Clinical Trials with Missing Data

MICHAEL O'KELLY, Senior Strategic Biostatistics Director, Quintiles Ireland Ltd, Ireland. BOHDANA RATITCH, Senior Biostatistician, Quintiles, Montreal, Canada.

• Preface xvReferences xviiAcknowledgments xixNotation xxiTable of SAS code fragments xxvContributors xxix1 What’s the problem with missing data? 1Michael O’Kelly and Bohdana Ratitch1.1 What do we mean by missing data? 21.1.1 Monotone and non-monotone missing data 31.1.2 Modeling missingness, modeling the missing value and ignorability 41.1.3 Types of missingness (MCAR, MAR and MNAR) 41.1.4 Missing data and study objectives 51.2 An illustration 61.3 Why can’t I use only the available primary endpoint data? 71.4 What’s the problem with using last observation carried forward? 91.5 Can we just assume that data are missing at random? 111.6 What can be done if data may be missing not at random? 141.7 Stress-testing study results for robustness to missing data 151.8 How the pattern of dropouts can bias the outcome 151.9 How do we formulate a strategy for missing data? 161.10 Description of example datasets 181.10.1 Example dataset in Parkinson’s disease treatment 181.10.2 Example dataset in insomnia treatment 231.10.3 Example dataset in mania treatment 28Appendix 1.A: Formal definitions of MCAR, MAR and MNAR 33References 342 The prevention of missing data 36Sara Hughes2.1 Introduction 362.2 The impact of “too much” missing data 372.2.1 Example from human immunodeficiency virus 382.2.2 Example from acute coronary syndrome 382.2.3 Example from studies in pain 392.3 The role of the statistician in the prevention of missing data 392.3.1 Illustrative example from HIV 412.4 Methods for increasing subject retention 482.5 Improving understanding of reasons for subject withdrawal 49Acknowledgments 49Appendix 2.A: Example protocol text for missing data prevention 49References 503 Regulatory guidance – a quick tour 53Michael O’Kelly3.1 International conference on harmonization guideline: Statistical principles for clinical trials: E9 543.2 The US and EU regulatory documents 553.3 Key points in the regulatory documents on missing data 553.4 Regulatory guidance on particular statistical approaches 573.4.1 Available cases 573.4.2 Single imputation methods 573.4.3 Methods that generally assume MAR 593.4.4 Methods that are used assuming MNAR 603.5 Guidance about how to plan for missing data in a study 623.6 Differences in emphasis between the NRC report and EU guidance documents 633.6.1 The term “conservative” 633.6.2 Last observation carried forward 633.6.3 Post hoc analyses 633.6.4 Non-monotone or intermittently missing data 633.6.5 Assumptions should be readily interpretable 653.6.6 Study report 653.6.7 Training 653.7 Other technical points from the NRC report 663.7.1 Time-to-event analyses 663.7.2 Tipping point sensitivity analyses 663.8 Other US/EU/international guidance documents that refer to missing data 663.8.1 Committee for medicinal products for human use guideline on anti-cancer products, recommendations on survival analysis 663.8.2 US guidance on considerations when research supported by office of human research protections is discontinued 673.8.3 FDA guidance on data retention 673.9 And in practice? 67References 694 A guide to planning for missing data 71Michael O’Kelly and Bohdana Ratitch4.1 Introduction 724.1.1 Missing data may bias trial results or make them more difficult to generalize to subjects outside the trial 724.1.2 Credibility of trial results when there is missing data 744.1.3 Demand for better practice with regard to missing data 744.2 Planning for missing data 764.2.1 The case report form and non-statistical sections of the protocol 764.2.2 The statistical sections of the protocol and the statistical analysis plan 814.2.3 Using historic data to narrow the choice of primary analysis and sensitivity analyses 884.2.4 Key points in choosing an approach for missing data 1084.3 Exploring and presenting missingness 1134.4 Model checking 1144.5 Interpreting model results when there is missing data 1164.6 Sample size and missing data 117Appendix 4.A: Sample protocol/SAP text for study in Parkinson’s disease 119Appendix 4.B: A formal definition of a sensitivity parameter 125References 1265 Mixed models for repeated measures using categorical time effects (MMRM) 130Sonia Davis5.1 Introduction 1315.2 Specifying the mixed model for repeated measures 1325.2.1 The mixed model 1325.2.2 Covariance structures 1355.2.3 Mixed model for repeated measures versus generalized estimating equations 1395.2.4 Mixed model for repeated measures versus last observation carried forward 1405.3 Understanding the data 1415.3.1 Parkinson’s disease example 1415.3.2 A second example showing the usefulness of plots: The CATIE study 1445.4 Applying the mixed model for repeated measures 1455.4.1 Specifying the model 1465.4.2 Interpreting and presenting results 1505.5 Additional mixed model for repeated measures topics 1625.5.1 Treatment by subgroup and treatment by site interactions 1625.5.2 Calculating the effect size 1645.5.3 Another strategy to model baseline 1665.6 Logistic regression mixed model for repeated measures using the generalized linear mixed model 1685.6.1 The generalized linear mixed model 1685.6.2 Specifying the model 1705.6.3 Interpreting and presenting results 1735.6.4 Other modeling options 181References 182Table of SAS Code Fragments 1836 Multiple imputation 185Bohdana Ratitch6.1 Introduction 1856.1.1 How is multiple imputation different from single imputation? 1866.1.2 How is multiple imputation different from maximum likelihood methods? 1876.1.3 Multiple imputation’s assumptions about missingness mechanism 1886.1.4 A general three-step process for multiple imputation and inference 1896.1.5 Imputation versus analysis model 1906.1.6 Note on notation use 1926.2 Imputation phase 1926.2.1 Missing patterns: Monotone and non-monotone 1926.2.2 How do we get multiple imputations? 1956.2.3 Imputation strategies: Sequential univariate versus joint multivariate 1976.2.4 Overview of the imputation methods 1996.2.5 Reusing the multiply-imputed dataset for different analyses or summary scales 2126.3 Analysis phase: Analyzing multiple imputed datasets 2136.4 Pooling phase: Combining results from multiple datasets 2166.4.1 Combination rules 2166.4.2 Pooling analyses of continuous outcomes 2196.4.3 Pooling analyses of categorical outcomes 2226.5 Required number of imputations 2276.6 Some practical considerations 2316.6.1 Choosing an imputation model 2316.6.2 Multivariate normality 2356.6.3 Rounding and restricting the range for the imputed values 2386.6.4 Convergence of Markov chain Monte Carlo 2406.7 Pre-specifying details of analysis with multiple imputation 244Appendix 6.A: Additional methods for multiple imputation 245References 251Table of SAS Code Fragments 2557 Analyses under missing-not-at-random assumptions 257Michael O’Kelly and Bohdana Ratitch7.1 Introduction 2587.2 Background to sensitivity analyses and pattern-mixture models 2597.2.1 The purpose of a sensitivity analysis 2597.2.2 Pattern-mixture models as sensitivity analyses 2617.3 Two methods of implementing sensitivity analyses via pattern-mixture models 2647.3.1 A sequential method of implementing pattern-mixture models with multiple imputation 2647.3.2 Providing stress-testing “what ifs” using pattern-mixture models 2667.3.3 Two implementations of pattern-mixture models for sensitivity analyses 2677.3.4 Characteristics and limitations of the sequential modeling method of implementing pattern-mixture models 2687.3.5 Pattern-mixture models implemented using the joint modeling method 2717.3.6 Characteristics of the joint modeling method of implementing pattern-mixture models 2797.3.7 Summary of differences between the joint modelling and sequential modeling methods 2817.4 A “toolkit”: Implementing sensitivity analyses via SAS 2847.4.1 Reminder: General approach using multiple imputation with regression 2847.4.2 Sensitivity analyses assuming withdrawals have trajectory of control arm 2887.4.3 Sensitivity analyses assuming withdrawals have distribution of control arm 2927.4.4 Baseline-observation-carried-forward-like and last-observation-carried-forward-like analyses 2977.4.5 The general principle of using selected subsets of observed data as the basis to implement “what if” stress tests 3067.4.6 Using a mixture of “what ifs,” depending on reason for discontinuation 3067.4.7 Assuming trajectory of withdrawals is worse by some 𝛿: Delta adjustment and tipping point analysis 3087.5 Examples of realistic strategies and results for illustrative datasets of three indications 3207.5.1 Parkinson’s disease 3207.5.2 Insomnia 3237.5.3 Mania 330Appendix 7.A How one could implement the neighboring case missing value assumption using visit-by-visit multiple imputation 335Appendix 7.B SAS code to model withdrawals from the experimental arm, using observed data from the control arm 336Appendix 7.C SAS code to model early withdrawals from the experimental arm, using the last-observation-carried-forward-like values 342Appendix 7.D SAS macro to impose delta adjustment on a responder variable in the mania dataset 345Appendix 7.E SAS code to implement tipping point via exhaustive scenarios for withdrawals in the mania dataset 346Appendix 7.F SAS code to perform sensitivity analyses for the Parkinson’s disease dataset 348Appendix 7.G SAS code to perform sensitivity analyses for the insomnia dataset 351Appendix 7.H SAS code to perform sensitivity analyses for the mania dataset 356Appendix 7.I Selection models 358Appendix 7.J Shared parameter models 362References 365Table of SAS Code Fragments 3688 Doubly robust estimation 369Belinda Hernandez, Ilya Lipkovich and Michael O’Kelly8.1 Introduction 3708.2 Inverse probability weighted estimation 3708.2.1 Inverse probability weighting estimators for estimating equations 3728.2.2 Summary of inverse probability weighting advantages 3738.2.3 Inverse probability weighting disadvantages 3738.3 Doubly robust estimation 3748.3.1 Doubly robust methods explained 3758.3.2 Advantages of doubly robust methods 3768.3.3 Limitations of doubly robust methods 3768.4 Vansteelandt et al. method for doubly robust estimation 3778.4.1 Theoretical justification for the Vansteelandt et al. method 3788.4.2 Implementation of the Vansteelandt et al. method for doubly robust estimation 3798.5 Implementing the Vansteelandt et al. method via SAS 3838.5.1 Mania dataset 3838.5.2 Insomnia dataset 390Appendix 8.A How to implement Vansteelandt et al. method for mania dataset (binary response) 392Appendix 8.B SAS code to calculate estimates from the bootstrapped datasets 400Appendix 8.C How to implement Vansteelandt et al. method for insomnia dataset 401References 408Table of SAS Code Fragments 408Bibliography 409Index 423

“In summary, the book is a must-have tool for any biostatistician dealing with missing data. It is an excellent reference book for postgraduate students or researchers working in the area of missing data.”  (Biometrical Journal, 1 June 2015)“This is an excellent addition to the field, dealing with problems arising from missing data or unobserved data in clinical trials. It successfully bridges the gap between clinicians and statisticians using relatively common language to build common ground.”   (Doody’s, 9 January 2015)