world, and is the author of the book Analysis of Repeated Measurements.

Both authors act as consultants in missing data problems in biostatistics for several major pharmaceutical companies. They have been funded since 2002 by the UK Economic and Social Research Council to develop multiple imputation software for multilevel data, and to provide training for research scientists in the handling of missing data from observational studies.

Résumé

A practical guide to analysing partially observed data.

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 complex data structures.

Multiple Imputation and its Application:

• Discusses the issues raised by the analysis of partially observed data, and the assumptions on which analyses rest.
• Presents a practical guide to the issues to consider when analysing incomplete data from both observational studies and randomized trials.
• Provides a detailed discussion of the practical use of MI with real-world examples drawn from medical and social statistics.
• Explores handling non-linear relationships and interactions with multiple imputation, survival analysis, multilevel multiple imputation, sensitivity analysis via multiple imputation, using non-response weights with multiple imputation and doubly robust multiple imputation.
  Multiple Imputation and its Application is aimed at quantitative researchers and students in the medical and social sciences with the aim of clarifying the issues raised by the analysis of incomplete data data, outlining the rationale for MI and describing how to consider and address the issues that arise in its application.

Contenu

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

PART II MULTIPLE IMPUTATION FOR CROSS SECTIONAL DATA 75

3 Multiple imputation of quantitative data 77

3.1 Regression imputation with a monotone missingness pattern 77

3.1.1 MAR mechanisms consistent with a monotone pattern 79

3.1.2 Justification 81

3.2 Joint modelling 81

3.2.1 Fitting the imputation model 82

3.3 Full conditional specification 85

3.3.1 Justification 86

3.4 Full conditional specification versus joint modelling 87

3.5 Software for multivariate normal imputation 88

3.6 Discussion 88

4 Multiple imputation of binary and ordinal data 90

4.1 Sequential imputation with monotone missingness pattern 90

4.2 Joint modelling with the multivariate normal distribution 92

4.3 Modelling binary data using latent normal variables 94

4.3.1 Latent normal model for ordinal data 98

4.4 General location model 103

4.5 Full conditional specification 103

4.5.1 Justification 103

4.6 Issues with over-fitting 104

4.7 Pros and cons of the various approaches 109

4.8 Software 110

4.9 Discussion 111

5 Multiple imputation of unordered categorical data 112

5.1 Monotone missing data 112

5.2 Multivariate normal imputation for categorical data 114

5.…