The R package mice imputes incomplete multivariate data by chained equations. The software mice 1.0 appeared in the year 2000 as an S-PLUS library, and in 2001 as an R package. mice 1.0 introduced predictor selection, passive imputation and automatic pooling. This article documents mice, which extends the functionality of mice 1.0 in several ways. In mice, the analysis of imputed data is made completely general, whereas the range of models under which pooling works is substantially extended. mice adds new functionality for imputing multilevel data, automatic predictor selection, data handling, post-processing imputed values, specialized pooling routines, model selection tools, and diagnostic graphs. Imputation of categorical data is improved in order to bypass problems caused by perfect prediction. Special attention is paid to transformations, sum scores, indices and interactions using passive imputation, and to the proper setup of the predictor matrix. mice can be downloaded from the Comprehensive R Archive Network. This article provides a hands-on, stepwise approach to solve applied incomplete data problems.

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mice: Multivariate Imputation by Chained Equations in R

The propensity score is the probability of treatment assignment conditional on observed baseline characteristics. The propensity score allows one to design and analyze an observational (nonrandomized) study so that it mimics some of the particular characteristics of a randomized controlled trial. In particular, the propensity score is a balancing score: conditional on the propensity score, the distribution of observed baseline covariates will be similar between treated and untreated subjects. I describe 4 different propensity score methods: matching on the propensity score, stratification on the propensity score, inverse probability of treatment weighting using the propensity score, and covariate adjustment using the propensity score. I describe balance diagnostics for examining whether the propensity score model has been adequately specified. Furthermore, I discuss differences between regression-based methods and propensity score-based methods for the analysis of observational data. I describe different causal average treatment effects and their relationship with propensity score analyses.

https://www.tandfonline.com/doi/pdf/10.1080/00273171.2011.568786

An Introduction to Propensity Score Methods for Reducing the Effects of Confounding in Observational Studies

Statistics for Spatial Data.

1. Introduction and Overview. 2. Detecting Influential Observations and Outliers. 3. Detecting and Assessing Collinearity. 4. Applications and Remedies. 5. Research Issues and Directions for Extensions. Bibliography. Author Index. Subject Index.

Regression Diagnostics: Identifying Influential Data and Sources of Collinearity

When estimating causal effects using observational data, it is desirable to replicate a randomized experiment as closely as possible by obtaining treated and control groups with similar covariate distributions. This goal can often be achieved by choosing well-matched samples of the original treated and control groups, thereby reducing bias due to the covariates. Since the 1970's, work on matching methods has examined how to best choose treated and control subjects for comparison. Matching methods are gaining popularity in fields such as economics, epidemiology, medicine, and political science. However, until now the literature and related advice has been scattered across disciplines. Researchers who are interested in using matching methods-or developing methods related to matching-do not have a single place to turn to learn about past and current research. This paper provides a structure for thinking about matching methods and guidance on their use, coalescing the existing research (both old and new) and providing a summary of where the literature on matching methods is now and where it should be headed.

/pdf/matching-methods-for-causal-inference-a-review-and-a-look-1133erv7vp.pdf

Matching Methods for Causal Inference: A Review and a Look Forward

Multiple Imputation for Statistical Disclosure Limitation

Multiple imputation was first conceived as a tool that statistical agencies could use to handle nonresponse in large-sample public use surveys. In the last two decades, the multiple-imputation framework has been adapted for other statistical contexts. For example, individual researchers use multiple imputation to handle missing data in small samples, statistical agencies disseminate multiply-imputed data sets for purposes of protecting data confidentiality, and survey methodologists and epidemiologists use multiple imputation to correct for measurement errors. In some of these settings, Rubin's original rules for combining the point and variance estimates from the multiply-imputed data sets are not appropriate, because what is known—and thus the conditional expectations and variances used to derive inferential methods—differs from that in the missing-data context. These applications require new combining rules and methods of inference. In fact, more than 10 combining rules exist in the published literatur...

The Multiple Adaptations of Multiple Imputation

Multiple imputation is particularly well suited to deal with missing data in large epidemiologic studies, because typically these studies support a wide range of analyses by many data users. Some of these analyses may involve complex modeling, including interactions and nonlinear relations. Identifying such relations and encoding them in imputation models, for example, in the conditional regressions for multiple imputation via chained equations, can be daunting tasks with large numbers of categorical and continuous variables. The authors present a nonparametric approach for implementing multiple imputation via chained equations by using sequential regression trees as the conditional models. This has the potential to capture complex relations with minimal tuning by the data imputer. Using simulations, the authors demonstrate that the method can result in more plausible imputations, and hence more reliable inferences, in complex settings than the naive application of standard sequential regression imputation techniques. They apply the approach to impute missing values in data on adverse birth outcomes with more than 100 clinical and survey variables. They evaluate the imputations using posterior predictive checks with several epidemiologic analyses of interest.

Multiple Imputation for Missing Data via Sequential Regression Trees

In many observational studies, analysts estimate treatment effects using propensity scores, e.g. by matching or sub-classifying on the scores. When some values of the covariates are missing, analysts can use multiple imputation to fill in the missing data, estimate propensity scores based on the m completed datasets, and use the propensity scores to estimate treatment effects. We compare two approaches to implement this process. In the first, the analyst estimates the treatment effect using propensity score matching within each completed data set, and averages the m treatment effect estimates. In the second approach, the analyst averages the m propensity scores for each record across the completed datasets, and performs propensity score matching with these averaged scores to estimate the treatment effect. We compare properties of both methods via simulation studies using artificial and real data. The simulations suggest that the second method has greater potential to produce substantial bias reductions than the first, particularly when the missing values are predictive of treatment assignment.

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A comparison of two methods of estimating propensity scores after multiple imputation

Summary. The paper presents an illustration and empirical study of releasing multiply imputed, fully synthetic public use microdata. Simulations based on data from the US Current Population Survey are used to evaluate the potential validity of inferences based on fully synthetic data for a variety of descriptive and analytic estimands, to assess the degree of protection of confidentiality that is afforded by fully synthetic data and to illustrate the specification of synthetic data imputation models. Benefits and limitations of releasing fully synthetic data sets are discussed.

/pdf/releasing-multiply-imputed-synthetic-public-use-microdata-an-1oa0rd6cjy.pdf

Jerome P. Reiter

Papers

Multiple Imputation for Statistical Disclosure Limitation

The Multiple Adaptations of Multiple Imputation

Multiple Imputation for Missing Data via Sequential Regression Trees

A comparison of two methods of estimating propensity scores after multiple imputation

Releasing multiply imputed, synthetic public use microdata: an illustration and empirical study