Multiple imputation by chained equations is a flexible and practical approach to handling missing data. We describe the principles of the method and show how to impute categorical and quantitative variables, including skewed variables. We give guidance on how to specify the imputation model and how many imputations are needed. We describe the practical analysis of multiply imputed data, including model building and model checking. We stress the limitations of the method and discuss the possible pitfalls. We illustrate the ideas using a data set in mental health, giving Stata code fragments. Copyright © 2010 John Wiley & Sons, Ltd.

Multiple imputation using chained equations: Issues and guidance for practice

This review presents a practical summary of the missing data literature, including a sketch of missing data theory and descriptions of normalmodel multiple imputation (MI) and maximum likelihood methods. Practical missing data analysis issues are discussed, most notably the inclusion of auxiliary variables for improving power and reducing bias. Solutions are given for missing data challenges such as handling longitudinal, categorical, and clustered data with normal-model MI; including interactions in the missing data model; and handling large numbers of variables. The discussion of attrition and nonignorable missingness emphasizes the need for longitudinal diagnostics and for reducing the uncertainty about the missing data mechanism under attrition. Strategies suggested for reducing attrition bias include using auxiliary variables, collecting follow-up data on a sample of those initially missing, and collecting data on intent to drop out. Suggestions are given for moving forward with research on missing data and attrition.

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Missing data analysis: making it work in the real world.

25. Multiple Imputation for Nonresponse in Surveys. By D. B. Rubin. ISBN 0 471 08705 X. Wiley, Chichester, 1987. 258 pp. £30.25.

Multiple Imputation for Nonresponse in Surveys

Basics Introduction The problem of missing data Concepts of MCAR, MAR and MNAR Simple solutions that do not (always) work Multiple imputation in a nutshell Goal of the book What the book does not cover Structure of the book Exercises Multiple imputation Historic overview Incomplete data concepts Why and when multiple imputation works Statistical intervals and tests Evaluation criteria When to use multiple imputation How many imputations? Exercises Univariate missing data How to generate multiple imputations Imputation under the normal linear normal Imputation under non-normal distributions Predictive mean matching Categorical data Other data types Classification and regression trees Multilevel data Non-ignorable methods Exercises Multivariate missing data Missing data pattern Issues in multivariate imputation Monotone data imputation Joint Modeling Fully Conditional Specification FCS and JM Conclusion Exercises Imputation in practice Overview of modeling choices Ignorable or non-ignorable? Model form and predictors Derived variables Algorithmic options Diagnostics Conclusion Exercises Analysis of imputed data What to do with the imputed data? Parameter pooling Statistical tests for multiple imputation Stepwise model selection Conclusion Exercises Case studies Measurement issues Too many columns Sensitivity analysis Correct prevalence estimates from self-reported data Enhancing comparability Exercises Selection issues Correcting for selective drop-out Correcting for non-response Exercises Longitudinal data Long and wide format SE Fireworks Disaster Study Time raster imputation Conclusion Exercises Extensions Conclusion Some dangers, some do's and some don'ts Reporting Other applications Future developments Exercises Appendices: Software R S-Plus Stata SAS SPSS Other software References Author Index Subject Index

Flexible Imputation of Missing Data

Multivariate imputation by chained equations (MICE) has emerged as a principled method of dealing with missing data. Despite properties that make MICE particularly useful for large imputation procedures and advances in software development that now make it accessible to many researchers, many psychiatric researchers have not been trained in these methods and few practical resources exist to guide researchers in the implementation of this technique. This paper provides an introduction to the MICE method with a focus on practical aspects and challenges in using this method. A brief review of software programs available to implement MICE and then analyze multiply imputed data is also provided.

Multiple Imputation by Chained Equations: What is it and how does it work?

Multiple imputation (MI) and full information maximum likelihood (FIML) are the two most common approaches to missing data analysis. In theory, MI and FIML are equivalent when identical models are tested using the same variables, and when m, the number of imputations performed with MI, approaches infinity. However, it is important to know how many imputations are necessary before MI and FIML are sufficiently equivalent in ways that are important to prevention scientists. MI theory suggests that small values of m, even on the order of three to five imputations, yield excellent results. Previous guidelines for sufficient m are based on relative efficiency, which involves the fraction of missing information (γ) for the parameter being estimated, and m. In the present study, we used a Monte Carlo simulation to test MI models across several scenarios in which γ and m were varied. Standard errors and p-values for the regression coefficient of interest varied as a function of m, but not at the same rate as relative efficiency. Most importantly, statistical power for small effect sizes diminished as m became smaller, and the rate of this power falloff was much greater than predicted by changes in relative efficiency. Based our findings, we recommend that researchers using MI should perform many more imputations than previously considered sufficient. These recommendations are based on γ, and take into consideration one’s tolerance for a preventable power falloff (compared to FIML) due to using too few imputations.

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How Many Imputations are Really Needed? Some Practical Clarifications of Multiple Imputation Theory

The authors describe 2 efficiency (planned missing data) designs for measurement: the 3-form design and the 2-method measurement design. The 3-form design, a kind of matrix sampling, allows researchers to leverage limited resources to collect data for 33% more survey questions than can be answered by any 1 respondent. Power tables for estimating correlation effects illustrate the benefit of this design. The 2-method measurement design involves a relatively cheap, less valid measure of a construct and an expensive, more valid measure of the same construct. The cost effectiveness of this design stems from the fact that few cases have both measures, and many cases have just the cheap measure. With 3 brief simulations involving structural equation models, the authors show that compared with the same-cost complete cases design, a 2-method measurement design yields lower standard errors and a higher effective sample size for testing important study parameters. With a large cost differential between cheap and expensive measures and small effect sizes, the benefits of the design can be enormous. Strategies for using these 2 designs are suggested.

Planned missing data designs in psychological research.

Objective Research demonstrates that interventions targeting multiple settings within a child's life are more effective in treating or preventing conduct disorder. One such program is the Incredible Years Series, which comprises three treatment components, each focused on a different context and type of daily social interaction that a child encounters. This article explores the cost-effectiveness of stacking multiple intervention components versus delivering single intervention components. Method The data involved 459 children, ages 3 to 8, who participated in clinical trials of the Incredible Years Series. Children randomized to one of six treatment conditions received one or more of the three following program components: a child-based program, a parent training program, and a teacher-based program instructing teachers in classroom management and in the delivery of a classroom-based social skills curriculum. Results Per-child treatment costs and child behavior outcomes (observer and teacher reported) were used to generate cost-effectiveness acceptability curves; results suggest that stacking intervention components is likely cost-effective, at least for willingness to pay above $3,000 per child treated. Conclusions Economic data may be used to compare competing intervention formats. In the case of this program, providing multiple intervention components was cost-effective.

http://incredibleyears.com/wp-content/uploads/is-stacking-intervention-components-cost-effective_10.pdf

Is stacking intervention components cost-effective? An analysis of the incredible years program

Multi-component interventions for conduct disorder target several contexts of a child's life (e.g., both home and school environments) and are generally more effective than single-component behavioral interventions. Whether the multi-component approach is cost-effective remains an unanswered question. This article analyzes two decades of data from the Incredible Years (IY) Series to examine the cost-effectiveness of delivering multiple, stacked intervention components versus a single-component delivery approach. Cost-effectiveness analysis (CEA) provides decision makers with important economic information that can be used to aid in the selection of a program delivery format from one of several competing approaches. CEA concepts, including explicit budget constraints and strict dominance, are demonstrated using IY data; guidelines for interpreting CEA results are provided. Our analyses suggest that combining intervention components is a cost-effective approach to treating behavioral problems in a clinic-based youth population. Keywords: cost-effectiveness, multi-component interventions, Incredible Years Series, conduct disorder. ********** Conduct disorder (CD) is among the most common emotional and behavioral disorders affecting youth (Institute of Medicine, 1989), occurring in an estimated 10 percent of preschool and early-school-age children (Institute of Medicine, 1989; Webster-Stratton & Reid, 2003). Children with CD often engage in a variety of behaviors that are detrimental to themselves, their families, and society (Institute of Medicine, 1989; Webster-Stratton & Reid, 2003). Youth diagnosed with CD exhibit persistent behaviors consistent with three or more of the following four behavioral categories: aggression toward people or animals; property destruction; deceitfulness or theft; and serious rule violations (DSM-IV, 1994). These children frequently lack critical social and self-regulation skills necessary for making friends, and, as a result, often endure peer rejection and isolation from an early age (Kaiser & Hester, 1997; Miller-Johnson, Coie, Maumary-Gremaud, Bierman, & CPPRG, 2002). CD puts youth at risk for other costly outcomes such as weapon use, alcohol use, and other drug use and increases the likelihood of teenage pregnancy, dropping out of school, and police contact (Robins and Price, 1991; Achenbach, Howell, McConaughy, & Stanger, 1998; Bardone, Moffitt, Caspi, Dickson, Stanton, & Silva, 1998; Scott, 1998). Scott, Knapp, Henderson, and Maughan (2001) found evidence of a linear relationship between severity of conduct problems and societal costs; children with conduct problems (but who did not meet diagnostic criteria for CD) and children diagnosed with CD generated societal costs three and ten times greater than children with no conduct problems, respectively. Children with CD often become involved with public, child-serving systems, such as juvenile justice. This involvement creates juvenile court costs, incarceration costs, costs of lost productivity due to incarceration, and victim costs (both tangible and intangible) all borne by society (Cohen, 1998). Cohen (1998) estimates that one life of crime results in societal costs ranging from $1.3 to $1.5 million. Research suggests that early intervention is most effective, especially for those at greatest risk. Although the incidence of CD is higher among adolescents (Searight, Rottnek, & Abby, 2001), a small minority of young children begin to display conduct disorder symptoms as early as preschool age (Moffitt, 1993). Without intervention, childhood-onset CD generally results in bleaker trajectories than adolescent-onset CD (Searight et al., 2001). Compared with their peers, children identified in kindergarten as high-risk for behavioral problems are more likely to be placed on medication, to repeat a grade, to receive mental health services, and to come in contact with police (Jones, Dodge, Foster, Nix, & CPPRG, 2002). …

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Implementing Behavioral Intervention Components in a Cost-Effective Manner: Analysis of the Incredible Years Program.

Research has supported a negative correlation between cigarette smoking and exercise; however, the temporal nature of this association is not obvious. We modeled the relationships among smoking, exercise, and self-perceived health over time, within a college population. We collected 5 waves of data from 1,023 undergraduate students over a 14-month period. The results verified that smoking and exercise each made independent contributions in the prediction of health. Smoking was associated with reduced exercise over time, while no evidence was found for the reverse relationship. Our final mediation model demonstrates that smoking is related to poorer self-perceived health, and that this effect is partially mediated by the fact that smokers are less likely to engage in exercise.

Allison E. Olchowski

Papers

How Many Imputations are Really Needed? Some Practical Clarifications of Multiple Imputation Theory

Planned missing data designs in psychological research.

Is stacking intervention components cost-effective? An analysis of the incredible years program

Implementing Behavioral Intervention Components in a Cost-Effective Manner: Analysis of the Incredible Years Program.

Cigarette Smoking, Physical Activity, and the Health Status of College Students