Table
of Contents
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I |
FOUNDATIONS |
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1 |
Introduction |
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1.1 |
Reasons for missing data |
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1.1.1 |
Patterns of missing data |
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1.1.2 |
Consequences of missing data |
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1.2 |
Inferential framework and notation |
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1.2.1 |
Missing Completely At Random (MCAR) |
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1.2.2 |
Missing At Random (MAR) |
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1.2.3 |
Missing Not At Random (MNAR) |
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1.2.4 |
Ignorability |
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1.3 |
Using observed data to inform assumptions about
the missingness
mechanism |
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1.4 |
Implications of missing data mechanisms for
regression analyses |
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1.4.1 |
Partially observed response |
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1.4.2 |
Missing covariates |
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1.4.3 |
Missing covariates and response |
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1.4.4 |
Subtle issues I: the odds ratio |
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1.4.5 |
Implication for linear regression |
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1.4.6 |
Subtle issues II: sub sample ignorability |
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1.4.7 |
Summary: when restricting to complete records is
valid |
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1.5 |
Summary |
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2 |
The Multiple Imputation Procedure and Its
Justification |
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2.1 |
Introduction |
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2.2 |
Intuitive outline of the MI procedure |
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2.3 |
The generic MI Procedure |
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2.4 |
Bayesian justification of MI |
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2.5 |
Frequentist Inference |
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2.6 |
Choosing the number of imputations |
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2.7 |
Some simple examples |
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2.8 |
MI in More General Settings |
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2.8.1 |
Survey Sample Settings |
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2.9 |
Practical considerations for choosing imputation
models |
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2.10 |
Discussion |
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II |
MULTIPLE
IMPUTATION FOR CROSS SECTIONAL DATA |
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3 |
Multiple imputation of quantitative data |
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3.1 |
Regression imputation with a monotone missingness
pattern |
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3.1.1 |
MAR mechanisms consistent with a monotone pattern |
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3.1.2 |
Justification |
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3.2 |
Joint modelling |
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3.2.1 |
Fitting the imputation model |
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3.3 |
Full conditional specification |
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3.3.1 |
Justification |
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3.4 |
Full conditional specification versus joint modelling |
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3.5 |
Software for multivariate normal imputation |
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3.6 |
Discussion |
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4 |
Multiple imputation of binary and ordinal data |
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4.1 |
Sequential imputation with monotone missingness
pattern |
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4.2 |
Joint modelling with the
multivariate normal distribution |
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4.3 |
Modelling binary data using latent normal
variables |
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4.3.1 |
Latent normal model for ordinal data |
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4.4 |
General location model |
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4.5 |
Full conditional specification |
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4.5.1 |
Justification |
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4.6 |
Issues with over-fitting |
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4.7 |
Pros and cons of the various approaches |
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4.8 |
Software |
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4.9 |
Discussion |
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5 |
Imputation of unordered categorical data |
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5.1 |
Monotone missing data |
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5.2 |
Multivariate normal imputation for categorical
data |
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5.3 |
Maximum indicant model |
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5.3.1 |
Continuous and categorical variable |
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5.3.2 |
Imputing missing data |
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5.3.3 |
More than one categorical variable |
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5.4 |
General location model |
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5.5 |
FCS with categorical data |
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5.6 |
Perfect prediction issues with categorical data |
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5.7 |
Software |
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5.8 |
Discussion |
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6 |
Non-linear relationships |
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6.1 |
Passive imputation |
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6.2 |
No missing data in non-linear relationships |
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6.3 |
Missing data in non-linear relationships |
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6.3.1 |
Predictive Mean Matching (PMM) |
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6.3.2 |
Just Another Variable (JAV) |
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6.3.3 |
Joint modelling approach |
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6.3.4 |
Extension to more general models and missing data
pattern |
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6.3.5 |
Metropolis |
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6.3.6 |
Rejection sampling |
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6.3.7 |
FCS approach |
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6.4 |
Discussion |
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7 |
Interactions |
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7.1 |
Interaction variables fully observed |
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7.2 |
Interactions of categorical variables |
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7.3 |
General non-linear relationships |
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7.4 |
Software |
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7.5 |
Discussion |
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III |
ADVANCED TOPICS |
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8 |
Survival data, skips and large datasets |
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8.1 |
Time to event data |
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8.1.1 |
Imputing missing covariate values |
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8.1.2 |
Survival data as categorical |
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8.1.3 |
Imputing censored survival times |
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8.2 |
Non-parametric, or `hot deck’ imputation |
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8.2.1 |
Non-parametric imputation for survival data |
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8.3 |
Multiple imputation for skips |
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8.4 |
Two-stage MI |
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8.5 |
Large datasets |
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8.5.1 |
Large datasets and joint modelling |
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8.5.2 |
Shrinkage by constraining parameters |
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8.5.3 |
Comparison of the two approaches |
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8.6 |
Multiple Imputation and record linkage |
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8.7 |
Measurement error |
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8.8 |
Multiple imputation for aggregated scores |
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8.9 |
Discussion |
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9 |
Multilevel multiple imputation |
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9.1 |
Multilevel imputation model |
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9.2 |
MCMC algorithm for imputation model |
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9.3 |
Imputing level 2 covariates using FCS |
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9.4 |
Individual patient meta-analysis |
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9.4.1 |
When to apply Rubin’s rules |
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9.5 |
Extensions |
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9.5.1 |
Random level-1 covariance matrices |
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9.5.2 |
Model_t |
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9.6 |
Discussion |
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10 |
Sensitivity analysis: MI unleashed |
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10.1 |
Review of MNAR modelling |
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10.2 |
Framing sensitivity analysis |
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10.3 |
Pattern mixture modelling
with MI |
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10.3.1 |
Missing covariates |
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10.3.2 |
Application to survival analysis |
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10.4 |
Pattern mixture approach with longitudinal data
via MI |
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10.4.1 |
Change in slope post-deviation |
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10.5 |
Piecing together post-deviation distributions
from other trial arms |
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10.6 |
Approximating a selection model by importance
weighting |
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10.6.1 |
Algorithm for approximate sensitivity analysis by
reweighting |
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10.7 |
Discussion |
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11 |
Including survey weights |
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11.1 |
Using model based predictions |
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11.2 |
Bias in the MI Variance Estimator |
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11.2.1 |
MI with weights |
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11.2.2 |
Estimation in Domains |
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11.3 |
A multilevel approach |
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11.4 |
Further developments |
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11.5 |
Discussion |
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12 |
Robust Multiple Imputation |
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12.1 |
Introduction |
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12.2 |
Theoretical background |
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12.2.1 |
Simple Estimating equations |
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12.2.2 |
The probability of missingness
(POM) model |
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12.2.3 |
Augmented inverse probability weighted estimating
equation |
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12.3 |
Robust Multiple Imputation |
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12.3.1 |
Univariate MAR missing data |
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12.3.2 |
Longitudinal MAR missing data |
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12.4 |
Simulation studies |
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12.4.1 |
Univariate MAR missing data |
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12.4.2 |
Longitudinal monotone MAR missing data |
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12.4.3 |
Longitudinal non-monotone MAR missing data |
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12.4.4 |
Non-longitudinal non-monotone MAR missing data |
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12.4.5 |
Conclusions |
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12.5 |
The RECORD study |
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12.6 |
Discussion |
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Appendix A |
Markov Chain |
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Appendix B |
Probability distributions |
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B.1 |
Posterior for the multivariate normal
distribution |
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Bibliography |
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Index |
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