Dealing with missing covariates in epidemiologic studies: a comparison between multiple imputation and a full Bayesian approach

Assessing treatment effect heterogeneity in the presence of missing effect modifier data in cluster-randomized trials

Understanding whether and how treatment effects vary across subgroups is crucial to inform clinical practice and recommendations. Accordingly, the assessment of heterogeneous treatment effects based on pre-specified potential effect modifiers has become a common goal in modern randomized trials. However, when one or more potential effect modifiers are missing, complete-case analysis may lead to bias and under-coverage. While statistical methods for handling missing data have been proposed and compared for individually randomized trials with missing effect modifier data, few guidelines exist for the cluster-randomized setting, where intracluster correlations in the effect modifiers, outcomes, or even missingness mechanisms may introduce further threats to accurate assessment of heterogeneous treatment effect. In this article, the performance of several missing data methods are compared through a simulation study of cluster-randomized trials with continuous outcome and missing binary effect modifier data, and further illustrated using real data from the Work, Family, and Health Study. Our results suggest that multilevel multiple imputation and Bayesian multilevel multiple imputation have better performance than other available methods, and that Bayesian multilevel multiple imputation has lower bias and closer to nominal coverage than standard multilevel multiple imputation when there are model specification or compatibility issues.

Comparing DIC and WAIC for multilevel models with missing data

In Bayesian statistics, the most widely used criteria of Bayesian model assessment and comparison are Deviance Information Criterion (DIC) and Watanabe-Akaike Information Criterion (WAIC). We use a multilevel mediation model as an illustrative example to compare different types of DIC and WAIC. More specifically, we aim to compare the performance of conditional and marginal DICs and WAICs, and investigate their performance with missing data. We focus on two versions of DIC ( D I C 1 and D I C 2 ) and one version of WAIC. In addition, we explore whether it is necessary to include the nuisance models of incomplete exogenous variables in likelihood. Based on the simulation results, whether D I C 2 is better than D I C 1 and WAIC and whether we should include the nuisance models of exogenous variables in likelihood functions depend on whether we use marginal or conditional likelihoods. Overall, we find that the marginal likelihood based- D I C 2 that excludes the likelihood of covariate models generally had the highest true model selection rates.

Environmental predictors of Escherichia coli concentration at marine beaches in Vancouver, Canada: a Bayesian mixed-effects modelling analysis

Understanding historical environmental determinants associated with the risk of elevated marine water contamination could enhance monitoring marine beaches in a Canadian setting, which can also inform predictive marine water quality models and ongoing climate change preparedness efforts. This study aimed to assess the combination of environmental factors that best predicts Escherichia coli (E. coli) concentration at public beaches in Metro Vancouver, British Columbia, by combining the region's microbial water quality data and publicly available environmental data from 2013 to 2021. We developed a Bayesian log-normal mixed-effects regression model to evaluate predictors of geometric E. coli concentrations at 15 beaches in the Metro Vancouver Region. We identified that higher levels of geometric mean E. coli levels were predicted by higher previous sample day E. coli concentrations, higher rainfall in the preceding 48 h, and higher 24-h average air temperature at the median or higher levels of the 24-h mean ultraviolet (UV) index. In contrast, higher levels of mean salinity were predicted to result in lower levels of E. coli. Finally, we determined that the average effects of the predictors varied highly by beach. Our findings could form the basis for building real-time predictive marine water quality models to enable more timely beach management decision-making.

Appropriately estimating the standardized average treatment effect with missing data: A simulation and primer

Reporting standardized effects in randomized treatment studies aids interpretation and facilitates future meta-analyses and policy considerations. However, when outcome data are missing, achieving an unbiased, accurate estimate of the standardized average treatment effect, sATE, can pose challenges even for those with general knowledge of missing data handling, given that the sATE is a ratio of a mean difference to a (within-group) standard deviation. Under both homogeneity and heterogeneity of variance, a Monte Carlo simulation study was conducted to compare missing data handling strategies in terms of bias and accuracy in the sATE, under specific missingness patterns plausible for randomized pretest posttest studies. Within two broad missing data handling approaches, maximum likelihood and multiple imputation, modeling choices were thoroughly investigated including the analysis model, variance estimator, imputation algorithm, and method of pooling results across imputed datasets. Results demonstrated that although the sATE can be estimated with little bias using either maximum likelihood or multiple imputation, particular attention should be paid to the model and variance estimator, especially at smaller sample sizes (i.e., N = 50). Differences in accuracy were driven by differences in bias. To improve estimation of the sATE in practice, recommendations and a software demonstration are provided. Moreover, a pedagogical explanation of the causes of bias, described separately for the numerator and denominator of the sATE is provided, demonstrating visually how and why bias occurs with certain methods.

A joint Bayesian framework for missing data and measurement error using integrated nested Laplace approximations

Measurement error (ME) and missing values in covariates are often unavoidable in disciplines that deal with data, and both problems have separately received considerable attention during the past decades. However, while most researchers are familiar with methods for treating missing data, accounting for ME in covariates of regression models is less common. In addition, ME and missing data are typically treated as two separate problems, despite practical and theoretical similarities. Here, we exploit the fact that missing data in a continuous covariate is an extreme case of classical ME, allowing us to use existing methodology that accounts for ME via a Bayesian framework that employs integrated nested Laplace approximations (INLA) and thus to simultaneously account for both ME and missing data in the same covariate. As a useful by-product, we present an approach to handle missing data in INLA since this corresponds to the special case when no ME is present. In addition, we show how to account for Berkson ME in the same framework. In its broadest generality, the proposed joint Bayesian framework can thus account for Berkson ME, classical ME, and missing data, or any combination of these in the same or different continuous covariates of the family of regression models that are feasible with INLA. The approach is exemplified using both simulated and real data. We provide extensive and fully reproducible Supporting Information with thoroughly documented examples using R-INLA and inlabru.

A Bayesian Approach Towards Missing Covariate Data in Multilevel Latent Regression Models

The measurement of latent traits and investigation of relations between these and a potentially large set of explaining variables is typical in psychology, economics, and the social sciences. Corresponding analysis often relies on surveyed data from large-scale studies involving hierarchical structures and missing values in the set of considered covariates. This paper proposes a Bayesian estimation approach based on the device of data augmentation that addresses the handling of missing values in multilevel latent regression models. Population heterogeneity is modeled via multiple groups enriched with random intercepts. Bayesian estimation is implemented in terms of a Markov chain Monte Carlo sampling approach. To handle missing values, the sampling scheme is augmented to incorporate sampling from the full conditional distributions of missing values. We suggest to model the full conditional distributions of missing values in terms of non-parametric classification and regression trees. This offers the possibility to consider information from latent quantities functioning as sufficient statistics. A simulation study reveals that this Bayesian approach provides valid inference and outperforms complete cases analysis and multiple imputation in terms of statistical efficiency and computation time involved. An empirical illustration using data on mathematical competencies demonstrates the usefulness of the suggested approach.

An Investigation of Factored Regression Missing Data Methods for Multilevel Models with Cross-Level Interactions

A growing body of literature has focused on missing data methods that factorize the joint distribution into a part representing the analysis model of interest and a part representing the distributions of the incomplete predictors. Relatively little is known about the utility of this method for multilevel models with interactive effects. This study presents a series of Monte Carlo computer simulations that investigates Bayesian and multiple imputation strategies based on factored regressions. When the model's distributional assumptions are satisfied, these methods generally produce nearly unbiased estimates and good coverage, with few exceptions. Severe misspecifications that arise from substantially non-normal distributions can introduce biased estimates and poor coverage. Follow-up simulations suggest that a Yeo-Johnson transformation can mitigate these biases. A real data example illustrates the methodology, and the paper suggests several avenues for future research.

Modeling geostatistical incomplete spatially correlated survival data with applications to COVID-19 mortality in Ghana

Survival models which incorporate frailties are common in time-to-event data collected over distinct spatial regions. While incomplete data are unavoidable and a common complication in statistical analysis of spatial survival research, most researchers still ignore the missing data problem. In this paper, we propose a geostatistical modeling approach for incomplete spatially correlated survival data. We achieve this by exploring missingness in outcome, covariates, and spatial locations. In the process, we analyze incomplete spatially-referenced survival data using a Weibull model for the baseline hazard function and correlated log-Gaussian frailties to model spatial correlation. We illustrate the proposed method with simulated data and an application to geo-referenced COVID-19 data from Ghana. There are several disagreements between parameter estimates and credible intervals widths obtained using our proposed approach and complete case analysis. Based on these findings, we argue that our approach provides more reliable parameter estimates and has higher predictive accuracy.

A monotone single index model for missing-at-random longitudinal proportion data

Beta distributions are commonly used to model proportion valued response variables, often encountered in longitudinal studies. In this article, we develop semi-parametric Beta regression models for proportion valued responses, where the aggregate covariate effect is summarized and flexibly modeled, using a interpretable monotone time-varying single index transform of a linear combination of the potential covariates. We utilize the potential of single index models, which are effective dimension reduction tools and accommodate link function misspecification in generalized linear mixed models. Our Bayesian methodology incorporates the missing-at-random feature of the proportion response and utilize Hamiltonian Monte Carlo sampling to conduct inference. We explore finite-sample frequentist properties of our estimates and assess the robustness via detailed simulation studies. Finally, we illustrate our methodology via application to a motivating longitudinal dataset on obesity research recording proportion body fat.

Noninterventional studies in the COVID-19 era: methodological considerations for study design and analysis

The global COVID-19 pandemic has generated enormous morbidity and mortality, as well as large health system disruptions including changes in use of prescription medications, outpatient encounters, emergency department admissions, and hospitalizations. These pandemic-related disruptions are reflected in real-world data derived from electronic medical records, administrative claims, disease or medication registries, and mobile devices. We discuss how pandemic-related disruptions in healthcare utilization may impact the conduct of noninterventional studies designed to characterize the utilization and estimate the effects of medical interventions on health-related outcomes. Using hypothetical studies, we highlight consequences that the pandemic may have on study design elements including participant selection and ascertainment of exposures, outcomes, and covariates. We discuss the implications of these pandemic-related disruptions on possible threats to external validity (participant selection) and internal validity (for example, confounding, selection bias, missing data bias). These concerns may be amplified in populations disproportionately impacted by COVID-19, such as racial/ethnic minorities, rural residents, or people experiencing poverty. We propose a general framework for researchers to carefully consider during the design and analysis of noninterventional studies that use real-world data from the COVID-19 era.

Compatibility in imputation specification

Missing data such as data missing at random (MAR) are unavoidable in real data and have the potential to undermine the validity of research results. Multiple imputation is one of the most widely used MAR-based methods in education and behavioral science applications. Arbitrarily specifying imputation models can lead to incompatibility and cause biased estimation. Building on the recent developments of model-based imputation and Arnold's compatibility work, this paper systematically summarizes when the traditional fully conditional specification (FCS) is applicable and how to specify a model-based imputation model if needed. We summarize two Compatibility Requirements to help researchers check compatibility more easily and a decision tree to check whether the traditional FCS is applicable in a given scenario. Additionally, we present a clear overview of two types of model-based imputation: the sequential and separate specifications. We illustrate how to specify model-based imputation with examples. Additionally, we provide example code of a free software program, Blimp, for implementing model-based imputation.

Evaluation of approaches for accommodating interactions and non-linear terms in multiple imputation of incomplete three-level data

Three-level data structures arising from repeated measures on individuals clustered within larger units are common in health research studies. Missing data are prominent in such studies and are often handled via multiple imputation (MI). Although several MI approaches can be used to account for the three-level structure, including adaptations to single- and two-level approaches, when the substantive analysis model includes interactions or quadratic effects, these too need to be accommodated in the imputation model. In such analyses, substantive model compatible (SMC) MI has shown great promise in the context of single-level data. Although there have been recent developments in multilevel SMC MI, to date only one approach that explicitly handles incomplete three-level data is available. Alternatively, researchers can use pragmatic adaptations to single- and two-level MI approaches, or two-level SMC-MI approaches. We describe the available approaches and evaluate them via simulations in the context of three three-level random effects analysis models involving an interaction between the incomplete time-varying exposure and time, an interaction between the time-varying exposure and an incomplete time-fixed confounder, or a quadratic effect of the exposure. Results showed that all approaches considered performed well in terms of bias and precision when the target analysis involved an interaction with time, but the three-level SMC MI approach performed best when the target analysis involved an interaction between the time-varying exposure and an incomplete time-fixed confounder, or a quadratic effect of the exposure. We illustrate the methods using data from the Childhood to Adolescence Transition Study.

Substantive model compatible multilevel multiple imputation: A joint modeling approach

BACKGROUND

Substantive model compatible multiple imputation (SMC-MI) is a relatively novel imputation method that is particularly useful when the analyst's model includes interactions, non-linearities, and/or partially observed random slope variables.

METHODS

Here we thoroughly investigate a SMC-MI strategy based on joint modeling of the covariates of the analysis model. We provide code to apply the proposed strategy and we perform an extensive simulation work to test it in various circumstances. We explore the impact on the results of various factors, including whether the missing data are at the individual or cluster level, whether there are non-linearities and whether the imputation model is correctly specified. Finally, we apply the imputation methods to the motivating example data.

RESULTS

SMC-JM appears to be superior to standard JM imputation, particularly in presence of large variation in random slopes, non-linearities, and interactions. Results seem to be robust to slight mis-specification of the imputation model for the covariates. When imputing level 2 data, enough clusters have to be observed in order to obtain unbiased estimates of the level 2 parameters.

CONCLUSIONS

SMC-JM is preferable to standard JM imputation in presence of complexities in the analysis model of interest, such as non-linearities or random slopes.

Assessing Alternative Imputation Strategies for Infrequently Missing Items on Multi-item Scales

Health-science researchers often measure psychological constructs using multi-item scales and encounter missing items on some participants. Multiple imputation (MI) has emerged as an alternative to ad-hoc methods (e.g., mean substitution) for handling incomplete data on multi-item scales, appealingly reflecting available information while accounting for uncertainty due to missing values in a unified inferential framework. However, MI can be implemented in a variety of ways. When the number of variables to impute gets large, some strategies yield unstable estimates of quantities of interest while others are not technically feasible to implement. These considerations raise pragmatic questions about the extent to which ad-hoc procedures would yield statistical properties that are competitive with theoretically motivated methods. Drawing on an HIV study where depression and anxiety symptoms are measured with multi-item scales, this empirical investigation contrasts ad-hoc methods for handling missing items with various MI implementations that differ as to whether imputation is at the item-level or scale-level and how auxiliary variables are incorporated. While the findings are consistent with previous reports favoring item-level imputation when feasible to implement, we found only subtle differences in statistical properties across procedures, suggesting that weaknesses of ad-hoc procedures may be muted when missing data percentages are modest.

Response Surface Analysis with Missing Data

Response Surface Analysis (RSA) is gaining popularity in psychological research as a tool for investigating congruence hypotheses (e.g., consequences of self-other agreement, person-job fit, dyadic similarity). RSA involves the estimation of a nonlinear polynomial regression model and the interpretation of the resulting response surface. However, little is known about how best to conduct RSA when the underlying data are incomplete. In this article, we compare different methods for handling missing data in RSA. This includes different strategies for multiple imputation (MI) and maximum-likelihood (ML) estimation. Specifically, we consider the "just another variable" (JAV) approach to MI and ML, an approach that is in regular use in applications of RSA, and the more novel "substantive-model-compatible" (SMC) approach. In a simulation study, we evaluate the impact of these methods on focal outcomes of RSA, including the accuracy of parameter estimates, the shape of the response surface, and the testing of congruence hypotheses. Our findings suggest that the JAV approach can sometimes distort parameter estimates and conclusions about the shape of the response surface, whereas the SMC approach performs well overall. We illustrate applications of the methods in a worked example with real data and provide recommendations for their application in practice.

MCMCINLA Estimation of Missing Data and Its Application to Public Health Development in China in the Post-Epidemic Era

Medical data are often missing during epidemiological surveys and clinical trials. In this paper, we propose the MCMCINLA estimation method to account for missing data. We introduce a new latent class into the spatial lag model (SLM) and use a conditional autoregressive specification (CAR) spatial model-based approach to impute missing values, making the model fit into the integrated nested Laplace approximation (INLA) framework. Combining the advantages of both the Markov chain Monte Carlo (MCMC) and INLA frameworks, the MCMCINLA algorithm is used to implement imputation of the missing data and fit the model to derive estimates of the parameters from the posterior margins. Finally, the economic data and the hemorrhagic fever with renal syndrome (HFRS) disease data of mainland China from 2016–2018 are used as examples to explore the development of public health in China in the post-epidemic era. The results show that compared with expectation maximization (EM) and full information maximum likelihood estimation (FIML), the predicted values of the missing data obtained using our method are closer to the true values, and the spatial distribution of HFRS in China can be inferred from the imputation results with a southern-heavy and northern-light distribution. It can provide some references for the development of public health in China in the post-epidemic era.

Estimation of treatment effects in short-term depression studies. An evaluation based on the ICH E9(R1) estimands framework

Estimands aim to incorporate intercurrent events in design, data collection and estimation of treatment effects in clinical trials. Our aim was to understand what estimands may correspond to efficacy analyses commonly employed in clinical trials conducted before publication of ICH E9(R1). We re‐analysed six clinical trials evaluating a new anti‐depression treatment. We selected the following analysis methods—ANCOVA on complete cases, following last observation carried forward (LOCF) imputation and following multiple imputation; mixed‐models for repeated measurements without imputation (MMRM), MMRM following LOCF imputation and following jump‐to‐reference imputation; and pattern‐mixture mixed models. We included a principal stratum analysis based on the predicted subset of the study population who would not discontinue due to adverse events or lack of efficacy. We translated each analysis into the implicitly targeted estimand, and formulated corresponding clinical questions. We could map six estimands to analysis methods. The same analysis method could be mapped to more than one estimand. The major difference between estimands was the strategy for intercurrent events, with other attributes mostly the same across mapped estimands. The quantitative differences in MADRS10 population‐level summaries between the estimands were 4–8 points. Not all six estimands had a clinically meaningful interpretation. Only a few analyses would target the same estimand, hence only few could be used as sensitivity analyses. The fact that an analysis could estimate different estimands emphasises the importance of prospectively defining the estimands targeting the primary objective of a trial. The fact that an estimand can be targeted by different analyses emphasises the importance of prespecifying precisely the estimator for the targeted estimand.

Multiple imputation for cause-specific Cox models: Assessing methods for estimation and prediction

In studies analyzing competing time-to-event outcomes, interest often lies in both estimating the effects of baseline covariates on the cause-specific hazards and predicting cumulative incidence functions. When missing values occur in these baseline covariates, they may be discarded as part of a complete-case analysis or multiply imputed. In the latter case, the imputations may be performed either compatibly with a substantive model pre-specified as a cause-specific Cox model [substantive model compatible fully conditional specification (SMC-FCS)], or approximately so [multivariate imputation by chained equations (MICE)]. In a large simulation study, we assessed the performance of these three different methods in terms of estimating cause-specific regression coefficients and predicting cumulative incidence functions. Concerning regression coefficients, results provide further support for use of SMC-FCS over MICE, particularly when covariate effects are large and the baseline hazards of the competing events are substantially different. Complete-case analysis also shows adequate performance in settings where missingness is not outcome dependent. With regard to cumulative incidence prediction, SMC-FCS and MICE are performed more similarly, as also evidenced in the illustrative analysis of competing outcomes following a hematopoietic stem cell transplantation. The findings are discussed alongside recommendations for practising statisticians.

Indications, Postoperative Management, and Long-term Prognosis of Crohn's Disease After Ileocecal Resection: A Multicenter Study Comparing the East and West

BACKGROUND

The Crohn's disease (CD) phenotype differs between Asian and Western countries and may affect disease management, including decisions on surgery. This study aimed to compare the indications, postoperative management, and long-term prognosis after ileocecal resection (ICR) in Hong Kong (HK) and the Netherlands (NL).

METHODS

CD patients with primary ICR between 2000 and 2019 were included. The endpoints were endoscopic (Rutgeerts score ≥i2b and/or radiologic recurrence), clinical (start or switch of inflammatory bowel disease medication), and surgical recurrences. Cumulative incidences of recurrence were estimated with a Bayesian multivariable proportional hazards model.

RESULTS

Eighty HK and 822 NL patients were included. The most common indication for ICR was penetrating disease (HK: 32.5%, NL: 22.5%) in HK vs stricturing disease (HK: 32.5%, NL: 48.8%) in the NL (P < .001). Postoperative prophylaxis was prescribed to 65 (81.3%) HK patients (28 [35.0%] aminosalicylates [5-aminosalicylic acid]; 30 [37.5%] immunomodulators; 0 biologicals) vs 388 (47.1%) NL patients (67 [8.2%] 5-aminosalicylic acid; 187 [22.8%] immunomodulators; 69 [8.4%] biologicals; 50 [6.1%] combination therapy) (P < .001). Endoscopic or radiologic evaluation within 18 months was performed in 36.3% HK vs 64.1% NL (P < .001) patients. No differences between both populations were observed for endoscopic (hazard ratio [HR], 0.53; 95% confidence interval [CI], 0.24-1.21), clinical (HR, 0.91; 95% CI, 0.62-1.32), or surgical (HR, 0.61; 95% CI, 0.31-1.13) recurrence risks.

CONCLUSION

The main indication for ICR in CD patients is penetrating disease in HK patients and stricturing disease in NL patients. Although considerable pre- and postoperative management differences were observed between the two geographical areas, the long-term prognosis after ICR is similar.

Effect of a Novel Intervention Targeting Appetitive Traits on Body Mass Index Among Adults With Overweight or Obesity: A Randomized Clinical Trial

IMPORTANCE

Behavioral weight loss (BWL) programs result in weight loss for some, but most individuals regain the weight. The behavioral susceptibility theory proposes that genetically determined appetitive traits, such as food responsiveness (FR) and satiety responsiveness (SR), interact with the environment and lead to overeating and weight gain; the regulation of cues (ROC) intervention was developed specifically to target FR and SR.

OBJECTIVE

To evaluate the efficacy of ROC, ROC combined with BWL (ROC+), BWL, and an active comparator (AC) over 12 months of treatment and 12 months of follow-up.

DESIGN, SETTING, AND PARTICIPANTS

This randomized clinical trial was conducted from December 2015 to December 2019 in a university clinic. A total of 1488 volunteers from the community inquired about the study; 1217 were excluded or declined to participate. Eligibility criteria included body mass index (BMI) of 25 to 45, age 18 to 65 years, and lack of comorbidities or other exclusionary criteria that would interfere with participation. Data were analyzed from September 2021 to January 2022.

INTERVENTIONS

ROC uniquely targeted FR and SR. BWL included energy restriction, increasing physical activity, and behavior therapy techniques. ROC+ combined ROC with BWL. AC included mindfulness, social support, and nutrition education.

MAIN OUTCOMES AND MEASURES

Change in body weight as measured by BMI.

RESULTS

A total of 271 adults (mean [SD] age, 46.97 [11.80] years; 81.6% female [221 participants]; mean [SD] BMI, 34.59 [5.28]; 61.9% White [167 participants]) were assessed at baseline, midtreatment, posttreatment, and 6-month and 12-month follow-up. Sixty-six participants were randomized to AC, 69 to ROC, 67 to ROC+, and 69 to BWL. Results showed that ROC, ROC+, and BWL interventions resulted in significantly lower BMI at the end of treatment (BMI ROC, -1.18; 95% CI, -2.10 to -0.35; BMI ROC+, -1.56; 95% CI, -2.43 to -0.67; BMI BWL, -1.58; 95% CI, -2.45 to -0.71). Compared with BWL, BMI at the end of treatment was not significantly different from ROC or ROC+ (BMI ROC, 0.40; 95% CI, -0.55 to 1.36; BMI ROC+, 0.03; 95% CI, -0.88 to 0.93); however, the BMI of the AC group was substantially higher (BMI AC, 1.58; 95% CI, 0.72 to 2.45). BMI reductions at 24 months after randomization were similar for ROC, ROC+, and BWL. Importantly, FR was a moderator of treatment effects with more weight loss for participants who scored higher in FR in the ROC and ROC+ groups.

CONCLUSIONS AND RELEVANCE

These findings suggest that ROC and ROC+ provide alternative weight loss approaches for adults. These models could be particularly effective for individuals who struggle with FR and could be used as a precision approach for weight loss.

TRIAL REGISTRATION

ClinicalTrials.gov Identifier: NCT02516839.

Psychological stress self-help interventions for healthcare workers in the context of COVID-19 in China: A randomized controlled trial protocol

BACKGROUND

Public health emergencies may lead to severe psychological stress, especially for healthcare workers, including frontline healthcare workers and public health workers. However, few stress management interventions have been implemented for healthcare workers even though they require more comprehensive interventions than the general public. Self-Help Plus (SH+) is a novel psychological self-help intervention developed by the World Health Organization. It is accessible, scalable, and cost-effective and has the potential to be quickly applied to help people cope with stress and adversity. The major objective of this study is to evaluate the effectiveness of SH+ interventions on the alleviation of stress levels and mental health problems among healthcare workers.

METHODS

A randomized controlled trial of SH+ will be conducted to investigate the stress level and mental health status of Chinese healthcare workers and control subjects in Guangzhou. Assessments will be performed before (baseline), at the end of (1 month), and 2 months after (3 months) the intervention. After completing the baseline screening questionnaire, eligible participants will be randomly assigned to one of the two groups in a 1:1 ratio by block randomization. During the 1-month intervention period, the intervention group will receive the SH+ intervention and the control group will receive information about mental health promotion. The intervention will be delivered by the research assistant via social media platforms. The primary outcome is the level of stress, which will be measured by a 10-item Perceived Stress Scale. Secondary outcomes including mental health symptoms will also be collected.

DISCUSSION

Given the potential for multiple COVID-19 waves and other infectious disease pandemics in the future, we expect that SH+ will be an effective stress management intervention for healthcare workers. The findings from this study will facilitate the application of SH+, and the trial is expected to be extended to a larger population in the future.

Early protein energy malnutrition impacts life-long developmental trajectories of the sources of EEG rhythmic activity

Protein Energy Malnutrition (PEM) has lifelong consequences on brain development and cognitive function. We studied the lifelong developmental trajectories of resting-state EEG source activity in 66 individuals with histories of Protein Energy Malnutrition (PEM) limited to the first year of life and in 83 matched classmate controls (CON) who are all participants of the 49 years longitudinal Barbados Nutrition Study (BNS). qEEGt source z-spectra measured deviation from normative values of EEG rhythmic activity sources at 5-11 years of age and 40 years later at 45-51 years of age. The PEM group showed qEEGt abnormalities in childhood, including a developmental delay in alpha rhythm maturation and an insufficient decrease in beta activity. These profiles may be correlated with accelerated cognitive decline.

A Bayesian Latent Variable Selection Model for Nonignorable Missingness

Missing data are exceedingly common across a variety of disciplines, such as educational, social, and behavioral science areas. Missing not at random (MNAR) mechanism where missingness is related to unobserved data is widespread in real data and has detrimental consequence. However, the existing MNAR-based methods have potential problems such as leaving the data incomplete and failing to accommodate incomplete covariates with interactions, non-linear terms, and random slopes. We propose a Bayesian latent variable imputation approach to impute missing data due to MNAR (and other missingness mechanisms) and estimate the model of substantive interest simultaneously. In addition, even when the incomplete covariates involves interactions, non-linear terms, and random slopes, the proposed method can handle missingness appropriately. Computer simulation results suggested that the proposed Bayesian latent variable selection model (BLVSM) was quite effective when the outcome and/or covariates were MNAR. Except when the sample size was small, estimates from the proposed BLVSM tracked closely with those from the complete data analysis. With a small sample size, when the outcome was less predictable from the covariates, the missingness proportions of the covariates and the outcome were larger, and the missingness selection processes of the covariates and the outcome were more MNAR and MAR, the performance of BLVSM was less satisfactory. When the sample size was large, BLVSM always performed well. In contrast, the method with an MAR assumption provided biased estimates and undercoverage confidence intervals when the missingness was MNAR. The robustness and the implementation of BLVSM in real data were also illustrated. The proposed method is available in the Blimp software application, and the paper includes a data analysis example illustrating its use.

Imputation of Below Detection Limit Missing Data in Chemical Mixture Analysis with Bayesian Group Index Regression

There is growing scientific interest in identifying the multitude of chemical exposures related to human diseases through mixture analysis. In this paper, we address the issue of below detection limit (BDL) missing data in mixture analysis using Bayesian group index regression by treating both regression effects and missing BDL observations as parameters in a model estimated through a Markov chain Monte Carlo algorithm that we refer to as pseudo-Gibbs imputation. We compare this with other Bayesian imputation methods found in the literature (Multiple Imputation by Chained Equations and Sequential Full Bayes imputation) as well as with a non-Bayesian single-imputation method. To evaluate our proposed method, we conduct simulation studies with varying percentages of BDL missingness and strengths of association. We apply our method to the California Childhood Leukemia Study (CCLS) to estimate concentrations of chemicals in house dust in a mixture analysis of potential environmental risk factors for childhood leukemia. Our results indicate that pseudo-Gibbs imputation has superior power for exposure effects and sensitivity for identifying individual chemicals at high percentages of BDL missing data. In the CCLS, we found a significant positive association between concentrations of polycyclic aromatic hydrocarbons (PAHs) in homes and childhood leukemia as well as significant positive associations for polychlorinated biphenyls (PCBs) and herbicides among children from the highest quartile of household income. In conclusion, pseudo-Gibbs imputation addresses a commonly encountered problem in environmental epidemiology, providing practitioners the ability to jointly estimate the effects of multiple chemical exposures with high levels of BDL missingness.

Peripheral Immune Cell Numbers and C-Reactive Protein in Parkinson's Disease: Results from a Population-Based Study

BACKGROUND

The immune system is known to be involved in Parkinson's disease (PD) pathogenesis, but the temporal relationship between peripheral immune responses and PD remains unknown.

OBJECTIVE

We determined the association between peripheral immune cell numbers, C-reactive protein (CRP), and prevalent as well as incident PD.

METHODS

This study was embedded in the population-based setting of the Rotterdam Study. We repeatedly measured peripheral immune cell numbers (differential leukocyte count and platelet count, granulocyte-to-lymphocyte ratio [GLR], platelet-to-lymphocyte ratio [PLR], and adapted systemic immune-inflammation index [adapted SII]) and CRP between 1990 and 2016. Participants were continuously followed-up for PD until 2018. We estimated the association of the markers with prevalent and incident PD using logistic regression models and joint models, respectively. Models were adjusted for age, sex, smoking, body mass index, and medication use. Odds ratios (OR) and hazard ratios (HR) are shown per doubling of the marker.

RESULTS

A total of 12,642 participants were included in this study. The mean age (standard deviation) was 65.1 (9.8) years and 57.5%were women. Participants with a higher lymphocyte count were less likely to have prevalent PD (adjusted OR: 0.34, 95%CI 0.17-0.68). Participants with a higher GLR, PLR, and adapted SII were more likely to have prevalent PD, but these effects were explained by the lymphocyte count. The peripheral immune cell numbers and CRP were not significantly associated with the risk of incident PD.

CONCLUSION

We found participants with a higher lymphocyte count to be less likely to have prevalent PD, but we did not find an association between peripheral immune cell numbers nor CRP and the risk of incident PD.

Qiviut cortisol is associated with metrics of health and other intrinsic and extrinsic factors in wild muskoxen (Ovibos moschatus)

Glucocorticoid (GC) levels are increasingly and widely used as biomarkers of hypothalamic-pituitary-adrenal (HPA) axis activity to study the effects of environmental changes and other perturbations on wildlife individuals and populations. However, identifying the intrinsic and extrinsic factors that influence GC levels is a key step in endocrinology studies to ensure accurate interpretation of GC responses. In muskoxen, qiviut (fine woolly undercoat hair) cortisol concentration is an integrative biomarker of HPA axis activity over the course of the hair's growth. We gathered data from 219 wild muskoxen harvested in the Canadian Arctic between October 2015 and May 2019. We examined the relationship between qiviut cortisol and various intrinsic (sex, age, body condition and incisor breakage) and extrinsic biotic factors (lungworm and gastrointestinal parasite infections and exposure to bacteria), as well as broader non-specific landscape and temporal features (geographical location, season and year). A Bayesian approach, which allows for the joint estimation of missing values in the data and model parameters estimates, was applied for the statistical analyses. The main findings include the following: (i) higher qiviut cortisol levels in males than in females; (ii) inter-annual variations; (iii) higher qiviut cortisol levels in a declining population compared to a stable population; (iv) a negative association between qiviut cortisol and marrow fat percentage; (v) a relationship between qiviut cortisol and the infection intensity of the lungworm Umingmakstrongylus pallikuukensis, which varied depending on the geographical location; and (vi) no association between qiviut cortisol and other pathogen exposure/infection intensity metrics. This study confirmed and further identified important sources of variability in qiviut cortisol levels, while providing important insights on the relationship between GC levels and pathogen exposure/infection intensity. Results support the use of qiviut cortisol as a tool to monitor temporal changes in HPA axis activity at a population level and to inform management and conservation actions.

An Introduction to Factored Regression Models with Blimp

In this paper, we provide an introduction to the factored regression framework. This modeling framework applies the rules of probability to break up or “factor” a complex joint distribution into a product of conditional regression models. Using this framework, we can easily specify the complex multivariate models that missing data modeling requires. The article provides a brief conceptual overview of factored regression and describes the functional notation used to conceptualize the models. Furthermore, we present a conceptual overview of how the models are estimated and imputations are obtained. Finally, we discuss how users can use the free software package, Blimp, to estimate the models in the context of a mediation example.

A Meta-Analytical Assessment of the Aggregation Parameter of the Binary Power Law for Characterizing Spatial Heterogeneity of Plant Disease Incidence

The binary power law (BPL) is often used to characterize spatial heterogeneity of disease incidence. A hierarchical mixed model, coupled with multiple imputation to randomly generate any missing standard errors, was used to conduct a meta-analysis of >200 published values of the estimated aggregation (b) parameter of the BPL. Approximately 50% of estimated b values ranged from 1.1 to 1.3. Moderator variable analysis showed that the number of individuals per sampling unit (n) had a strong positive effect on b, with a linear relation between estimated b and ln(n). Estimated expected value of b for the population of published regressions at a reference n of 15 was 1.22. The increase in the variance due to the imputations was only 0.03, and the efficiency exceeded 0.98. Results were confirmed with an alternative mixed model that considered a range of possible within-trial correlations of the estimated b values and with a random-coefficient mixed model fitted to the subset of the data. Cropping system, dispersal mode, and pathogen type all had significant effects on b, with annuals having larger expected value than woody perennials, soilborne and rain-splashed dispersed pathogens having the largest expected values for dispersal mode, and bacteria and oomycetes having the largest expected values for pathogen type. However, there was considerable variation within each of the levels of the moderators, and the differences of expected values from smallest to largest were small, ≤0.16. Results are discussed in relation to previously published findings from stochastic simulations.

wEight chanGes, caRdio-mEtabolic risks and morTality in patients with hyperthyroidism (EGRET): a protocol for a CPRD-HES linked cohort study

INTRODUCTION

Hyperthyroidism is a common condition affecting up to 3% of the UK population. Treatment improves symptoms and reduces the risk of atrial fibrillation and stroke that contribute to increased mortality. The most common symptom is weight loss, which is reversed during treatment. However, the weight regain may be excessive, contributing to increased risk of obesity. Current treatment options include antithyroid drugs, radioiodine and thyroidectomy. Whether there are differences in either weight change or the long-term cardiometabolic risk between the three treatments is unclear.

METHODS AND ANALYSIS

The study will establish the natural history of weight change in hyperthyroidism, investigate the risk of obesity and risks of cardiometabolic conditions and death relative to the treatment. The data on patients diagnosed with hyperthyroidism between 1 January 1996 and 31 December 2015 will come from Clinical Practice Research Datalink linked to Hospital Episode Statistics and Office of National Statistics Death Registry. The weight changes will be modelled using a flexible joint modelling, accounting for mortality. Obesity prevalence in the general population will be sourced from Health Survey for England and compared with the post-treatment prevalence of obesity in patients with hyperthyroidism. The incidence and time-to-event of major adverse cardiovascular events, other cardiometabolic outcomes and mortality will be compared between the treatments using the inverse propensity weighting model. Incidence rate ratios of outcomes will be modelled with Poisson regression. Time to event will be analysed using Cox proportional hazards model. A competing risks approach will be adopted to estimate comparative incidences to allow for the impact of mortality.

ETHICS AND DISSEMINATION

The study will bring new knowledge on the risk of developing obesity, cardiometabolic morbidity and mortality following treatment for hyperthyroidism to inform clinical practice and public health policies. The results will be disseminated via open-access peer-reviewed publications and directly to the patients and public groups (Independent Scientific Advisory Committee protocol approval #20_000185).

From first to second wave: follow-up of the prospective COVID-19 cohort (KoCo19) in Munich (Germany)

BACKGROUND

In the 2nd year of the COVID-19 pandemic, knowledge about the dynamics of the infection in the general population is still limited. Such information is essential for health planners, as many of those infected show no or only mild symptoms and thus, escape the surveillance system. We therefore aimed to describe the course of the pandemic in the Munich general population living in private households from April 2020 to January 2021.

METHODS

The KoCo19 baseline study took place from April to June 2020 including 5313 participants (age 14 years and above). From November 2020 to January 2021, we could again measure SARS-CoV-2 antibody status in 4433 of the baseline participants (response 83%). Participants were offered a self-sampling kit to take a capillary blood sample (dry blood spot; DBS). Blood was analysed using the Elecsys® Anti-SARS-CoV-2 assay (Roche). Questionnaire information on socio-demographics and potential risk factors assessed at baseline was available for all participants. In addition, follow-up information on health-risk taking behaviour and number of personal contacts outside the household (N = 2768) as well as leisure time activities (N = 1263) were collected in summer 2020.

RESULTS

Weighted and adjusted (for specificity and sensitivity) SARS-CoV-2 sero-prevalence at follow-up was 3.6% (95% CI 2.9-4.3%) as compared to 1.8% (95% CI 1.3-3.4%) at baseline. 91% of those tested positive at baseline were also antibody-positive at follow-up. While sero-prevalence increased from early November 2020 to January 2021, no indication of geospatial clustering across the city of Munich was found, although cases clustered within households. Taking baseline result and time to follow-up into account, men and participants in the age group 20-34 years were at the highest risk of sero-positivity. In the sensitivity analyses, differences in health-risk taking behaviour, number of personal contacts and leisure time activities partly explained these differences.

CONCLUSION

The number of citizens in Munich with SARS-CoV-2 antibodies was still below 5% during the 2nd wave of the pandemic. Antibodies remained present in the majority of SARS-CoV-2 sero-positive baseline participants. Besides age and sex, potentially confounded by differences in behaviour, no major risk factors could be identified. Non-pharmaceutical public health measures are thus still important.

Clinical Outcome Evaluations and CBT Response Prediction in Myotonic Dystrophy

BACKGROUND

The European OPTIMISTIC clinical trial has demonstrated a significant, yet heterogenous effect of Cognitive Behavioural Therapy (CBT) for Myotonic Dystrophy type 1 (DM1) patients. One of its remaining aims was the assessment of efficacy and adequacy of clinical outcome measures, including the relatively novel primary trial outcome, the DM1-Activ-c questionnaire.

OBJECTIVES

Assessment of the relationship between the Rasch-built DM1-Activ-c questionnaire and 26 commonly used clinical outcome measurements. Identification of variables associated with CBT response in DM1 patients.

METHODS

Retrospective analysis of the to date largest clinical trial in DM1 (OPTIMISTIC), comprising of 255 genetically confirmed DM1 patients randomized to either standard care or CBT with optionally graded exercise therapy. Correlations of 27 different outcome measures were calculated at baseline (cross-sectional) and of their respective intervention induced changes (longitudinal). Bootstrap enhanced Elastic-Net (BeEN) regression was validated and implemented to select variables associated with CBT response.

RESULTS

In cross-sectional data, DM1-Activ-c correlated significantly with the majority of other outcome measures, including Six Minute Walk Test and Myotonic Dystrophy Health Index. Fewer and weaker significant longitudinal correlations were observed. Nine variables potentially associated with CBT response were identified, including measures of disease severity, executive cognitive functioning and perceived social support.

CONCLUSIONS

The DM1-Activ-c questionnaire appears to be a well suited cross-sectional instrument to assess a variety of clinically relevant dimensions in DM1. Yet, apathy and experienced social support measures were less well captured. CBT response was heterogenous, requiring careful selection of outcome measures for different disease aspects.

Multiple imputation of missing data in multilevel models with the R package mdmb: a flexible sequential modeling approach

Multilevel models often include nonlinear effects, such as random slopes or interaction effects. The estimation of these models can be difficult when the underlying variables contain missing data. Although several methods for handling missing data such as multiple imputation (MI) can be used with multilevel data, conventional methods for multilevel MI often do not properly take the nonlinear associations between the variables into account. In the present paper, we propose a sequential modeling approach based on Bayesian estimation techniques that can be used to handle missing data in a variety of multilevel models that involve nonlinear effects. The main idea of this approach is to decompose the joint distribution of the data into several parts that correspond to the outcome and explanatory variables in the intended analysis, thus generating imputations in a manner that is compatible with the substantive analysis model. In three simulation studies, we evaluate the sequential modeling approach and compare it with conventional as well as other substantive-model-compatible approaches to multilevel MI. We implemented the sequential modeling approach in the R package mdmb and provide a worked example to illustrate its application.

Pharmacometabonomics: data processing and statistical analysis

Individual variations in drug efficacy, side effects and adverse drug reactions are still challenging that cannot be ignored in drug research and development. The aim of pharmacometabonomics is to better understand the pharmacokinetic properties of drugs and monitor the drug effects on specific metabolic pathways. Here, we systematically reviewed the recent technological advances in pharmacometabonomics for better understanding the pathophysiological mechanisms of diseases as well as the metabolic effects of drugs on bodies. First, the advantages and disadvantages of all mainstream analytical techniques were compared. Second, many data processing strategies including filtering, missing value imputation, quality control-based correction, transformation, normalization together with the methods implemented in each step were discussed. Third, various feature selection and feature extraction algorithms commonly applied in pharmacometabonomics were described. Finally, the databases that facilitate current pharmacometabonomics were collected and discussed. All in all, this review provided guidance for researchers engaged in pharmacometabonomics and metabolomics, and it would promote the wide application of metabolomics in drug research and personalized medicine.

Approaches to addressing missing values, measurement error, and confounding in epidemiologic studies

OBJECTIVES

Epidemiologic studies often suffer from incomplete data, measurement error (or misclassification), and confounding. Each of these can cause bias and imprecision in estimates of exposure-outcome relations. We describe and compare statistical approaches that aim to control all three sources of bias simultaneously.

STUDY DESIGN AND SETTING

We illustrate four statistical approaches that address all three sources of bias, namely, multiple imputation for missing data and measurement error, multiple imputation combined with regression calibration, full information maximum likelihood within a structural equation modeling framework, and a Bayesian model. In a simulation study, we assess the performance of the four approaches compared with more commonly used approaches that do not account for measurement error, missing values, or confounding.

RESULTS

The results demonstrate that the four approaches consistently outperform the alternative approaches on all performance metrics (bias, mean squared error, and confidence interval coverage). Even in simulated data of 100 subjects, these approaches perform well.

CONCLUSION

There can be a large benefit of addressing measurement error, missing values, and confounding to improve the estimation of exposure-outcome relations, even when the available sample size is relatively small.

Multiple imputation and selection of ordinal level 2 predictors in multilevel models: An analysis of the relationship between student ratings and teacher practices and attitudes

The article is motivated by the analysis of the relationship between university student ratings and teacher practices and attitudes, which are measured via a set of binary and ordinal items collected by an innovative survey. The analysis is conducted through a two-level random intercept model, where student ratings are nested within teachers. The analysis must face two issues about the items measuring teacher practices and attitudes, which are level 2 predictors: (a) the items are severely affected by missingness due to teacher non-response and (b) there is redundancy in both the number of items and the number of categories of their measurement scale. We tackle the missing data issue by considering a multiple imputation strategy exploiting information at both student and teacher levels. For the redundancy issue, we rely on regularization techniques for ordinal predictors, also accounting for the multilevel data structure. The proposed solution addresses the problem at hand in an original way, and it can be applied whenever it is required to select level 2 predictors affected by missing values. The results obtained with the final model indicate that ratings on teacher ability to motivate students are related to certain teacher practices and attitudes.

Decline of ovarian function in patients with rheumatoid arthritis: serum anti-Müllerian hormone levels in a longitudinal cohort

OBJECTIVE

Rheumatoid arthritis (RA) often affects women in their fertile age, and is known to compromise female fertility. Serum anti-Müllerian hormone (AMH) levels are a proxy for the total number of primordial follicles, and a reliable predictor of the age at menopause. Our objective was to study the longitudinal intra-individual decline of serum AMH levels in female RA patients.

METHODS

Female RA patients from a nationwide prospective cohort (2002-2008) were re-assessed in 2015-2016. Serum AMH levels were measured using the picoAMH assay and compared with healthy controls. A linear mixed model (LMM) was built to assess the effect of RA-related clinical factors on the decline of AMH levels.

RESULTS

A group of 128 women were re-assessed at an age of 42.6±4.4 years, with a median disease duration of 15.8 (IQR 12.7-21.5) years. The time between first and last AMH assessments was 10.7±1.8 (range 6.4-13.7) years. Participants represented a more fertile selection of the original cohort. At follow-up, 39% of patients had AMH levels below the 10th percentile of controls (95% CI 31% to 48%), compared with 16% (95% CI 9.3% to 22%) at baseline. The LMM showed a significant decline of AMH with increasing age, but no significant effect of RA-related factors on AMH.

CONCLUSION

AMH levels in RA patients showed a more pronounced decline over time than expected, supporting the idea that in chronic inflammatory conditions, reproductive function is compromised, resulting in a faster decline of ovarian function over time and probably an earlier age at menopause.

Adherence to a plant-based, high-fibre dietary pattern is related to regression of non-alcoholic fatty liver disease in an elderly population

Dietary lifestyle intervention is key in treating non-alcoholic fatty liver disease (NAFLD). We aimed to examine the longitudinal relation between well-established dietary patterns as well as population-specific dietary patterns and NAFLD. Participants from two subsequent visits of the Rotterdam Study were included. All underwent serial abdominal ultrasonography (median follow-up: 4.4 years) and filled in a food frequency questionnaire. Secondary causes of steatosis were excluded. Dietary data from 389 items were collapsed into 28 food groups and a posteriori dietary patterns were identified using factor analysis. Additionally, we scored three a priori dietary patterns (Mediterranean Diet Score, Dutch Dietary Guidelines and WHO-score). Logistic mixed regression models were used to examine the relation between dietary patterns and NAFLD. Analyses were adjusted for demographic, lifestyle and metabolic factors. We included 963 participants of whom 343 had NAFLD. Follow-up data was available in 737 participants. Incident NAFLD was 5% and regressed NAFLD was 30%. We identified five a posteriori dietary patterns (cumulative explained variation [R²] = 20%). The patterns were characterised as: vegetable and fish, red meat and alcohol, traditional, salty snacks and sauces, high fat dairy & refined grains pattern. Adherence to the traditional pattern (i.e. high intake of vegetable oils/stanols, margarines/butters, potatoes, whole grains and sweets/desserts) was associated with regression of NAFLD per SD increase in Z-score (0.40, 95% CI 0.15–1.00). Adherence to the three a priori patterns all showed regression of NAFLD, but only the WHO-score showed a distinct association (0.73, 95% CI 0.53–1.00). Hence, in this large elderly population, adherence to a plant-based, high-fibre and low-fat diet was related to regression of NAFLD.

Construction and assessment of prediction rules for binary outcome in the presence of missing predictor data using multiple imputation and cross-validation: Methodological approach and data-based evaluation

We investigate calibration and assessment of predictive rules when missing values are present in the predictors. Our paper has two key objectives. The first is to investigate how the calibration of the prediction rule can be combined with use of multiple imputation to account for missing predictor observations. The second objective is to propose such methods that can be implemented with current multiple imputation software, while allowing for unbiased predictive assessment through validation on new observations for which outcome is not yet available. We commence with a review of the methodological foundations of multiple imputation as a model estimation approach as opposed to a purely algorithmic description. We specifically contrast application of multiple imputation for parameter (effect) estimation with predictive calibration. Based on this review, two approaches are formulated, of which the second utilizes application of the classical Rubin's rules for parameter estimation, while the first approach averages probabilities from models fitted on single imputations to directly approximate the predictive density for future observations. We present implementations using current software that allow for validation and estimation of performance measures by cross-validation, as well as imputation of missing data in predictors on the future data where outcome is missing by definition. To simplify, we restrict discussion to binary outcome and logistic regression throughout. Method performance is verified through application on two real data sets. Accuracy (Brier score) and variance of predicted probabilities are investigated. Results show substantial reductions in variation of calibrated probabilities when using the first approach.

Identifying the source of food-borne disease outbreaks: An application of Bayesian variable selection

Early identification of contaminated food products is crucial in reducing health burdens of food-borne disease outbreaks. Analytic case-control studies are primarily used in this identification stage by comparing exposures in cases and controls using logistic regression. Standard epidemiological analysis practice is not formally defined and the combination of currently applied methods is subject to issues such as response misclassification, missing values, multiple testing problems and small sample estimation problems resulting in biased and possibly misleading results. In this paper, we develop a formal Bayesian variable selection method to account for misclassified responses and missing covariates, which are common complications in food-borne outbreak investigations. We illustrate the implementation and performance of our method on a Salmonella Thompson outbreak in the Netherlands in 2012. Our method is shown to perform better than the standard logistic regression approach with respect to earlier identification of contaminated food products. It also allows relatively easy implementation of otherwise complex methodological issues.

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).

Bayesian imputation of time-varying covariates in linear mixed models

Studies involving large observational datasets commonly face the challenge of dealing with multiple missing values. The most popular approach to overcome this challenge, multiple imputation using chained equations, however, has been shown to be sub-optimal in complex settings, specifically in settings with longitudinal outcomes, which cannot be easily and adequately included in the imputation models. Bayesian methods avoid this difficulty by specification of a joint distribution and thus offer an alternative. A popular choice for that joint distribution is the multivariate normal distribution. In more complicated settings, as in our two motivating examples that involve time-varying covariates, additional issues require consideration: the endo- or exogeneity of the covariate and its functional relation with the outcome. In such situations, the implied assumptions of standard methods may be violated, resulting in bias. In this work, we extend and study a more flexible, Bayesian alternative to the multivariate normal approach, to better handle complex incomplete longitudinal data. We discuss and compare assumptions of the two Bayesian approaches about the endo- or exogeneity of the covariates and the functional form of the association with the outcome, and illustrate and evaluate consequences of violations of those assumptions using simulation studies and two real data examples.

Mothers' intake of sugar-containing beverages during pregnancy and body composition of their children during childhood: the Generation R Study

Background: High intake of sugar-containing beverages (SCBs) has been linked to increased risk of obesity. However, associations of SCB intake during pregnancy with child body composition have been unclear.Objectives: We explored whether SCB intake during pregnancy was associated with children's body mass index (BMI) and detailed measures of body composition. In addition, we examined different types of SCBs (i.e., fruit juice, soda, and concentrate).Design: We included 3312 mother-child pairs of the Generation R Study, a prospective cohort from fetal life onward in the Netherlands. Energy-adjusted SCB intake was assessed in the first trimester with a food-frequency questionnaire. Anthropometric data of the children were collected repeatedly ≤6 y of age, and BMI was calculated. At 6 y of age, we further measured fat mass index (FMI) and fat-free mass index with dual-energy X-ray absorptiometry. All outcomes were sex- and age-standardized. Associations of SCB intake with children's BMI trajectories and body composition were analyzed with multivariable linear mixed and regression models.Results: Results from linear mixed models showed that, after adjustment for confounders including the SCB intake of the child itself, mothers' total SCB intake was positively associated with children's BMI ≤6 y of age [per serving per day: 0.04 SD score (SDS); 95% CI: 0.00, 0.07 SDS]. In addition, intakes of total SCBs and fruit juice, but not of soda or concentrate, were associated with a higher FMI [total SCBs: 0.05 SDS (95% CI: 0.01, 0.08 SDS); fruit juice: 0.04 SDS (95% CI: 0.01, 0.06 SDS)] of the 6-y-old children. These associations remained significant (P < 0.05) after additional adjustment for gestational weight gain, birth weight, and children's insulin concentrations.Conclusion: Our study suggests that maternal SCB intake during pregnancy is positively associated with children's BMI during early childhood and particularly with higher fat mass.

Higher CD163 levels are associated with insulin resistance in hepatitis C virus-infected and HIV-infected adults

OBJECTIVES

HIV/hepatitis C virus (HCV) coinfection is associated with insulin resistance, but the mechanism is unclear. We hypothesized that intestinal epithelial damage and the consequent monocyte/macrophage activation and inflammation explain this perturbation.

DESIGN

Cross-sectional study of 519 adults (220 HIV+/HCV-; 64 HIV-/HCV+; 89 HIV+/HCV+; 146 HIV-/HCV-).

METHODS

We used multivariable linear regression to evaluate associations of HIV and HCV with the homeostasis model assessment of insulin resistance (HOMA-IR) and if intestinal fatty (FA) acid binding protein (I-FABP, a marker of gut epithelial integrity), soluble CD14 (sCD14) and soluble CD163 (sCD163) (markers of monocyte/macrophage activation), and IL-6 (an inflammatory cytokine) mediated this association.

RESULTS

HIV+/HCV+ and HIV-/HCV+ had greater demographic-adjusted HOMA-IR [mean (95% confidence interval (CI)): 1.96 (1.51, 2.54) and 1.65 (1.22, 2.24)] than HIV+/HCV- and HIV-/HCV-[1.41 (1.18, 1.67) and 1.44 (1.17, 1.75), respectively]. After additional adjustment for lifestyle and metabolic factors, HIV+/HCV+ remained associated with 36% (95% CI: 4, 80%) greater HOMA-IR relative to HIV-/HCV-, whereas HIV-/HCV+ and HIV+/HCV- had smaller differences. Adjustment for sCD163 substantially attenuated the difference between HIV+/HCV+ and HIV-/HCV-; adjustment for I-FABP, sCD14, and IL-6 had little effect. Higher sCD163 was independently associated with 19% (95% CI: 7, 33%), 26% (95% CI: 15, 39%), 25% (95% CI: 14, 37%), and 23% (95% CI: 11, 36%) greater HOMA-IR in HIV+/HCV+, HIV-/HCV+, HIV+/HCV-, and HIV-/HCV- (all estimates per doubling of sCD163). I-FABP, sCD14, and IL-6 were not associated with HOMA-IR.

CONCLUSION

HIV/HCV coinfection is associated with greater HOMA-IR, even after controlling for demographic, lifestyle, and metabolic factors. sCD163, which appears independent of intestinal epithelial damage and inflammation, partly explains this association. Our findings that the association of sCD163 with HOMA-IR occurred even in the absence of HIV and HCV, indicate that viral and nonviral factors affect sCD163 levels. Its role in insulin resistance needs elucidation.

Multiple imputation as a flexible tool for missing data handling in clinical research

The last 20 years has seen an uptick in research on missing data problems, and most software applications now implement one or more sophisticated missing data handling routines (e.g., multiple imputation or maximum likelihood estimation). Despite their superior statistical properties (e.g., less stringent assumptions, greater accuracy and power), the adoption of these modern analytic approaches is not uniform in psychology and related disciplines. Thus, the primary goal of this manuscript is to describe and illustrate the application of multiple imputation. Although maximum likelihood estimation is perhaps the easiest method to use in practice, psychological data sets often feature complexities that are currently difficult to handle appropriately in the likelihood framework (e.g., mixtures of categorical and continuous variables), but relatively simple to treat with imputation. The paper describes a number of practical issues that clinical researchers are likely to encounter when applying multiple imputation, including mixtures of categorical and continuous variables, item-level missing data in questionnaires, significance testing, interaction effects, and multilevel missing data. Analysis examples illustrate imputation with software packages that are freely available on the internet.

A Priori and a Posteriori Dietary Patterns during Pregnancy and Gestational Weight Gain: The Generation R Study

Abnormal gestational weight gain (GWG) is associated with adverse pregnancy outcomes. We examined whether dietary patterns are associated with GWG. Participants included 3374 pregnant women from a population-based cohort in the Netherlands. Dietary intake during pregnancy was assessed with food-frequency questionnaires. Three a posteriori-derived dietary patterns were identified using principal component analysis: a "Vegetable, oil and fish", a "Nuts, high-fiber cereals and soy", and a "Margarine, sugar and snacks" pattern. The a priori-defined dietary pattern was based on national dietary recommendations. Weight was repeatedly measured around 13, 20 and 30 weeks of pregnancy; pre-pregnancy and maximum weight were self-reported. Normal weight women with high adherence to the "Vegetable, oil and fish" pattern had higher early-pregnancy GWG than those with low adherence (43 g/week (95% CI 16; 69) for highest vs. lowest quartile (Q)). Adherence to the "Margarine, sugar and snacks" pattern was associated with a higher prevalence of excessive GWG (OR 1.45 (95% CI 1.06; 1.99) Q4 vs. Q1). Normal weight women with higher scores on the "Nuts, high-fiber cereals and soy" pattern had more moderate GWG than women with lower scores (-0.01 (95% CI -0.02; -0.00) per SD). The a priori-defined pattern was not associated with GWG. To conclude, specific dietary patterns may play a role in early pregnancy but are not consistently associated with GWG.