A Simplified Framework for Using Multiple Imputation in Social Work Research

Multiple imputation and maximum likelihood estimation (via the expectation‐maximization algorithm) are two well‐known methods readily used for analyzing data with missing values. While these two methods are often considered as being distinct from one another, multiple imputation (when using improper imputation) is actually equivalent to a stochastic expectation‐maximization approximation to the likelihood. In this article, we exploit this key result to show that familiar likelihood‐based approaches to model selection, such as Akaike's information criterion (AIC) and the Bayesian information criterion (BIC), can be used to choose the imputation model that best fits the observed data. Poor choice of imputation model is known to bias inference, and while sensitivity analysis has often been used to explore the implications of different imputation models, we show that the data can be used to choose an appropriate imputation model via conventional model selection tools. We show that BIC can be consistent for selecting the correct imputation model in the presence of missing data. We verify these results empirically through simulation studies, and demonstrate their practicality on two classical missing data examples. An interesting result we saw in simulations was that not only can parameter estimates be biased by misspecifying the imputation model, but also by overfitting the imputation model. This emphasizes the importance of using model selection not just to choose the appropriate type of imputation model, but also to decide on the appropriate level of imputation model complexity.

The full-information maximum likelihood (FIML) is a popular estimation method for missing data in structural equation modeling (SEM). However, previous research has shown that SEM approximate fit indices (AFIs) such as the root mean square error of approximation (RMSEA) and the comparative fit index (CFI) can be distorted relative to their complete data counterparts when they are computed following the FIML estimation. The main goal of the current paper is to propose and examine an alternative approach for computing AFIs following the FIML estimation, which we refer to as the FIML-corrected or FIML-C approach. The secondary goal of the article is to examine another existing estimation method, the two-stage (TS) approach, for computing AFIs in the presence of missing data. Both FIML-C and TS approaches remove the bias due to missing data, so that the resulting incomplete data AFIs estimate the same population values as their complete data counterparts. For both approaches, we also propose a series of small sample corrections to improve the estimates of AFIs. In two simulation studies, we found that the FIML-C and TS approaches, when implemented with small sample corrections, estimated the population-complete-data AFIs with little bias across a variety of conditions, although the FIML-C approach can fail in a small number of conditions with a high percentage of missing data and a high degree of model misspecification. In contrast, the FIML AFIs as currently computed often performed poorly. We recommend FIML-C and TS approaches for computing AFIs in SEM. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

A Comparison of Multiple Imputation and Optimal Estimation for Missing and Uncertain Urban Air Toxics Data

BackgroundMultiple imputation is frequently used to deal with missing data in healthcare research. Although it is known that the outcome should be included in the imputation model when imputing missing covariate values, it is not known whether it should be imputed. Similarly no clear recommendations exist on: the utility of incorporating a secondary outcome, if available, in the imputation model; the level of protection offered when data are missing not-at-random; the implications of the dataset size and missingness levels.MethodsWe used realistic assumptions to generate thousands of datasets across a broad spectrum of contexts: three mechanisms of missingness (completely at random; at random; not at random); varying extents of missingness (20–80% missing data); and different sample sizes (1,000 or 10,000 cases). For each context we quantified the performance of a complete case analysis and seven multiple imputation methods which deleted cases with missing outcome before imputation, after imputation or not at all; included or did not include the outcome in the imputation models; and included or did not include a secondary outcome in the imputation models. Methods were compared on mean absolute error, bias, coverage and power over 1,000 datasets for each scenario.ResultsOverall, there was very little to separate multiple imputation methods which included the outcome in the imputation model. Even when missingness was quite extensive, all multiple imputation approaches performed well. Incorporating a secondary outcome, moderately correlated with the outcome of interest, made very little difference. The dataset size and the extent of missingness affected performance, as expected. Multiple imputation methods protected less well against missingness not at random, but did offer some protection.ConclusionsAs long as the outcome is included in the imputation model, there are very small performance differences between the possible multiple imputation approaches: no outcome imputation, imputation or imputation and deletion. All informative covariates, even with very high levels of missingness, should be included in the multiple imputation model. Multiple imputation offers some protection against a simple missing not at random mechanism.

Missing data are frequently encountered in biomedical, epidemiologic and social research. It is well known that a naive analysis without adequate handling of missing data may lead to bias and/or loss of efficiency. Partly due to its ease of use, multiple imputation has become increasingly popular in practice for handling missing data. However, it is unclear what is the best strategy to conduct multiple imputation in the presence of high-dimensional data. To answer this question, we investigate several approaches of using regularized regression and Bayesian lasso regression to impute missing values in the presence of high-dimensional data. We compare the performance of these methods through numerical studies, in which we also evaluate the impact of the dimension of the data, the size of the true active set for imputation, and the strength of correlation. Our numerical studies show that in the presence of high-dimensional data the standard multiple imputation approach performs poorly and the imputation approach using Bayesian lasso regression achieves, in most cases, better performance than the other imputation methods including the standard imputation approach using the correctly specified imputation model. Our results suggest that Bayesian lasso regression and its extensions are better suited for multiple imputation in the presence of high-dimensional data than the other regression methods.

Fraction of missing information λ j is a useful measure of the impact of missing data on the quality of estimation of a particular parameter. This measure can be computed for all parameters in the model, and it communicates the relative loss of efficiency in the estimation of a particular parameter due to missing data. It has been recommended that researchers working with incomplete data sets routinely report this measure, as it is more informative than percent missing data (Bodner, 2008; Schafer, 1997). However, traditional estimates of λ j require the implementation of multiple imputation (MI). Many researchers prefer to fit structural equation models using full information maximum likelihood rather than MI. This article demonstrates how to obtain an estimate of λ j using maximum likelihood estimation routines only and argues that this estimate is superior to the estimate obtained via MI when the number of imputations is small. Interpretation of λ j is also addressed.

We propose using latent class analysis as an alternative to log-linear analysis for the multiple imputation of incomplete categorical data. Similar to log-linear models, latent class models can be used to describe complex association structures between the variables used in the imputation model. However, unlike log-linear models, latent class models can be used to build large imputation models containing more than a few categorical variables. To obtain imputations reflecting uncertainty about the unknown model parameters, we use a nonparametric bootstrap procedure as an alternative to the more common full Bayesian approach. The proposed multiple imputation method, which is implemented in Latent GOLD software for latent class analysis, is illustrated with two examples. In a simulated data example, we compare the new method to well-established methods such as maximum likelihood estimation with incomplete data and multiple imputation using a saturated log-linear model. This example shows that the proposed method yields unbiased parameter estimates and standard errors. The second example concerns an application using a typical social sciences data set. It contains 79 variables that are all included in the imputation model. The proposed method is especially useful for such large data sets because standard methods for dealing with missing data in categorical variables break down when the number of variables is so large.

Previous articleNext article FreeThe Life and Career of Matthew O. HowardJeffrey M. JensonJeffrey M. JensonUniversity of Denver Search for more articles by this author PDFPDF PLUSFull Text Add to favoritesDownload CitationTrack CitationsPermissionsReprints Share onFacebookTwitterLinked InRedditEmailQR Code SectionsMoreMatthew O. HowardView Large ImageDownload PowerPointOn December 15, 2018, social work and the Journal of the Society for Social Work and Research (JSSWR) lost one of its most prolific scholars, outstanding teachers, and thoughtful mentors in recent memory. Matthew O. Howard, PhD—the Frank A. Daniels Distinguished Professor of Human Services Policy Information and associate dean for doctoral education in the School of Social Work at the University of North Carolina at Chapel Hill—passed away following a lengthy hospitalization. As an associate editor for JSSWR, Matthew had a significant impact on improving the quality and influence of the journal. He will be sorely missed by our editorial team.Matthew was a consummate scholar who possessed a singular ability to understand and conceptualize social problems of all types. His research contributed greatly to existing knowledge of the etiology, prevention, and treatment of substance abuse, alcohol dependence, and mental health disorders. And, Matthew’s provocative articles assessing the state of social work education, practice, and research set forth ideas that will affect the trajectory of social work for years to come. His passion for knowledge—conveyed quietly and effectively to countless graduate students—was felt deeply by the many lives he touched over the course of an academic career that included appointments in the Department of Psychiatry and Behavioral Sciences at the University of Washington, the Department of Psychiatry at the Oregon Health Sciences University, the George Warren Brown School of Social Work at Washington University in St. Louis, the School of Social Work and the Department of Psychiatry at the University of Michigan, and the University of North Carolina at Chapel Hill.Matthew’s training in social work coincided with my own enrollment in the University of Washington School of Social Work doctoral program in 1984. Matthew and I became immediate and close friends during our graduate studies in Seattle, and we spent hours discussing social work, class assignments, and the research projects we worked on as doctoral students. Many of these conversations occurred in an alley coffee shop in Seattle’s University District, just a stone’s throw from the School of Social Work. Known by the employees as “Matt and Jeff,” we were treated as regulars who would sit at our customary window table for what was likely far too long. It was a time of great intellectual pursuit, and I had found the perfect colleague and friend with whom to share ideas and discuss future plans. It was the beginning of a personal friendship and professional relationship that lasted 34 years.Matthew entered doctoral education with a well-developed interest in understanding the etiology of alcohol and other substance use disorders. Over the nearly four decades that followed, he devoted his career to conducting basic and applied research aimed at ameliorating substance abuse dependence and co-occurring problems associated with alcohol and drug abuse. He became particularly well known for his basic research and intervention studies addressing the vexing problem of inhalant abuse (e.g., Howard, Balster, Cottler, Wu, & Vaughn, 2008; Howard, Bowen, Garland, Perron, & Vaughn, 2011; Howard & Jenson, 1999b). Matthew’s innovative and rigorous research in this area led to three grants from the National Institute on Drug Abuse and to widespread recognition as one of the world’s foremost experts on inhalant abuse. In recent years, Matthew extended his work to testing mindfulness-oriented interventions for people with chronic pain and opioid misuse. His coinvestigator in much of this work was Eric Garland, professor and associate dean for research in the University of Utah College of Social Work. Eric, a former student of Matthew’s at the University of North Carolina at Chapel Hill, describes some of the important lessons he learned under Matthew’s tutelage in an accompanying article in this issue (Garland, 2019).Matthew also made significant contributions to social work education and research. In the Aaron Rosen Lecture at the 2015 Annual Conference of the Society for Social Work and Research, Matthew traced key developments in social work during the past 30 years and reflected on a vision of the field that stretched to 2044—30 years into the future (Howard & Garland, 2015). The ideas he shared in this lecture have provided a useful framework for assessing the relatively recent history of social work and addressing the challenges in educating master’s-level practitioners and doctoral students in the future. Matthew delivered a similarly thought-provoking lecture on the current state and future of social work doctoral education at the 2016 Annual Conference of the Group for the Advancement of Doctoral Education. Ideas presented in his lectures were coupled with action. One such example is illustrated by Matthew’s early development of a University of North Carolina at Chapel Hill doctoral-level course on conducting systematic reviews. Students in this class often produced publishable papers as a result of Matthew’s fastidious attention to breadth and quality. In earlier work at the Brown School of Social Work at Washington University in St. Louis, Matthew and colleagues advanced the idea of evidence-based practice as a paradigm for training MSW social work practitioners (Howard, McMillen, & Pollio, 2003). Enola Proctor, the Shanti K. Khinduka Distinguished Professor in the Brown School of Social Work at Washington University in St. Louis, was a colleague of Matthew’s at the time. She remembers Matthew as… a brilliant scholar and dear person. Highly regarded for his excellence in the classroom at the Brown School, he was demanding yet was a frequent winner of student-elected teaching awards. Matthew used his seemingly boundless energy to better the fields of addiction research and social work practice. He had my highest respect and unending affection. His passing is a tremendous loss to our field and community of scholars [and] saddens me deeply. (E. Proctor, personal communication, January 9, 2019)In 1999, Matthew and I had the good fortune to guest edit a special issue of Research on Social Work Practice that explored the utility of clinical practice guidelines for social work practice (Howard & Jenson, 1999a). Collectively, Matthew’s lectures and published papers assessing the state of social work education and practice stimulated debate and produced tangible curricula changes in schools across the country.A prolific writer, Matthew published more than 250 peer-reviewed papers in his career. His written work also included 40 book reviews, editorials, and government reports. Matthew’s h-index of 55 and nearly 9,000 citations of his work to date illustrate just how much his scholarship was valued by colleagues. His written contributions will be recognized and used by practitioners, policymakers, and researchers for decades to come.Matthew was a fellow and a board member of the American Academy of Social Work and Social Welfare and a fellow of the Society for Social Work and Research. A proponent of interdisciplinary work, he also was a faculty research fellow in the Cecil G. Sheps Center for Health Services Research at the University of North Carolina at Chapel Hill at the time of his passing. Matthew’s devotion to empirical research and scholarship is widely recognized. However, what may be most impressive about Matthew’s career is the recognition he received as both a scholar and a teacher. He was awarded eight outstanding teaching and mentoring awards from students and colleagues at Washington University in St. Louis and the University of North Carolina at Chapel Hill. Two of Matthew’s doctoral students at North Carolina (Eric Garland, University of Utah; and Carrie Pettus-Davis, Florida State University) received Doctoral Fellow Awards from the Society for Social Work and Research. Matthew connected with his students by combining high scientific standards with a compassionate approach to helping people succeed. He was soft-spoken, but his ideas and words carried great weight and influence.Matthew’s service to the fields of social work and addiction was also exemplary. He reviewed manuscripts for more than 60 different academic journals in his career. He was on the editorial boards of more than 50 journals—including serving a JSSWR associate editor for the past several years—and he previously served as editor-in-chief of the Journal of Social Service Research, Social Work Research, and the Journal of Addictive Diseases. Matthew also was vice president and served on the Society for Social Work and Research Board of Directors from 2005 to 2008.The task of summarizing the life and career of a prolific and impactful scholar, teacher, and mentor like Matthew is daunting. Mark Fraser, professor emeritus at the University of North Carolina at Chapel Hill and the founding editor of JSSWR, was a longtime friend, collaborator, and colleague. Reflecting on Matthew’s career, he recalls,As a scholar and a teacher, Matthew was eloquent and encyclopedic. Students flocked to his classes. A gentle spirit who treasured collaboration with others, his greatest joys came in exploring new ideas and reading recent research. In the profession as a thought leader, Matthew was a tour de force. At once, he was creative, insightful, sensitive, critical, and thorough. Matthew was—quite simply—incomparable. (M. Fraser, personal communication, January 8, 2019)Tangible accomplishments like those summarized here do not tell the complete story of a person. Matthew had an uncanny ability to effectively express his strong personal beliefs and ethical values in everyday interactions with friends and colleagues. He had a deep interest in applying the lessons gained from his own empirical work to promote fairness and equity for all people. Matthew’s invaluable input and feedback to students and colleagues about their ideas, papers, or projects came with great civility and kindness. He was an insatiable reader whose knowledge extended to topics well beyond social work or the addictions. In this sense, one could discuss a wide range of topics with Matthew with the preordained understanding that he had very likely already read much of what had been written on the topic. Matthew’s longstanding practice of underscoring written text with yellow highlighters was applied to thousands of empirical and conceptual articles and manuscripts during his career.On a personal level, Matthew enjoyed taking walks, listening to music, and reading novels and poetry. His wry sense of humor often left many of his closest friends and colleagues writhing in laughter. I was among them.JSSWR is proud to count Matthew as one of its most influential associate editors and contributors. His place as an important teacher and scholar in social work education and research is secure. Matthew’s many contributions will be discovered anew by emerging scholars for decades to come. His presence in social work and the broad field of the addictions will be missed by us all.NotesJeffrey M. Jenson, PhD, is Editor-in-Chief of the Journal of the Society for Social Work and Research and the Phillip D. & Eleanor G. Winn Endowed Professor Children and Youth at the University of Denver Graduate School of Social Work.Correspondence regarding this article should be directed to Jeffrey M. Jenson, University of Denver, 2148 S. High St., Denver, CO 80208 or via e-mail to [email protected]ReferencesGarland, E. L. (2019). Standing on the shoulders of giants: Matthew O. Howard as a mentor and his influence on the science of mindfulness as a treatment for addiction. Journal of the Society for Social Work and Research. Advance online publication. doi:10.1086/702654First citation in articleGoogle ScholarHoward, M. O. (2016, March 31). Hot topics in doctoral education. Presentation at the 2016 Annual Conference of the Group for the Advancement of Doctoral Education, Chapel Hill, NC.First citation in articleGoogle ScholarHoward, M. O., Balster, R., Cottler, L. B., Wu, L., & Vaughn, M. G. (2008). Inhalant use among incarcerated adolescents: Prevalence, characteristics, and predictors of use. Drug and Alcohol Dependence, 93, 197–209. https://doi.org/10.1016/j.drugalcdep.2007.08.023First citation in articleCrossrefGoogle ScholarHoward, M. O., Bowen, S., Garland, E. L., Perron, B. E., & Vaughn, M. G. (2011). Inhalant use and inhalant use disorders in the United States. Addiction Science & Clinical Practice, 6, 18–31.First citation in articleGoogle ScholarHoward, M. O., & Garland, E. L. (2015). Social work research: 2044. Journal of the Society for Social Work and Research, 6, 173–200. https://doi.org/10.1086/681099First citation in articleLinkGoogle ScholarHoward, M. O., & Jenson, J. M. (1999a). Clinical practice guidelines: Should social work develop them? Research on Social Work Practice, 9, 283–301. https://doi.org/10.1177/104973159900900302First citation in articleCrossrefGoogle ScholarHoward, M. O., & Jenson, J. M. (1999b). Inhalant use among antisocial youth: Prevalence and correlates. Addictive Behaviors, 24, 59–74. https://doi.org/10.1016/s0306-4603(98)00039-2First citation in articleCrossrefGoogle ScholarHoward, M. O., McMillen, J. C., & Pollio, D. (2003). Teaching evidence-based practice: Toward a new paradigm for social work education. Research on Social Work Practice, 13, 234–259. https://doi.org/10.1177/1049731502250404First citation in articleCrossrefGoogle Scholar Previous articleNext article DetailsFiguresReferencesCited by Journal of the Society for Social Work and Research Volume 10, Number 1Spring 2019 Published for the Society for Social Work and Research Article DOIhttps://doi.org/10.1086/702653HistoryPublished online February 04, 2019 © 2019 by the Society for Social Work and Research. All rights reserved.PDF download Crossref reports no articles citing this article.

Propensity score analysis is a popular method to control for confounding in observational studies. A challenge in propensity methods is missing values in confounders. Several strategies for handling missing values exist, but guidance in choosing the best method is needed. In this simulation study, we compared four strategies of handling missing covariate values in propensity matching and propensity weighting. These methods include: complete case analysis, missing indicator method, multiple imputation and combining multiple imputation and missing indicator method. Concurrently, we aimed to provide guidance in choosing the optimal strategy. Simulated scenarios varied regarding missing mechanism, presence of effect modification or unmeasured confounding. Additionally, we demonstrated how missingness graphs help clarifying the missing structure. When no effect modification existed, complete case analysis yielded valid causal treatment effects even when data were missing not at random. In some situations, complete case analysis was also able to partially correct for unmeasured confounding. Multiple imputation worked well if the data were missing (completely) at random, and if the imputation model was correctly specified. In the presence of effect modification, more complex imputation models than default options of commonly used statistical software were required. Multiple imputation may fail when data are missing not at random. Here, combining multiple imputation and the missing indicator method reduced the bias as the missing indicator variable can be a proxy for unobserved confounding. The optimal way to handle missing values in covariates of propensity score models depends on the missing data structure and the presence of effect modification. When effect modification is present, default settings of imputation methods may yield biased results even if data are missing at random.

BackgroundMissing data are a common problem in prospective studies with a long follow-up, and the volume, pattern and reasons for missing data may be relevant when estimating the cost of illness. We aimed to evaluate the effects of different methods for dealing with missing longitudinal cost data and for costing caregiver time on total societal costs in Alzheimer’s disease (AD).MethodsGERAS is an 18-month observational study of costs associated with AD. Total societal costs included patient health and social care costs, and caregiver health and informal care costs. Missing data were classified as missing completely at random (MCAR), missing at random (MAR) or missing not at random (MNAR). Simulation datasets were generated from baseline data with 10–40 % missing total cost data for each missing data mechanism. Datasets were also simulated to reflect the missing cost data pattern at 18 months using MAR and MNAR assumptions. Naïve and multiple imputation (MI) methods were applied to each dataset and results compared with complete GERAS 18-month cost data. Opportunity and replacement cost approaches were used for caregiver time, which was costed with and without supervision included and with time for working caregivers only being costed.ResultsTotal costs were available for 99.4 % of 1497 patients at baseline. For MCAR datasets, naïve methods performed as well as MI methods. For MAR, MI methods performed better than naïve methods. All imputation approaches were poor for MNAR data. For all approaches, percentage bias increased with missing data volume. For datasets reflecting 18-month patterns, a combination of imputation methods provided more accurate cost estimates (e.g. bias: −1 % vs −6 % for single MI method), although different approaches to costing caregiver time had a greater impact on estimated costs (29–43 % increase over base case estimate).ConclusionsMethods used to impute missing cost data in AD will impact on accuracy of cost estimates although varying approaches to costing informal caregiver time has the greatest impact on total costs. Tailoring imputation methods to the reason for missing data will further our understanding of the best analytical approach for studies involving cost outcomes.Electronic supplementary materialThe online version of this article (doi:10.1186/s12874-016-0188-1) contains supplementary material, which is available to authorized users.

The occurrence of missing data due to protocol deviations is inevitable in clinical trials. When missing data exist, analyses rely on assumptions about the behaviour of the individuals after dropping out. As a result, sensitivity analysis, which is now advocated by regulatory bodies, should be performed to explore the robustness of the inference to those assumptions. These assumptions should be relevant to the estimand of the study and be practically accessible by all parties. The aim of this document is twofold: to assess the statistical validity of a new method for sensitivity analysis, and apply this method to a published Alzheimer’s study. At the beginning of the thesis, a description of the Alzheimer’s study and issues with missing data encountered therein, take place. This study was mainly set up to investigate the effect rosiglitazone, as an adjunct therapy in Alzheimer’s patients. Two different doses of the drug were compared to placebo. The study suffered from a moderate degree of missing data in each treatment arm. The thesis proceeds with a critique on the per-protocol and intention-to-treat estimands, and revisits their meaning when missing data occur. Two new estimands are introduced, which are particularly amenable to studies with missing data. They are termed de-jure and de-facto. Following that, the main methods for dealing with missing data are introduced, with a particular emphasis on multiple imputation, and how it can easily incorporate missing not at random (MNAR) analyses. A thorough presentation of the new methodology is given. This is built around a set of assumptions, that reflect possible distributional behaviours of the subjects after protocol deviation. The assumptions are Randomised-treatment Missing at Random (MAR), Jump to Reference, Last Mean Carried Forward, Copy Increments in Reference, and Copy Reference. Estimation and inference is achieved via multiple imputation, and it is shown how the predictive distribution of the imputation model can be constructed from parameters borrowed from an MAR model and manipulated in a pattern-mixture model approach, to obtain the five assumptions for the 4 unobserved component of groups of individuals. A number of simulations whose aim is to explore the statistical properties of the new method, are carried out. The simulated datasets, which are based on the parameters from the Alzheimer’s study, focus on the estimator bias, the size and power of the methods, the bias of the variance estimator, and coverage. The results obtained from the simulations show the method has sensible properties; no bias for the estimator was detectable and the sizes and power of the methods agreed closely with their theoretical equivalents. The main result however, pertains to Rubin’s variance estimator, which proves to appropriately reflect the loss of information from missing data. It is therefore argued, it is the right estimator to use in this setting. The results from the application of the proposed method on the Alzheimer’s dataset are presented in tables. Inferences from the sensitivity analysis assumptions were consistent with those from the original MAR analyses. The comparison between high dose rosiglitazone and placebo did not show any evidence in favour of the treatment under any sensitivity assumption. Some evidence of treatment difference existed when the low dose treatment was compared to placebo. This finding though, should be interpreted with caution, as the differences were obtained from analyses not subjected to the rigorous inferential process that was used in the Harringtons study. It was further argued, this finding might have been due to chance, and it was not replicated in a different study.

BackgroundWithin routinely collected health data, missing data for an individual might provide useful information in itself. This occurs, for example, in the case of electronic health records, where the presence or absence of data is informative. While the naive use of missing indicators to try to exploit such information can introduce bias, its use in conjunction with multiple imputation may unlock the potential value of missingness to reduce bias in causal effect estimation, particularly in missing not at random scenarios and where missingness might be associated with unmeasured confounders.MethodsWe conducted a simulation study to determine when the use of a missing indicator, combined with multiple imputation, would reduce bias for causal effect estimation, under a range of scenarios including unmeasured variables, missing not at random, and missing at random mechanisms. We use directed acyclic graphs and structural models to elucidate a variety of causal structures of interest. We handled missing data using complete case analysis, and multiple imputation with and without missing indicator terms.ResultsWe find that multiple imputation combined with a missing indicator gives minimal bias for causal effect estimation in most scenarios. In particular the approach: 1) does not introduce bias in missing (completely) at random scenarios; 2) reduces bias in missing not at random scenarios where the missing mechanism depends on the missing variable itself; and 3) may reduce or increase bias when unmeasured confounding is present.ConclusionIn the presence of missing data, careful use of missing indicators, combined with multiple imputation, can improve causal effect estimation when missingness is informative, and is not detrimental when missingness is at random.

The usual methods for analyzing case-cohort studies rely on sometimes not fully efficient weighted estimators. Multiple imputation might be a good alternative because it uses all the data available and approximates the maximum partial likelihood estimator. This method is based on the generation of several plausible complete data sets, taking into account uncertainty about missing values. When the imputation model is correctly defined, the multiple imputation estimator is asymptotically unbiased and its variance is correctly estimated. We show that a correct imputation model must be estimated from the fully observed data (cases and controls), using the case status among the explanatory variable. To validate the approach, we analyzed case-cohort studies first with completely simulated data and then with case-cohort data sampled from two real cohorts. The analyses of simulated data showed that, when the imputation model was correct, the multiple imputation estimator was unbiased and efficient. The observed gain in precision ranged from 8 to 37 per cent for phase-1 variables and from 5 to 19 per cent for the phase-2 variable. When the imputation model was misspecified, the multiple imputation estimator was still more efficient than the weighted estimators but it was also slightly biased. The analyses of case-cohort data sampled from complete cohorts showed that even when no strong predictor of the phase-2 variable was available, the multiple imputation was unbiased, as precised as the weighted estimator for the phase-2 variable and slightly more precise than the weighted estimators for the phase-1 variables. However, the multiple imputation estimator was found to be biased when, because of interaction terms, some coefficients of the imputation model had to be estimated from small samples. Multiple imputation is an efficient technique for analyzing case-cohort data. Practically, we suggest building the analysis model using only the case-cohort data and weighted estimators. Multiple imputation can eventually be used to reanalyze the data using the selected model in order to improve the precision of the results.

ObjectivesResearchers are concerned whether multiple imputation (MI) or complete case analysis should be used when a large proportion of data are missing. We aimed to provide guidance for drawing conclusions from data with a large proportion of missingness. Study Design and SettingVia simulations, we investigated how the proportion of missing data, the fraction of missing information (FMI), and availability of auxiliary variables affected MI performance. Outcome data were missing completely at random or missing at random (MAR). ResultsProvided sufficient auxiliary information was available; MI was beneficial in terms of bias and never detrimental in terms of efficiency. Models with similar FMI values, but differing proportions of missing data, also had similar precision for effect estimates. In the absence of bias, the FMI was a better guide to the efficiency gains using MI than the proportion of missing data. ConclusionWe provide evidence that for MAR data, valid MI reduces bias even when the proportion of missingness is large. We advise researchers to use FMI to guide choice of auxiliary variables for efficiency gain in imputation analyses, and that sensitivity analyses including different imputation models may be needed if the number of complete cases is small.

BackgroundDespite recent advances in causal inference methods, outcome regression remains the most widely used approach for estimating causal effects in epidemiological studies with a single-point exposure and outcome. Missing data are common in these studies, and complete-case analysis (CCA) and multiple imputation (MI) are two frequently used methods for handling them. In randomised controlled trials (RCTs), it has been shown that MI should be conducted separately by treatment group. In observational studies, causal inference is now understood as the task of emulating an RCT, which raises the question of whether MI should be conducted by exposure group in such studies.MethodsWe addressed this question by evaluating the performance of seven methods for handling missing data when estimating causal effects with outcome regression. We conducted an extensive simulation study based on an illustrative case study from the Victorian Adolescent Health Cohort Study, assessing a range of scenarios, including seven outcome generation models with exposure-confounder interactions of differing strength.ResultsThe simulation results showed that MI by exposure group led to the least bias when the size of the smallest exposure group was relatively large, followed by MI approaches that included the exposure-confounder interactions.ConclusionsThe findings from our simulation study, which was designed based on a real case study, suggest that current practice for the conduct of MI in causal inference may need to shift to stratifying by exposure group where feasible, or otherwise including exposure-confounder interactions in the imputation model.