Multiple Imputation and Its Application

Klappentext 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. Zusammenfassung 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 ...

List of contents

I Foundations1 Introduction1.1 Reasons for missing data1.1.1 Patterns of missing data1.1.2 Consequences of missing data1.2 Inferential framework and notation1.2.1 Missing Completely At Random (MCAR)1.2.2 Missing At Random (MAR)1.2.3 Missing Not At Random (MNAR)1.2.4 Ignorability1.3 Using observed data to inform assumptions about the missingness mechanism1.4 Implications of missing data mechanisms for regression analyses1.4.1 Partially observed response1.4.2 Missing covariates1.4.3 Missing covariates and response1.4.4 Subtle issues I: the odds ratio1.4.5 Implication for linear regression1.4.6 Subtle issues II: sub sample ignorability1.4.7 Summary: when restricting to complete records is valid1.5 Summary2 The Multiple Imputation Procedure and Its Justification2.1 Introduction2.2 Intuitive outline of the MI procedure2.3 The generic MI Procedure2.4 Bayesian justification of MI2.5 Frequentist Inference2.6 Choosing the number of imputations2.7 Some simple examples2.8 MI in More General Settings2.8.1 Survey Sample Settings2.9 Practical considerations for choosing imputation models2.10 DiscussionII Multiple imputation for cross sectional data3 Multiple imputation of quantitative data3.1 Regression imputation with a monotone missingness pattern3.1.1 MAR mechanisms consistent with a monotone pattern3.1.2 Justification3.2 Joint modelling3.2.1 Fitting the imputation model3.3 Full conditional specification3.3.1 Justification3.4 Full conditional specification versus joint modelling3.5 Software for multivariate normal imputation3.6 Discussion4 Multiple imputation of binary and ordinal data4.1 Sequential imputation with monotone missingness pattern4.2 Joint modelling with the multivariate normal distribution4.3 Modelling binary data using latent normal variables4.3.1 Latent normal model for ordinal data4.4 General location model4.5 Full conditional specification4.5.1 Justification4.6 Issues with over-fitting4.7 Pros and cons of the various approaches4.8 Software4.9 Discussion5 Imputation of unordered categorical data5.1 Monotone missing data5.2 Multivariate normal imputation for categorical data5.3 Maximum indicant model5.3.1 Continuous and categorical variable5.3.2 Imputing missing data5.3.3 More than one categorical variable5.4 General location model5.5 FCS with categorical data5.6 Perfect prediction issues with categorical data5.7 Software5.8 Discussion6 Non-linear relationships6.1 Passive imputation6.2 No missing data in non-linear relationships6.3 Missing data in non-linear relationships6.3.1 Predictive Mean Matching (PMM)6.3.2 Just Another Variable (JAV)6.3.3 Joint modelling approach6.3.4 Extension to more general models and missing data pattern6.3.5 Metropolis Hastings sampling6.3.6 Rejection sampling6.3.7 FCS approach6.4 Discussion7 Interactions7.1 Interaction variables fully observed7.2 Interactions of categorical variables7.3 General non-linear relationships7.4 Software7.5 DiscussionIII Advanced Topics8 Survival data, skips and large datasets8.1 Time to event data8.1.1 Imputing missing covariate values8.1.2 Survival data as categorical8.1.3 Imputing censored survival times8.2 Non-parametric, or `hot deck' imputation8.2.1 Non-parametric imputation for survival data8.3 Multiple imputation for skips8.4 Two-stage MI8.5 Large datasets8.5.1 Large datasets and joint modelling8.5.2 Shrinkage by constraining parameters8.5.3 Comparison of the two approaches8.6 Multiple Imputation and record linkage8.7 Measurement error8.8 Multiple imputation for aggregated scores8.9 Discussion9 Multilevel multiple imputation9.1 Multilevel imputation model9.2 MCMC algorithm for imputation model9.3 Imputing level 2 covariates using FCS9.4 Individual patient meta-analysis9.4.1 When to apply Rubin's rules9.5 Extensions9.5.1 Random level-1 covariance matrices9.5.2 Model_t9.6 Discussion10 Sensitivity analysis: MI unleashed10.1 Review of MNAR modelling10.2 Framing sensitivity analysis10.3 Pattern mixture modelling with MI10.3.1 Missing covariates10.3.2 Application to survival analysis10.4 Pattern mixture approach with longitudinaldata via MI10.4.1 Change in slope post-deviation10.5 Piecing together post-deviation distributions from other trial arms10.6 Approximating a selection model by importance weighting10.6.1 Algorithm for approximate sensitivity analysis by reweighting10.7 Discussion11 Including survey weights11.1 Using model based predictions11.2 Bias in the MI Variance Estimator11.2.1 MI with weights11.2.2 Estimation in Domains11.3 A multilevel approach11.4 Further developments11.5 Discussion12 Robust Multiple Imputation12.1 Introduction12.2 Theoretical background12.2.1 Simple Estimating equations12.2.2 The probability of missingness (POM) model12.2.3 Augmented inverse probability weightedestimating equation12.3 Robust Multiple Imputation12.3.1 Univariate MAR missing data12.3.2 Longitudinal MAR missing data12.4 Simulation studies12.4.1 Univariate MAR missing data12.4.2 Longitudinal monotone MAR missing data12.4.3 Longitudinal non-monotone MAR missing data12.4.4 Non-longitudinal non-monotone MAR missing data12.4.5 Conclusions12.5 The RECORD study12.6 DiscussionAppendix A Markov Chain Monte CarloAppendix B Probability distributionsB.1 Posterior for the multivariate normal distributionBibliographyIndex

Product details

• Authors: Jame Carpenter, James Carpenter, James (Department of Medical Statistics Carpenter, James Kenward Carpenter, James R. Carpenter, James/ Kenward Carpenter, Jr Carpenter, CARPENTER JAMES KENWARD MICHAEL, Michael Kenward, Michael G. Kenward
• Publisher: Wiley, John and Sons Ltd
• Languages: English
• Product format: Hardback
• Released: 18.01.2013
• EAN: 9780470740521
• ISBN: 978-0-470-74052-1
• No. of pages: 368
• Series: Statistics in Practice; Statistics in Practice
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Probability theory, stochastic theory, mathematical statistics; Epidemiologie und medizinische Statistik