Impact of non-normal random effects on inference by multiple imputation: A simulation assessment

Making Sense of Censored Covariates: Statistical Methods for Studies of Huntington's Disease

The landscape of survival analysis is constantly being revolutionized to answer biomedical challenges, most recently the statistical challenge of censored covariates rather than outcomes. There are many promising strategies to tackle censored covariates, including weighting, imputation, maximum likelihood, and Bayesian methods. Still, this is a relatively fresh area of research, different from the areas of censored outcomes (i.e., survival analysis) or missing covariates. In this review, we discuss the unique statistical challenges encountered when handling censored covariates and provide an in-depth review of existing methods designed to address those challenges. We emphasize each method's relative strengths and weaknesses, providing recommendations to help investigators pinpoint the best approach to handling censored covariates in their data.

The handling of missing data in trial-based economic evaluations: should data be multiply imputed prior to longitudinal linear mixed-model analyses?

INTRODUCTION

For the analysis of clinical effects, multiple imputation (MI) of missing data were shown to be unnecessary when using longitudinal linear mixed-models (LLM). It remains unclear whether this also applies to trial-based economic evaluations. Therefore, this study aimed to assess whether MI is required prior to LLM when analyzing longitudinal cost and effect data.

METHODS

Two-thousand complete datasets were simulated containing five time points. Incomplete datasets were generated with 10, 25, and 50% missing data in follow-up costs and effects, assuming a Missing At Random (MAR) mechanism. Six different strategies were compared using empirical bias (EB), root-mean-squared error (RMSE), and coverage rate (CR). These strategies were: LLM alone (LLM) and MI with LLM (MI-LLM), and, as reference strategies, mean imputation with LLM (M-LLM), seemingly unrelated regression alone (SUR-CCA), MI with SUR (MI-SUR), and mean imputation with SUR (M-SUR).

RESULTS

For costs and effects, LLM, MI-LLM, and MI-SUR performed better than M-LLM, SUR-CCA, and M-SUR, with smaller EBs and RMSEs as well as CRs closers to nominal levels. However, even though LLM, MI-LLM and MI-SUR performed equally well for effects, MI-LLM and MI-SUR were found to perform better than LLM for costs at 10 and 25% missing data. At 50% missing data, all strategies resulted in relatively high EBs and RMSEs for costs.

CONCLUSION

LLM should be combined with MI when analyzing trial-based economic evaluation data. MI-SUR is more efficient and can also be used, but then an average intervention effect over time cannot be estimated.

Missing data in longitudinal studies: Comparison of multiple imputation methods in a real clinical setting

RATIONALE, AIMS, AND OBJECTIVES

Missing data represent a challenge in longitudinal studies. The aim of the study is to compare the performance of the multivariate normal imputation and the fully conditional specification methods, using real data set with missing data partially completed 2 years later.

METHOD

The data used came from an ongoing randomized controlled trial with 5-year follow-up. At a certain time, we observed a number of patients with missing data and a number of patients whose data were unobserved because they were not yet eligible for a given follow-up. Both unobserved and missing data were imputed. The imputed unobserved data were compared with the corresponding real information obtained 2 years later.

RESULTS

Both imputation methods showed similar performance on the accuracy measures and produced minimally biased estimates.

CONCLUSION

Despite the large number of repeated measures with intermittent missing data and the non-normal multivariate distribution of data, both methods performed well and was not possible to determine which was better.

Local average treatment effects estimation via substantive model compatible multiple imputation

Nonadherence to assigned treatment is common in randomized controlled trials (RCTs). Recently, there has been increased interest in estimating causal effects of treatment received, for example, the so-called local average treatment effect (LATE). Instrumental variables (IV) methods can be used for identification, with estimation proceeding either via fully parametric mixture models or two-stage least squares (TSLS). TSLS is popular but can be problematic for binary outcomes where the estimand of interest is a causal odds ratio. Mixture models are rarely used in practice, perhaps because of their perceived complexity and need for specialist software. Here, we propose using multiple imputation (MI) to impute the latent compliance class appearing in the mixture models. Since such models include an interaction term between the latent compliance class and randomized treatment, we use "substantive model compatible" MI (SMC MIC), which can additionally handle missing data in outcomes and other variables in the model, before fitting the mixture models via maximum likelihood to the MI data sets and combining results via Rubin's rules. We use simulations to compare the performance of SMC MIC to existing approaches and also illustrate the methods by reanalyzing an RCT in UK primary health. We show that SMC MIC can be more efficient than full Bayesian estimation when auxiliary variables are incorporated, and is superior to two-stage methods, especially for binary outcomes.

A Comparison of Multilevel Imputation Schemes for Random Coefficient Models: Fully Conditional Specification and Joint Model Imputation with Random Covariance Matrices

Literature addressing missing data handling for random coefficient models is particularly scant, and the few studies to date have focused on the fully conditional specification framework and "reverse random coefficient" imputation. Although it has not received much attention in the literature, a joint modeling strategy that uses random within-cluster covariance matrices to preserve cluster-specific associations is a promising alternative for random coefficient analyses. This study is apparently the first to directly compare these procedures. Analytic results suggest that both imputation procedures can introduce bias-inducing incompatibilities with a random coefficient analysis model. Problems with fully conditional specification result from an incorrect distributional assumption, whereas joint imputation uses an underparameterized model that assumes uncorrelated intercepts and slopes. Monte Carlo simulations suggest that biases from these issues are tolerable if the missing data rate is 10% or lower and the sample is composed of at least 30 clusters with 15 observations per group. Furthermore, fully conditional specification tends to be superior with intraclass correlations that are typical of crosssectional data (e.g., ICC = .10), whereas the joint model is preferable with high values typical of longitudinal designs (e.g., ICC = .50).

Multiple Imputation in Two-Stage Cluster Samples Using The Weighted Finite Population Bayesian Bootstrap

Multistage sampling is often employed in survey samples for cost and convenience. However, accounting for clustering features when generating datasets for multiple imputation is a nontrivial task, particularly when, as is often the case, cluster sampling is accompanied by unequal probabilities of selection, necessitating case weights. Thus, multiple imputation often ignores complex sample designs and assumes simple random sampling when generating imputations, even though failing to account for complex sample design features is known to yield biased estimates and confidence intervals that have incorrect nominal coverage. In this article, we extend a recently developed, weighted, finite-population Bayesian bootstrap procedure to generate synthetic populations conditional on complex sample design data that can be treated as simple random samples at the imputation stage, obviating the need to directly model design features for imputation. We develop two forms of this method: one where the probabilities of selection are known at the first and second stages of the design, and the other, more common in public use files, where only the final weight based on the product of the two probabilities is known. We show that this method has advantages in terms of bias, mean square error, and coverage properties over methods where sample designs are ignored, with little loss in efficiency, even when compared with correct fully parametric models. An application is made using the National Automotive Sampling System Crashworthiness Data System, a multistage, unequal probability sample of U.S. passenger vehicle crashes, which suffers from a substantial amount of missing data in "Delta-V," a key crash severity measure.

Multiple imputation methods for bivariate outcomes in cluster randomised trials

Missing observations are common in cluster randomised trials. The problem is exacerbated when modelling bivariate outcomes jointly, as the proportion of complete cases is often considerably smaller than the proportion having either of the outcomes fully observed. Approaches taken to handling such missing data include the following: complete case analysis, single‐level multiple imputation that ignores the clustering, multiple imputation with a fixed effect for each cluster and multilevel multiple imputation.

We contrasted the alternative approaches to handling missing data in a cost‐effectiveness analysis that uses data from a cluster randomised trial to evaluate an exercise intervention for care home residents.

We then conducted a simulation study to assess the performance of these approaches on bivariate continuous outcomes, in terms of confidence interval coverage and empirical bias in the estimated treatment effects. Missing‐at‐random clustered data scenarios were simulated following a full‐factorial design.

Across all the missing data mechanisms considered, the multiple imputation methods provided estimators with negligible bias, while complete case analysis resulted in biased treatment effect estimates in scenarios where the randomised treatment arm was associated with missingness. Confidence interval coverage was generally in excess of nominal levels (up to 99.8%) following fixed‐effects multiple imputation and too low following single‐level multiple imputation. Multilevel multiple imputation led to coverage levels of approximately 95% throughout. © 2016 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd.

Auxiliary variables in multiple imputation in regression with missing X: a warning against including too many in small sample research

BACKGROUND

Multiple imputation is becoming increasingly popular. Theoretical considerations as well as simulation studies have shown that the inclusion of auxiliary variables is generally of benefit.

METHODS

A simulation study of a linear regression with a response Y and two predictors X1 and X2 was performed on data with n = 50, 100 and 200 using complete cases or multiple imputation with 0, 10, 20, 40 and 80 auxiliary variables. Mechanisms of missingness were either 100% MCAR or 50% MAR + 50% MCAR. Auxiliary variables had low (r=.10) vs. moderate correlations (r=.50) with X's and Y.

RESULTS

The inclusion of auxiliary variables can improve a multiple imputation model. However, inclusion of too many variables leads to downward bias of regression coefficients and decreases precision. When the correlations are low, inclusion of auxiliary variables is not useful.

CONCLUSION

More research on auxiliary variables in multiple imputation should be performed. A preliminary rule of thumb could be that the ratio of variables to cases with complete data should not go below 1 : 3.

Validity and power of missing data imputation for extreme sampling and terminal measures designs in mediation analysis

Several authors have acknowledged that testing mediational hypotheses between treatments, genes, physiological measures, and behaviors may substantially advance our understanding of how these associations operate. In psychiatric research, the costs of measuring the putative mediator or the outcome can be prohibitive. Extreme sampling designs have been validated as methods for reducing study costs by increasing power per subject measured on the more expensive variable when assessing bivariate relationships. However, there exist concerns about how missing data can potentially bias the results. Additionally, most mediation analysis techniques presuppose the joint measurement of mediators and outcomes for all subjects. There have been limited methodological developments for techniques that can evaluate putative mediators in studies that have employed extreme sampling, resulting in missing data. We demonstrate that extreme (selective) sampling strategies can be beneficial in the context of mediation analyses. Handling the missing data with maximum likelihood (ML) resulted in minimal power loss and unbiased parameter estimates. We must be cautious, though, in recommending the ML approach for extreme sampling designs because it yielded inflated Type 1 error rates under some null conditions. Yet, the use of extreme sampling designs and methods to handle the resultant missing data presents a viable research strategy.

Mental health matters in elementary school: first-grade screening predicts fourth grade achievement test scores

The objective of the study was to evaluate whether mental health problems identified through screens administered in first grade are related to poorer academic achievement test scores in the fourth grade. The government of Chile uses brief teacher- and parent-completed measures [Teacher Observation of Classroom Adaptation-Revised (TOCA-RR) and Pediatric Symptom Checklist (PSC-Cl)] to screen for mental health problems in about one-fifth of the country's elementary schools. In fourth grade, students take the national achievement tests (SIMCE) of language, mathematics and science. This study examined whether mental health problems identified through either or both screens predicted achievement test scores after controlling for student and family risk factors. A total of 17,252 students had complete first grade teacher forms and these were matched with fourth grade SIMCE data for 11,185 students, 7,903 of whom also had complete parent form data from the first grade. Students at risk on either the TOCA-RR or the PSC-Cl or both performed significantly worse on all SIMCE subtests. Even after controlling for covariates and adjusting for missing data, students with mental health problems on one screen in first grade had fourth grade achievement scores that were 14-18 points (~1/3 SD) lower than students screened as not at risk. Students at risk on both screens had scores that were on average 33 points lower than students at risk on either screen. Mental health problems in first grade were one of the strongest predictors of lower achievement test scores 3 years later, supporting the premise that for children mental health matters in the real world.

Association of brain-type natriuretic protein and cardiac troponin I with incipient cardiovascular disease in chimpanzees (Pan troglodytes)

Cardiovascular disease (CVD) is the primary cause of morbidity and mortality in chimpanzees, but its etiology and clinical presentations remain poorly understood. The disease in chimpanzees differs sufficiently from that in humans that simple extrapolation from human findings are inadequate to guide clinical diagnoses. Nevertheless, the burden of disease posed by CVD made it important to attempt to identify specific chimpanzees at risk of developing CVD to allow clinical intervention prior to clinical presentation of advanced disease. We screened 4 CVD biomarkers used in human and veterinary medicine to identify markers with prognostic value in chimpanzees. Biomarkers included complete lipid panel, C-reactive protein, brain-type natriuretic protein, and cardiac troponin I. Serum levels of brain-type natriuretic protein differed between chimpanzees with CVD and heart-healthy controls. Cardiac troponin I gave mixed results. C-reactive protein and lipid panel values were not informative for cardiovascular disease, although total cholesterol, LDL-cholesterol, and triglycerides increased significantly with decade of life. Values of braintype natriuretic protein exceeding 163 mg/mL had a specificity of 90.5% for CVD, whereas levels of cardiac troponin I above the threshold of detection (0.20 ng/mL) appeared to be clinically relevant. More extensive clinical studies are recommended to validate these specific values. We conclude that brain-type natriuretic protein and possibly cardiac troponin I are useful diagnostic biomarkers for incipient CVD processes in chimpanzees.