Michael O'Kelly, Bohdana Ratitch
Clinical Trials with Missing Data (eBook, PDF)
A Guide for Practitioners
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Michael O'Kelly, Bohdana Ratitch
Clinical Trials with Missing Data (eBook, PDF)
A Guide for Practitioners
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This book provides practical guidance for statisticians, clinicians, and researchers involved in clinical trials in the biopharmaceutical industry, medical and public health organisations. Academics and students needing an introduction to handling missing data will also find this book invaluable. The authors describe how missing data can affect the outcome and credibility of a clinical trial, show by examples how a clinical team can work to prevent missing data, and present the reader with approaches to address missing data effectively. The book is illustrated throughout with realistic case…mehr
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This book provides practical guidance for statisticians, clinicians, and researchers involved in clinical trials in the biopharmaceutical industry, medical and public health organisations. Academics and students needing an introduction to handling missing data will also find this book invaluable. The authors describe how missing data can affect the outcome and credibility of a clinical trial, show by examples how a clinical team can work to prevent missing data, and present the reader with approaches to address missing data effectively. The book is illustrated throughout with realistic case studies and worked examples, and presents clear and concise guidelines to enable good planning for missing data. The authors show how to handle missing data in a way that is transparent and easy to understand for clinicians, regulators and patients. New developments are presented to improve the choice and implementation of primary and sensitivity analyses for missing data. Many SAS code examples are included - the reader is given a toolbox for implementing analyses under a variety of assumptions.
Produktdetails
- Produktdetails
- Verlag: John Wiley & Sons
- Seitenzahl: 472
- Erscheinungstermin: 14. Februar 2014
- Englisch
- ISBN-13: 9781118762509
- Artikelnr.: 40502122
- Verlag: John Wiley & Sons
- Seitenzahl: 472
- Erscheinungstermin: 14. Februar 2014
- Englisch
- ISBN-13: 9781118762509
- Artikelnr.: 40502122
MICHAEL O'KELLY, Senior Strategic Biostatistics Director, Quintiles Ireland Ltd, Ireland. BOHDANA RATITCH, Senior Biostatistician, Quintiles, Montreal, Canada.
Preface References Acknowledgements Notation 1. What's the problem with
missing data? 1.1 What do we mean by missing data? 1.1.1 Monotone and
non-monotone missing data 1.1.2 Modeling missingness, modeling the missing
value and ignorability 1.1.3 Types of missingness (MCAR, MAR, and MNAR)
1.1.4 Missing data and study objectives 1.2 An illustration 1.3 Why can't I
use only the available primary endpoint data? 1.4 What's the problem with
using last observation carried forward? 1.5 Can we just assume that data
are missing at random? 1.6 What can be done if data may be missing not at
random? 1.7 Stress-testing study results for robustness to missing data 1.8
How the pattern of dropouts can bias the outcome 1.9 How do we formulate a
strategy for missing data? 1.10 Description of Example Datasets 1.10.1
Example dataset in Parkinson's disease treatment 1.10.2 Example dataset in
insomnia treatment 1.10.3 Example dataset in mania treatment 1.A Appendix:
Formal definitions of MCAR, MAR, and MNAR References 2 The prevention of
missing data 2.1 Introduction 2.2 The impact of 'too much' missing data
2.2.1 Example from human immunodeficiency virus 2.2.2 Example from acute
coronary syndrome 2.2.3 Example from studies in pain 2.3 The role of the
statistician in the prevention of missing data 2.3.1 Illustrative example
from HIV Step 1: Quantifying the amount of missing data in previous trials,
and its resultant impact Step 2: Identifying subgroups of subjects who
require an increased level of trial retention support Step 3: Translating
statistical analysis of previous trial data into information to inform
future subject care Step 4: Education of the clinical trial team and
participation in the creation of missing data prevention plans 2.4 Methods
for increasing subject retention 2.5 Improving understanding of reasons for
subject withdrawal 2.6 Acknowledgements 2.7 Appendix 2.A: example protocol
text for missing data prevention References 3 Regulatory guidance - a quick
tour 3.1 International Conference on Harmonization guideline: Statistical
principles for clinical trials: E9 3.2 The U.S. and EU regulatory documents
3.3 Key points in the regulatory documents on missing data 3.4 Regulatory
guidance on particular statistical approaches 3.4.1 Available cases 3.4.2
Single imputation methods 3.4.3 Methods that generally assume MAR 3.4.4
Methods that are used assuming MNAR 3.5 Guidance about how to plan for
missing data in a study 3.6 Differences in emphasis between the NRC report
and EU guidance documents 3.6.1 The term "conservative" 3.6.2 Last
observation carried forward 3.6.3 Post hoc analyses 3.6.4 Non-monotone or
intermittently missing data 3.6.5 Assumptions should be readily
interpretable 3.6.6 Study report 3.6.7 Training 3.7 Other technical points
from the NRC report 3.7.1 Time-to-event analyses 3.7.2 Tipping point
sensitivity analyses 3.8 Other U.S./EU/international guidance documents
that refer to missing data 3.8.1 Committee for Medicinal Products for Human
Use guideline on anticancer products, recommendations on survival analysis
3.8.2 U.S. guidance on considerations when research supported by Office of
Human Research Protections is discontinued 3.8.3 FDA guidance on data
retention 3.9 And in practice? References 4 A guide to planning for missing
data 4.1 Introduction 4.1.1 Missing data may bias trial results or make
them more difficult to generalize to subjects outside the trial 4.1.2
Credibility of trial results when there is missing data 4.1.3 Demand for
better practice with regard to missing data 4.2 Planning for missing data
4.2.1 The case report form and non-statistical sections of the protocol
4.2.2 The statistical sections of the protocol and the statistical analysis
plan 4.2.3 Using historic data to narrow the choice of primary analysis and
sensitivity analyses 4.2.4 Key points in choosing an approach for missing
data MAR LOCF-like approaches BOCF-like and worst-case approaches Control
based or reference-based imputation Assuming a variety of outcomes for
missing values, depending on reason for discontinuation Likelihood based
analysis of continuous outcome variables Likelihood based analysis of
binary response variables using longitudinal generalized linear mixed
models (GLMM) Doubly robust estimation Multiple imputation Pattern-mixture
models Selection models and shared parameter models 4.3 Exploring and
presenting missingness 4.4 Model checking 4.5 Interpreting model results
when there is missing data 4.6 Sample size and missing data Appendix 4.A:
Sample protocol/SAP text for study in Parkinson's disease Appendix 4.B: A
formal definition of a sensitivity parameter References 5 Mixed Models for
Repeated Measures Using Categorical Time Effects (MMRM) 5.1 Introduction
5.2 Specifying the MMRM 5.2.1 The mixed model 5.2.2 Covariance structures
5.2.3 MMRM versus generalized estimating equations (GEE) 5.2.4 MMRM versus
LOCF 5.3 Understanding the data 5.3.1 Parkinson's disease example 5.3.2 A
second example showing the usefulness of plots: CATIE 5.4 Applying the MMRM
5.4.1 Specifying the model 5.4.2 Interpreting and presenting results 5.5
Additional MMRM topics 5.5.1 Treatment by subgroup and treatment by site
interactions 5.5.2 Calculating the effect size 5.5.3 Another strategy to
model baseline 5.6 Logistic regression MMRM with generalized linear mixed
model (GLMM) 5.6.1 The generalized linear mixed model 5.6.2 Specifying the
model 5.6.3 Interpreting and presenting results 5.6.4 Other modeling
options References Table of SAS Code Fragments 6 Multiple imputation 6.1
Introduction 6.1.1 How is MI different from single imputation? 6.1.2 How is
MI different from maximum likelihood methods? 6.1.3 MI's assumptions about
missingness mechanism 6.1.4 A general 3-step process for multiple
imputation and inference 6.1.5 Imputation versus analysis model 6.1.6 Note
on notation use 6.2 Imputation Phase 6.2.1 Missing patterns: monotone and
non-monotone 6.2.2 How do we get multiple imputations? 6.2.3 Imputation
strategies: sequential univariate versus joint multivariate 6.2.4 Overview
of the imputation methods 6.2.5 Reusing the multiply-imputed dataset for
different analyses or summary scales 6.3 Analysis phase: analyzing multiple
imputed datasets 6.4 Pooling phase: combining results from multiple
datasets 6.4.1 Combination rules 6.4.2 Pooling analyses of continuous
outcomes 6.4.3 Pooling analyses of categorical outcomes 6.5 Required number
of imputations 6.6 Some practical considerations 6.6.1 Choosing an
imputation model 6.6.2 Multivariate normality 6.6.3 Rounding and
restricting the range for the imputed values 6.6.4 Convergence of MCMC 6.7
Pre-specifying details of analysis with multiple imputation 6.A Appendix:
Additional methods for multiple imputation References 7 Analyses under
missing-not-at-random assumptions 7.1 Introduction 7.2 Background to
sensitivity analyses and pattern-mixture models 7.2.1 The purpose of a
sensitivity analysis 7.2.2 Pattern-mixture models as sensitivity analyses
7.3 Two methods of implementing sensitivity analyses via PMMs 7.3.1 A
sequential method of implementing pattern-mixture models with MI 7.3.2
Providing stress-testing "what ifs" using pattern-mixture models 7.3.3 Two
implementations of pattern-mixture models for sensitivity analyses 7.3.4
Characteristics and limitations of the sequential modeling method of
implementing PMMs 7.3.5 PMMs implemented using the joint modeling method
7.3.6 Characteristics of the joint modeling method of implementing PMMs
7.3.7 Summary of differences between the joint modeling and sequential
modeling methods 7.4 A "toolkit": implementing sensitivity analyses via SAS
7.4.1 Reminder: general approach using MI with regression 7.4.2 Sensitivity
analyses assuming withdrawals have trajectory of control arm 7.4.3
Sensitivity analyses assuming withdrawals have distribution of control arm
7.4.4 BOCF-like and LOCF-like analyses 7.4.5 The general principle of using
selected subsets of observed data as the basis to implement "what if"
stress-tests 7.4.6 Using a mixture of "what ifs," depending on reason for
discontinuation 7.4.7 Assuming trajectory of withdrawals is worse by some
delta: delta adjustment and tipping point analysis 7.5 Examples of
realistic strategies and results for illustrative datasets of three
indications 7.5.1 Parkinson's disease 7.5.2 Insomnia 7.5.3 Mania Appendix
7.A: How one could implement NCMV using visit-by-visit MI for the example
trial Appendix 7.B: SAS code to model withdrawals from the experimental
arm, using observed data from the control arm Appendix 7.C: SAS code to
model early withdrawals from the experimental arm, using the LOCF-like
values Appendix 7.D: SAS macro to impose delta adjustment on a responder
variable in the mania dataset Appendix 7.E: SAS code to implement tipping
point via exhaustive scenarios for the withdrawals in the mania dataset
Appendix 7.F: Code to perform sensitivity analyses for the Parkinson's
disease dataset Appendix 7.G: Code to perform sensitivity analyses for the
insomnia dataset Appendix 7.H: Code to perform sensitivity analyses for the
mania dataset Appendix 7.I: Selection models Appendix 7.J: Shared parameter
models References Table of SAS Code Fragments 8 Doubly Robust Estimation
8.1 Introduction 8.2 Inverse probability weighted estimation 8.2.1 IPW
estimators for estimating equations 8.2.2 Summary of IPW advantages 8.2.3
IPW disadvantages 8.3 Doubly robust estimation 8.3.1 Doubly robust methods
explained 8.3.2 Advantages of DR methods 8.3.3 Limitations of DR methods
8.4 Vansteelandt et al. method for doubly robust estimation 8.4.1
Theoretical justification for the Vansteelandt et al. method 8.4.2
Implementation of the Vansteelandt et al. method for DR estimation
Non-monotone missing data How regression parameters are estimated
Restrictions on regression parameters Missing covariates Binary covariates
Binary responses Auxiliary variables 8.5 Implementing the Vansteelandt et
al. method via SAS 8.5.1 Mania dataset 8.5.2 Insomnia dataset Appendix 8.A:
How to implement Vansteelandt et al. method for mania dataset (binary
response) Appendix 8.B: SAS code to calculate estimates from the
bootstrapped data sets Appendix 8.C: How to implement Vansteelandt et al.
method for insomnia dataset References Table of SAS Code Fragments
Bibliography
missing data? 1.1 What do we mean by missing data? 1.1.1 Monotone and
non-monotone missing data 1.1.2 Modeling missingness, modeling the missing
value and ignorability 1.1.3 Types of missingness (MCAR, MAR, and MNAR)
1.1.4 Missing data and study objectives 1.2 An illustration 1.3 Why can't I
use only the available primary endpoint data? 1.4 What's the problem with
using last observation carried forward? 1.5 Can we just assume that data
are missing at random? 1.6 What can be done if data may be missing not at
random? 1.7 Stress-testing study results for robustness to missing data 1.8
How the pattern of dropouts can bias the outcome 1.9 How do we formulate a
strategy for missing data? 1.10 Description of Example Datasets 1.10.1
Example dataset in Parkinson's disease treatment 1.10.2 Example dataset in
insomnia treatment 1.10.3 Example dataset in mania treatment 1.A Appendix:
Formal definitions of MCAR, MAR, and MNAR References 2 The prevention of
missing data 2.1 Introduction 2.2 The impact of 'too much' missing data
2.2.1 Example from human immunodeficiency virus 2.2.2 Example from acute
coronary syndrome 2.2.3 Example from studies in pain 2.3 The role of the
statistician in the prevention of missing data 2.3.1 Illustrative example
from HIV Step 1: Quantifying the amount of missing data in previous trials,
and its resultant impact Step 2: Identifying subgroups of subjects who
require an increased level of trial retention support Step 3: Translating
statistical analysis of previous trial data into information to inform
future subject care Step 4: Education of the clinical trial team and
participation in the creation of missing data prevention plans 2.4 Methods
for increasing subject retention 2.5 Improving understanding of reasons for
subject withdrawal 2.6 Acknowledgements 2.7 Appendix 2.A: example protocol
text for missing data prevention References 3 Regulatory guidance - a quick
tour 3.1 International Conference on Harmonization guideline: Statistical
principles for clinical trials: E9 3.2 The U.S. and EU regulatory documents
3.3 Key points in the regulatory documents on missing data 3.4 Regulatory
guidance on particular statistical approaches 3.4.1 Available cases 3.4.2
Single imputation methods 3.4.3 Methods that generally assume MAR 3.4.4
Methods that are used assuming MNAR 3.5 Guidance about how to plan for
missing data in a study 3.6 Differences in emphasis between the NRC report
and EU guidance documents 3.6.1 The term "conservative" 3.6.2 Last
observation carried forward 3.6.3 Post hoc analyses 3.6.4 Non-monotone or
intermittently missing data 3.6.5 Assumptions should be readily
interpretable 3.6.6 Study report 3.6.7 Training 3.7 Other technical points
from the NRC report 3.7.1 Time-to-event analyses 3.7.2 Tipping point
sensitivity analyses 3.8 Other U.S./EU/international guidance documents
that refer to missing data 3.8.1 Committee for Medicinal Products for Human
Use guideline on anticancer products, recommendations on survival analysis
3.8.2 U.S. guidance on considerations when research supported by Office of
Human Research Protections is discontinued 3.8.3 FDA guidance on data
retention 3.9 And in practice? References 4 A guide to planning for missing
data 4.1 Introduction 4.1.1 Missing data may bias trial results or make
them more difficult to generalize to subjects outside the trial 4.1.2
Credibility of trial results when there is missing data 4.1.3 Demand for
better practice with regard to missing data 4.2 Planning for missing data
4.2.1 The case report form and non-statistical sections of the protocol
4.2.2 The statistical sections of the protocol and the statistical analysis
plan 4.2.3 Using historic data to narrow the choice of primary analysis and
sensitivity analyses 4.2.4 Key points in choosing an approach for missing
data MAR LOCF-like approaches BOCF-like and worst-case approaches Control
based or reference-based imputation Assuming a variety of outcomes for
missing values, depending on reason for discontinuation Likelihood based
analysis of continuous outcome variables Likelihood based analysis of
binary response variables using longitudinal generalized linear mixed
models (GLMM) Doubly robust estimation Multiple imputation Pattern-mixture
models Selection models and shared parameter models 4.3 Exploring and
presenting missingness 4.4 Model checking 4.5 Interpreting model results
when there is missing data 4.6 Sample size and missing data Appendix 4.A:
Sample protocol/SAP text for study in Parkinson's disease Appendix 4.B: A
formal definition of a sensitivity parameter References 5 Mixed Models for
Repeated Measures Using Categorical Time Effects (MMRM) 5.1 Introduction
5.2 Specifying the MMRM 5.2.1 The mixed model 5.2.2 Covariance structures
5.2.3 MMRM versus generalized estimating equations (GEE) 5.2.4 MMRM versus
LOCF 5.3 Understanding the data 5.3.1 Parkinson's disease example 5.3.2 A
second example showing the usefulness of plots: CATIE 5.4 Applying the MMRM
5.4.1 Specifying the model 5.4.2 Interpreting and presenting results 5.5
Additional MMRM topics 5.5.1 Treatment by subgroup and treatment by site
interactions 5.5.2 Calculating the effect size 5.5.3 Another strategy to
model baseline 5.6 Logistic regression MMRM with generalized linear mixed
model (GLMM) 5.6.1 The generalized linear mixed model 5.6.2 Specifying the
model 5.6.3 Interpreting and presenting results 5.6.4 Other modeling
options References Table of SAS Code Fragments 6 Multiple imputation 6.1
Introduction 6.1.1 How is MI different from single imputation? 6.1.2 How is
MI different from maximum likelihood methods? 6.1.3 MI's assumptions about
missingness mechanism 6.1.4 A general 3-step process for multiple
imputation and inference 6.1.5 Imputation versus analysis model 6.1.6 Note
on notation use 6.2 Imputation Phase 6.2.1 Missing patterns: monotone and
non-monotone 6.2.2 How do we get multiple imputations? 6.2.3 Imputation
strategies: sequential univariate versus joint multivariate 6.2.4 Overview
of the imputation methods 6.2.5 Reusing the multiply-imputed dataset for
different analyses or summary scales 6.3 Analysis phase: analyzing multiple
imputed datasets 6.4 Pooling phase: combining results from multiple
datasets 6.4.1 Combination rules 6.4.2 Pooling analyses of continuous
outcomes 6.4.3 Pooling analyses of categorical outcomes 6.5 Required number
of imputations 6.6 Some practical considerations 6.6.1 Choosing an
imputation model 6.6.2 Multivariate normality 6.6.3 Rounding and
restricting the range for the imputed values 6.6.4 Convergence of MCMC 6.7
Pre-specifying details of analysis with multiple imputation 6.A Appendix:
Additional methods for multiple imputation References 7 Analyses under
missing-not-at-random assumptions 7.1 Introduction 7.2 Background to
sensitivity analyses and pattern-mixture models 7.2.1 The purpose of a
sensitivity analysis 7.2.2 Pattern-mixture models as sensitivity analyses
7.3 Two methods of implementing sensitivity analyses via PMMs 7.3.1 A
sequential method of implementing pattern-mixture models with MI 7.3.2
Providing stress-testing "what ifs" using pattern-mixture models 7.3.3 Two
implementations of pattern-mixture models for sensitivity analyses 7.3.4
Characteristics and limitations of the sequential modeling method of
implementing PMMs 7.3.5 PMMs implemented using the joint modeling method
7.3.6 Characteristics of the joint modeling method of implementing PMMs
7.3.7 Summary of differences between the joint modeling and sequential
modeling methods 7.4 A "toolkit": implementing sensitivity analyses via SAS
7.4.1 Reminder: general approach using MI with regression 7.4.2 Sensitivity
analyses assuming withdrawals have trajectory of control arm 7.4.3
Sensitivity analyses assuming withdrawals have distribution of control arm
7.4.4 BOCF-like and LOCF-like analyses 7.4.5 The general principle of using
selected subsets of observed data as the basis to implement "what if"
stress-tests 7.4.6 Using a mixture of "what ifs," depending on reason for
discontinuation 7.4.7 Assuming trajectory of withdrawals is worse by some
delta: delta adjustment and tipping point analysis 7.5 Examples of
realistic strategies and results for illustrative datasets of three
indications 7.5.1 Parkinson's disease 7.5.2 Insomnia 7.5.3 Mania Appendix
7.A: How one could implement NCMV using visit-by-visit MI for the example
trial Appendix 7.B: SAS code to model withdrawals from the experimental
arm, using observed data from the control arm Appendix 7.C: SAS code to
model early withdrawals from the experimental arm, using the LOCF-like
values Appendix 7.D: SAS macro to impose delta adjustment on a responder
variable in the mania dataset Appendix 7.E: SAS code to implement tipping
point via exhaustive scenarios for the withdrawals in the mania dataset
Appendix 7.F: Code to perform sensitivity analyses for the Parkinson's
disease dataset Appendix 7.G: Code to perform sensitivity analyses for the
insomnia dataset Appendix 7.H: Code to perform sensitivity analyses for the
mania dataset Appendix 7.I: Selection models Appendix 7.J: Shared parameter
models References Table of SAS Code Fragments 8 Doubly Robust Estimation
8.1 Introduction 8.2 Inverse probability weighted estimation 8.2.1 IPW
estimators for estimating equations 8.2.2 Summary of IPW advantages 8.2.3
IPW disadvantages 8.3 Doubly robust estimation 8.3.1 Doubly robust methods
explained 8.3.2 Advantages of DR methods 8.3.3 Limitations of DR methods
8.4 Vansteelandt et al. method for doubly robust estimation 8.4.1
Theoretical justification for the Vansteelandt et al. method 8.4.2
Implementation of the Vansteelandt et al. method for DR estimation
Non-monotone missing data How regression parameters are estimated
Restrictions on regression parameters Missing covariates Binary covariates
Binary responses Auxiliary variables 8.5 Implementing the Vansteelandt et
al. method via SAS 8.5.1 Mania dataset 8.5.2 Insomnia dataset Appendix 8.A:
How to implement Vansteelandt et al. method for mania dataset (binary
response) Appendix 8.B: SAS code to calculate estimates from the
bootstrapped data sets Appendix 8.C: How to implement Vansteelandt et al.
method for insomnia dataset References Table of SAS Code Fragments
Bibliography
Preface References Acknowledgements Notation 1. What's the problem with
missing data? 1.1 What do we mean by missing data? 1.1.1 Monotone and
non-monotone missing data 1.1.2 Modeling missingness, modeling the missing
value and ignorability 1.1.3 Types of missingness (MCAR, MAR, and MNAR)
1.1.4 Missing data and study objectives 1.2 An illustration 1.3 Why can't I
use only the available primary endpoint data? 1.4 What's the problem with
using last observation carried forward? 1.5 Can we just assume that data
are missing at random? 1.6 What can be done if data may be missing not at
random? 1.7 Stress-testing study results for robustness to missing data 1.8
How the pattern of dropouts can bias the outcome 1.9 How do we formulate a
strategy for missing data? 1.10 Description of Example Datasets 1.10.1
Example dataset in Parkinson's disease treatment 1.10.2 Example dataset in
insomnia treatment 1.10.3 Example dataset in mania treatment 1.A Appendix:
Formal definitions of MCAR, MAR, and MNAR References 2 The prevention of
missing data 2.1 Introduction 2.2 The impact of 'too much' missing data
2.2.1 Example from human immunodeficiency virus 2.2.2 Example from acute
coronary syndrome 2.2.3 Example from studies in pain 2.3 The role of the
statistician in the prevention of missing data 2.3.1 Illustrative example
from HIV Step 1: Quantifying the amount of missing data in previous trials,
and its resultant impact Step 2: Identifying subgroups of subjects who
require an increased level of trial retention support Step 3: Translating
statistical analysis of previous trial data into information to inform
future subject care Step 4: Education of the clinical trial team and
participation in the creation of missing data prevention plans 2.4 Methods
for increasing subject retention 2.5 Improving understanding of reasons for
subject withdrawal 2.6 Acknowledgements 2.7 Appendix 2.A: example protocol
text for missing data prevention References 3 Regulatory guidance - a quick
tour 3.1 International Conference on Harmonization guideline: Statistical
principles for clinical trials: E9 3.2 The U.S. and EU regulatory documents
3.3 Key points in the regulatory documents on missing data 3.4 Regulatory
guidance on particular statistical approaches 3.4.1 Available cases 3.4.2
Single imputation methods 3.4.3 Methods that generally assume MAR 3.4.4
Methods that are used assuming MNAR 3.5 Guidance about how to plan for
missing data in a study 3.6 Differences in emphasis between the NRC report
and EU guidance documents 3.6.1 The term "conservative" 3.6.2 Last
observation carried forward 3.6.3 Post hoc analyses 3.6.4 Non-monotone or
intermittently missing data 3.6.5 Assumptions should be readily
interpretable 3.6.6 Study report 3.6.7 Training 3.7 Other technical points
from the NRC report 3.7.1 Time-to-event analyses 3.7.2 Tipping point
sensitivity analyses 3.8 Other U.S./EU/international guidance documents
that refer to missing data 3.8.1 Committee for Medicinal Products for Human
Use guideline on anticancer products, recommendations on survival analysis
3.8.2 U.S. guidance on considerations when research supported by Office of
Human Research Protections is discontinued 3.8.3 FDA guidance on data
retention 3.9 And in practice? References 4 A guide to planning for missing
data 4.1 Introduction 4.1.1 Missing data may bias trial results or make
them more difficult to generalize to subjects outside the trial 4.1.2
Credibility of trial results when there is missing data 4.1.3 Demand for
better practice with regard to missing data 4.2 Planning for missing data
4.2.1 The case report form and non-statistical sections of the protocol
4.2.2 The statistical sections of the protocol and the statistical analysis
plan 4.2.3 Using historic data to narrow the choice of primary analysis and
sensitivity analyses 4.2.4 Key points in choosing an approach for missing
data MAR LOCF-like approaches BOCF-like and worst-case approaches Control
based or reference-based imputation Assuming a variety of outcomes for
missing values, depending on reason for discontinuation Likelihood based
analysis of continuous outcome variables Likelihood based analysis of
binary response variables using longitudinal generalized linear mixed
models (GLMM) Doubly robust estimation Multiple imputation Pattern-mixture
models Selection models and shared parameter models 4.3 Exploring and
presenting missingness 4.4 Model checking 4.5 Interpreting model results
when there is missing data 4.6 Sample size and missing data Appendix 4.A:
Sample protocol/SAP text for study in Parkinson's disease Appendix 4.B: A
formal definition of a sensitivity parameter References 5 Mixed Models for
Repeated Measures Using Categorical Time Effects (MMRM) 5.1 Introduction
5.2 Specifying the MMRM 5.2.1 The mixed model 5.2.2 Covariance structures
5.2.3 MMRM versus generalized estimating equations (GEE) 5.2.4 MMRM versus
LOCF 5.3 Understanding the data 5.3.1 Parkinson's disease example 5.3.2 A
second example showing the usefulness of plots: CATIE 5.4 Applying the MMRM
5.4.1 Specifying the model 5.4.2 Interpreting and presenting results 5.5
Additional MMRM topics 5.5.1 Treatment by subgroup and treatment by site
interactions 5.5.2 Calculating the effect size 5.5.3 Another strategy to
model baseline 5.6 Logistic regression MMRM with generalized linear mixed
model (GLMM) 5.6.1 The generalized linear mixed model 5.6.2 Specifying the
model 5.6.3 Interpreting and presenting results 5.6.4 Other modeling
options References Table of SAS Code Fragments 6 Multiple imputation 6.1
Introduction 6.1.1 How is MI different from single imputation? 6.1.2 How is
MI different from maximum likelihood methods? 6.1.3 MI's assumptions about
missingness mechanism 6.1.4 A general 3-step process for multiple
imputation and inference 6.1.5 Imputation versus analysis model 6.1.6 Note
on notation use 6.2 Imputation Phase 6.2.1 Missing patterns: monotone and
non-monotone 6.2.2 How do we get multiple imputations? 6.2.3 Imputation
strategies: sequential univariate versus joint multivariate 6.2.4 Overview
of the imputation methods 6.2.5 Reusing the multiply-imputed dataset for
different analyses or summary scales 6.3 Analysis phase: analyzing multiple
imputed datasets 6.4 Pooling phase: combining results from multiple
datasets 6.4.1 Combination rules 6.4.2 Pooling analyses of continuous
outcomes 6.4.3 Pooling analyses of categorical outcomes 6.5 Required number
of imputations 6.6 Some practical considerations 6.6.1 Choosing an
imputation model 6.6.2 Multivariate normality 6.6.3 Rounding and
restricting the range for the imputed values 6.6.4 Convergence of MCMC 6.7
Pre-specifying details of analysis with multiple imputation 6.A Appendix:
Additional methods for multiple imputation References 7 Analyses under
missing-not-at-random assumptions 7.1 Introduction 7.2 Background to
sensitivity analyses and pattern-mixture models 7.2.1 The purpose of a
sensitivity analysis 7.2.2 Pattern-mixture models as sensitivity analyses
7.3 Two methods of implementing sensitivity analyses via PMMs 7.3.1 A
sequential method of implementing pattern-mixture models with MI 7.3.2
Providing stress-testing "what ifs" using pattern-mixture models 7.3.3 Two
implementations of pattern-mixture models for sensitivity analyses 7.3.4
Characteristics and limitations of the sequential modeling method of
implementing PMMs 7.3.5 PMMs implemented using the joint modeling method
7.3.6 Characteristics of the joint modeling method of implementing PMMs
7.3.7 Summary of differences between the joint modeling and sequential
modeling methods 7.4 A "toolkit": implementing sensitivity analyses via SAS
7.4.1 Reminder: general approach using MI with regression 7.4.2 Sensitivity
analyses assuming withdrawals have trajectory of control arm 7.4.3
Sensitivity analyses assuming withdrawals have distribution of control arm
7.4.4 BOCF-like and LOCF-like analyses 7.4.5 The general principle of using
selected subsets of observed data as the basis to implement "what if"
stress-tests 7.4.6 Using a mixture of "what ifs," depending on reason for
discontinuation 7.4.7 Assuming trajectory of withdrawals is worse by some
delta: delta adjustment and tipping point analysis 7.5 Examples of
realistic strategies and results for illustrative datasets of three
indications 7.5.1 Parkinson's disease 7.5.2 Insomnia 7.5.3 Mania Appendix
7.A: How one could implement NCMV using visit-by-visit MI for the example
trial Appendix 7.B: SAS code to model withdrawals from the experimental
arm, using observed data from the control arm Appendix 7.C: SAS code to
model early withdrawals from the experimental arm, using the LOCF-like
values Appendix 7.D: SAS macro to impose delta adjustment on a responder
variable in the mania dataset Appendix 7.E: SAS code to implement tipping
point via exhaustive scenarios for the withdrawals in the mania dataset
Appendix 7.F: Code to perform sensitivity analyses for the Parkinson's
disease dataset Appendix 7.G: Code to perform sensitivity analyses for the
insomnia dataset Appendix 7.H: Code to perform sensitivity analyses for the
mania dataset Appendix 7.I: Selection models Appendix 7.J: Shared parameter
models References Table of SAS Code Fragments 8 Doubly Robust Estimation
8.1 Introduction 8.2 Inverse probability weighted estimation 8.2.1 IPW
estimators for estimating equations 8.2.2 Summary of IPW advantages 8.2.3
IPW disadvantages 8.3 Doubly robust estimation 8.3.1 Doubly robust methods
explained 8.3.2 Advantages of DR methods 8.3.3 Limitations of DR methods
8.4 Vansteelandt et al. method for doubly robust estimation 8.4.1
Theoretical justification for the Vansteelandt et al. method 8.4.2
Implementation of the Vansteelandt et al. method for DR estimation
Non-monotone missing data How regression parameters are estimated
Restrictions on regression parameters Missing covariates Binary covariates
Binary responses Auxiliary variables 8.5 Implementing the Vansteelandt et
al. method via SAS 8.5.1 Mania dataset 8.5.2 Insomnia dataset Appendix 8.A:
How to implement Vansteelandt et al. method for mania dataset (binary
response) Appendix 8.B: SAS code to calculate estimates from the
bootstrapped data sets Appendix 8.C: How to implement Vansteelandt et al.
method for insomnia dataset References Table of SAS Code Fragments
Bibliography
missing data? 1.1 What do we mean by missing data? 1.1.1 Monotone and
non-monotone missing data 1.1.2 Modeling missingness, modeling the missing
value and ignorability 1.1.3 Types of missingness (MCAR, MAR, and MNAR)
1.1.4 Missing data and study objectives 1.2 An illustration 1.3 Why can't I
use only the available primary endpoint data? 1.4 What's the problem with
using last observation carried forward? 1.5 Can we just assume that data
are missing at random? 1.6 What can be done if data may be missing not at
random? 1.7 Stress-testing study results for robustness to missing data 1.8
How the pattern of dropouts can bias the outcome 1.9 How do we formulate a
strategy for missing data? 1.10 Description of Example Datasets 1.10.1
Example dataset in Parkinson's disease treatment 1.10.2 Example dataset in
insomnia treatment 1.10.3 Example dataset in mania treatment 1.A Appendix:
Formal definitions of MCAR, MAR, and MNAR References 2 The prevention of
missing data 2.1 Introduction 2.2 The impact of 'too much' missing data
2.2.1 Example from human immunodeficiency virus 2.2.2 Example from acute
coronary syndrome 2.2.3 Example from studies in pain 2.3 The role of the
statistician in the prevention of missing data 2.3.1 Illustrative example
from HIV Step 1: Quantifying the amount of missing data in previous trials,
and its resultant impact Step 2: Identifying subgroups of subjects who
require an increased level of trial retention support Step 3: Translating
statistical analysis of previous trial data into information to inform
future subject care Step 4: Education of the clinical trial team and
participation in the creation of missing data prevention plans 2.4 Methods
for increasing subject retention 2.5 Improving understanding of reasons for
subject withdrawal 2.6 Acknowledgements 2.7 Appendix 2.A: example protocol
text for missing data prevention References 3 Regulatory guidance - a quick
tour 3.1 International Conference on Harmonization guideline: Statistical
principles for clinical trials: E9 3.2 The U.S. and EU regulatory documents
3.3 Key points in the regulatory documents on missing data 3.4 Regulatory
guidance on particular statistical approaches 3.4.1 Available cases 3.4.2
Single imputation methods 3.4.3 Methods that generally assume MAR 3.4.4
Methods that are used assuming MNAR 3.5 Guidance about how to plan for
missing data in a study 3.6 Differences in emphasis between the NRC report
and EU guidance documents 3.6.1 The term "conservative" 3.6.2 Last
observation carried forward 3.6.3 Post hoc analyses 3.6.4 Non-monotone or
intermittently missing data 3.6.5 Assumptions should be readily
interpretable 3.6.6 Study report 3.6.7 Training 3.7 Other technical points
from the NRC report 3.7.1 Time-to-event analyses 3.7.2 Tipping point
sensitivity analyses 3.8 Other U.S./EU/international guidance documents
that refer to missing data 3.8.1 Committee for Medicinal Products for Human
Use guideline on anticancer products, recommendations on survival analysis
3.8.2 U.S. guidance on considerations when research supported by Office of
Human Research Protections is discontinued 3.8.3 FDA guidance on data
retention 3.9 And in practice? References 4 A guide to planning for missing
data 4.1 Introduction 4.1.1 Missing data may bias trial results or make
them more difficult to generalize to subjects outside the trial 4.1.2
Credibility of trial results when there is missing data 4.1.3 Demand for
better practice with regard to missing data 4.2 Planning for missing data
4.2.1 The case report form and non-statistical sections of the protocol
4.2.2 The statistical sections of the protocol and the statistical analysis
plan 4.2.3 Using historic data to narrow the choice of primary analysis and
sensitivity analyses 4.2.4 Key points in choosing an approach for missing
data MAR LOCF-like approaches BOCF-like and worst-case approaches Control
based or reference-based imputation Assuming a variety of outcomes for
missing values, depending on reason for discontinuation Likelihood based
analysis of continuous outcome variables Likelihood based analysis of
binary response variables using longitudinal generalized linear mixed
models (GLMM) Doubly robust estimation Multiple imputation Pattern-mixture
models Selection models and shared parameter models 4.3 Exploring and
presenting missingness 4.4 Model checking 4.5 Interpreting model results
when there is missing data 4.6 Sample size and missing data Appendix 4.A:
Sample protocol/SAP text for study in Parkinson's disease Appendix 4.B: A
formal definition of a sensitivity parameter References 5 Mixed Models for
Repeated Measures Using Categorical Time Effects (MMRM) 5.1 Introduction
5.2 Specifying the MMRM 5.2.1 The mixed model 5.2.2 Covariance structures
5.2.3 MMRM versus generalized estimating equations (GEE) 5.2.4 MMRM versus
LOCF 5.3 Understanding the data 5.3.1 Parkinson's disease example 5.3.2 A
second example showing the usefulness of plots: CATIE 5.4 Applying the MMRM
5.4.1 Specifying the model 5.4.2 Interpreting and presenting results 5.5
Additional MMRM topics 5.5.1 Treatment by subgroup and treatment by site
interactions 5.5.2 Calculating the effect size 5.5.3 Another strategy to
model baseline 5.6 Logistic regression MMRM with generalized linear mixed
model (GLMM) 5.6.1 The generalized linear mixed model 5.6.2 Specifying the
model 5.6.3 Interpreting and presenting results 5.6.4 Other modeling
options References Table of SAS Code Fragments 6 Multiple imputation 6.1
Introduction 6.1.1 How is MI different from single imputation? 6.1.2 How is
MI different from maximum likelihood methods? 6.1.3 MI's assumptions about
missingness mechanism 6.1.4 A general 3-step process for multiple
imputation and inference 6.1.5 Imputation versus analysis model 6.1.6 Note
on notation use 6.2 Imputation Phase 6.2.1 Missing patterns: monotone and
non-monotone 6.2.2 How do we get multiple imputations? 6.2.3 Imputation
strategies: sequential univariate versus joint multivariate 6.2.4 Overview
of the imputation methods 6.2.5 Reusing the multiply-imputed dataset for
different analyses or summary scales 6.3 Analysis phase: analyzing multiple
imputed datasets 6.4 Pooling phase: combining results from multiple
datasets 6.4.1 Combination rules 6.4.2 Pooling analyses of continuous
outcomes 6.4.3 Pooling analyses of categorical outcomes 6.5 Required number
of imputations 6.6 Some practical considerations 6.6.1 Choosing an
imputation model 6.6.2 Multivariate normality 6.6.3 Rounding and
restricting the range for the imputed values 6.6.4 Convergence of MCMC 6.7
Pre-specifying details of analysis with multiple imputation 6.A Appendix:
Additional methods for multiple imputation References 7 Analyses under
missing-not-at-random assumptions 7.1 Introduction 7.2 Background to
sensitivity analyses and pattern-mixture models 7.2.1 The purpose of a
sensitivity analysis 7.2.2 Pattern-mixture models as sensitivity analyses
7.3 Two methods of implementing sensitivity analyses via PMMs 7.3.1 A
sequential method of implementing pattern-mixture models with MI 7.3.2
Providing stress-testing "what ifs" using pattern-mixture models 7.3.3 Two
implementations of pattern-mixture models for sensitivity analyses 7.3.4
Characteristics and limitations of the sequential modeling method of
implementing PMMs 7.3.5 PMMs implemented using the joint modeling method
7.3.6 Characteristics of the joint modeling method of implementing PMMs
7.3.7 Summary of differences between the joint modeling and sequential
modeling methods 7.4 A "toolkit": implementing sensitivity analyses via SAS
7.4.1 Reminder: general approach using MI with regression 7.4.2 Sensitivity
analyses assuming withdrawals have trajectory of control arm 7.4.3
Sensitivity analyses assuming withdrawals have distribution of control arm
7.4.4 BOCF-like and LOCF-like analyses 7.4.5 The general principle of using
selected subsets of observed data as the basis to implement "what if"
stress-tests 7.4.6 Using a mixture of "what ifs," depending on reason for
discontinuation 7.4.7 Assuming trajectory of withdrawals is worse by some
delta: delta adjustment and tipping point analysis 7.5 Examples of
realistic strategies and results for illustrative datasets of three
indications 7.5.1 Parkinson's disease 7.5.2 Insomnia 7.5.3 Mania Appendix
7.A: How one could implement NCMV using visit-by-visit MI for the example
trial Appendix 7.B: SAS code to model withdrawals from the experimental
arm, using observed data from the control arm Appendix 7.C: SAS code to
model early withdrawals from the experimental arm, using the LOCF-like
values Appendix 7.D: SAS macro to impose delta adjustment on a responder
variable in the mania dataset Appendix 7.E: SAS code to implement tipping
point via exhaustive scenarios for the withdrawals in the mania dataset
Appendix 7.F: Code to perform sensitivity analyses for the Parkinson's
disease dataset Appendix 7.G: Code to perform sensitivity analyses for the
insomnia dataset Appendix 7.H: Code to perform sensitivity analyses for the
mania dataset Appendix 7.I: Selection models Appendix 7.J: Shared parameter
models References Table of SAS Code Fragments 8 Doubly Robust Estimation
8.1 Introduction 8.2 Inverse probability weighted estimation 8.2.1 IPW
estimators for estimating equations 8.2.2 Summary of IPW advantages 8.2.3
IPW disadvantages 8.3 Doubly robust estimation 8.3.1 Doubly robust methods
explained 8.3.2 Advantages of DR methods 8.3.3 Limitations of DR methods
8.4 Vansteelandt et al. method for doubly robust estimation 8.4.1
Theoretical justification for the Vansteelandt et al. method 8.4.2
Implementation of the Vansteelandt et al. method for DR estimation
Non-monotone missing data How regression parameters are estimated
Restrictions on regression parameters Missing covariates Binary covariates
Binary responses Auxiliary variables 8.5 Implementing the Vansteelandt et
al. method via SAS 8.5.1 Mania dataset 8.5.2 Insomnia dataset Appendix 8.A:
How to implement Vansteelandt et al. method for mania dataset (binary
response) Appendix 8.B: SAS code to calculate estimates from the
bootstrapped data sets Appendix 8.C: How to implement Vansteelandt et al.
method for insomnia dataset References Table of SAS Code Fragments
Bibliography