Missing Data In Longitudinal Studies Research Articles

The Social and Emotional Education and Development intervention to address wellbeing in primary school age children: the SEED cluster RCT.

Stronger social and emotional well-being during primary school is positively associated with the health and educational outcomes of young people. However, there is little evidence on which programmes are the most effective for improving social and emotional well-being. The objective was to rigorously evaluate the Social and Emotional Education and Development (SEED) intervention process for improving pupils' social and emotional well-being. This was a stratified cluster randomised controlled trial with embedded process and economic evaluations. Thirty-eight primary schools were randomly assigned to the SEED intervention or to the control group. Hierarchical regression analysis allowing for clustering at school learning community level was conducted in R (statistical package). The SEED intervention is a whole-school intervention; it involved all school staff and two cohorts of pupils, one starting at 4 or 5 years of age and the second starting at 8 or 9 years of age, across all 38 schools. A total of 2639 pupils in Scotland. The SEED intervention used an iterative process that involved three components to facilitate selection and implementation of school-based actions: (1) questionnaire completion, (2) benchmarked feedback to all staff and (3) reflective discussions (all staff and an educational psychologist). The primary outcome was pupils' Strengths and Difficulties Questionnaire-Total Difficulties Score when pupils were 4 years older than at baseline. The primary outcome, pupils' Strengths and Difficulties Questionnaire-Total Difficulties Score at follow-up 3, showed improvements for intervention arm pupils, compared with those in the control arm [relative risk -1.30 (95% confidence interval -1.87 to -0.73), standardised effect size -0.27 (95% confidence interval -0.39 to -0.15)]. There was no evidence of intervention effects according to deprivation: the results were significant for both affluent and deprived pupils. Subgroup analysis showed that all effect sizes were larger for the older cohort, particularly boys [relative risk -2.36 (95% confidence interval -3.62 to -1.11), standardised effect size -0.42 (95% confidence interval -0.64 to -0.20)]. Although there was no statistically significant difference in incremental cost and quality-adjusted life-years, the probability that the intervention is cost-effective at a willingness-to-pay threshold of £20,000 per quality-adjusted life-year was high, at 88%. Particularly valued mechanisms of the SEED intervention were its provision of time to reflect on and discuss social and emotional well-being and its contribution to a culture of evaluating practice. It was a challenge to retain schools over five waves of data collection. This trial demonstrated that the SEED intervention is an acceptable, cost-effective way to modestly improve pupil well-being and improve school climate, particularly for older boys and those with greater levels of psychological difficulties. It was beneficial during the transition from primary to secondary school, but this diminished after 6 years. The SEED intervention can be implemented alongside existing systems for addressing pupil well-being and can be complementary to other interventions. Assess whether or not the SEED intervention has a beneficial impact on academic attainment, is transferable to other countries and other organisational settings, would be strengthened by adding core training elements to the intervention process and is transferable to secondary schools. Understand the gender differences illustrated by the outcomes of this trial. Conduct further statistical research on how to handle missing data in longitudinal studies of complex social interventions. This trial is registered as ISRCTN51707384. This award was funded by the National Institute for Health and Care Research (NIHR) Public Health Research programme (NIHR award ref: 10/3006/13) and is published in full in Public Health Research; Vol. 12, No. 6. See the NIHR Funding and Awards website for further award information.

Methods for handling missing data in serially sampled sputum specimens for mycobacterial culture conversion calculation

BackgroundThe occurrence and timing of mycobacterial culture conversion is used as a proxy for tuberculosis treatment response. When researchers serially sample sputum during tuberculosis studies, contamination or missed visits leads to missing data points. Traditionally, this is managed by ignoring missing data or simple carry-forward techniques. Statistically advanced multiple imputation methods potentially decrease bias and retain sample size and statistical power.MethodsWe analyzed data from 261 participants who provided weekly sputa for the first 12 weeks of tuberculosis treatment. We compared methods for handling missing data points in a longitudinal study with a time-to-event outcome. Our primary outcome was time to culture conversion, defined as two consecutive weeks with no Mycobacterium tuberculosis growth. Methods used to address missing data included: 1) available case analysis, 2) last observation carried forward, and 3) multiple imputation by fully conditional specification. For each method, we calculated the proportion culture converted and used survival analysis to estimate Kaplan-Meier curves, hazard ratios, and restricted mean survival times. We compared methods based on point estimates, confidence intervals, and conclusions to specific research questions.ResultsThe three missing data methods lead to differences in the number of participants achieving conversion; 78 (32.8%) participants converted with available case analysis, 154 (64.7%) converted with last observation carried forward, and 184 (77.1%) converted with multiple imputation. Multiple imputation resulted in smaller point estimates than simple approaches with narrower confidence intervals. The adjusted hazard ratio for smear negative participants was 3.4 (95% CI 2.3, 5.1) using multiple imputation compared to 5.2 (95% CI 3.1, 8.7) using last observation carried forward and 5.0 (95% CI 2.4, 10.6) using available case analysis.ConclusionWe showed that accounting for missing sputum data through multiple imputation, a statistically valid approach under certain conditions, can lead to different conclusions than naïve methods. Careful consideration for how to handle missing data must be taken and be pre-specified prior to analysis. We used data from a TB study to demonstrate these concepts, however, the methods we described are broadly applicable to longitudinal missing data. We provide valuable statistical guidance and code for researchers to appropriately handle missing data in longitudinal studies.

The reporting and handling of missing data in longitudinal studies of older adults is suboptimal: a methodological survey of geriatric journals

BackgroundMissing data are common in longitudinal studies, and more so, in studies of older adults, who are susceptible to health and functional decline that limit completion of assessments. We assessed the extent, current reporting, and handling of missing data in longitudinal studies of older adults.MethodsMedline and Embase databases were searched from 2015 to 2019 for publications on longitudinal observational studies conducted among persons ≥55 years old. The search was restricted to 10 general geriatric journals published in English. Reporting and handling of missing data were assessed using questions developed from the recommended standards. Data were summarised descriptively as frequencies and proportions.ResultsA total of 165 studies were included in the review from 7032 identified records. In approximately half of the studies 97 (62.5%), there was either no comment on missing data or unclear descriptions. The percentage of missing data varied from 0.1 to 55%, with a 14% average among the studies that reported having missing data. Complete case analysis was the most common method for handling missing data with nearly 75% of the studies (n = 52) excluding individual observations due to missing data, at the initial phase of study inclusion or at the analysis stage. Of the 10 studies where multiple imputation was used, only 1 (10.0%) study followed the guideline for reporting the procedure fully using online supplementary documents.ConclusionThe current reporting and handling of missing data in longitudinal observational studies of older adults are inadequate. Journal endorsement and implementation of guidelines may potentially improve the quality of missing data reporting. Further, authors should be encouraged to use online supplementary files to provide additional details on how missing data were addressed, to allow for more transparency and comprehensive appraisal of studies.

Simulation study on missing data imputation methods for longitudinal data in cohort studies

Objective: Data being missed is an unavoidable problem in cohort studies. This paper compares the imputation effect of eight common missing data imputation methods involved in cutting longitudinal data through simulation study to provide a valuable reference for the treatment of missing data in longitudinal studies. Methods: The simulation study is based on R language software and generates missing longitudinal data by the Monte Carlo method. By comparing the average absolute deviation, average relative deviation, and TypeⅠerror from the regression analysis of different imputation methods, the imputation effect of varying imputation methods on missing longitudinal data and the influence on subsequent multivariate analysis are evaluated. Results: The mean imputation, k nearest neighbor (KNN), regression imputation, and random forest all have a similar imputation effect, which is also steady. However, the hot deck is inferior to the above imputation methods. K-means clustering and expectation maximization (EM) algorithm are among the worst and unstable. Mean imputation, EM algorithm, random forest, KNN, and regression imputation can control TypeⅠerror. Still, multiple imputations, hot deck, and K-means clustering cannot effectively manage the TypeⅠerror. Conclusions: For missing data in longitudinal studies, mean imputation, KNN, regression imputation, and random forest can be used as better imputation methods under the mechanism of missing at random. When the missing ratio is not too large, multiple imputations and hot deck can also perform well, but K-means clustering and EM algorithm are not recommended.

Infant Cognitive Scores Prediction with Multi-stream Attention-Based Temporal Path Signature Features.

There is stunning rapid development of human brains in the first year of life. Some studies have revealed the tight connection between cognition skills and cortical morphology in this period. Nonetheless, it is still a great challenge to predict cognitive scores using brain morphological features, given issues like small sample size and missing data in longitudinal studies. In this work, for the first time, we introduce the path signature method to explore hidden analytical and geometric properties of longitudinal cortical morphology features. A novel BrainPSNet is proposed with a differentiable temporal path signature layer to produce informative representations of different time points and various temporal granules. Further, a two-stream neural network is included to combine groups of raw features and path signature features for predicting the cognitive score. More importantly, considering different influences of each brain region on the cognitive function, we design a learning-based attention mask generator to automatically weight regions correspondingly. Experiments are conducted on an in-house longitudinal dataset. By comparing with several recent algorithms, the proposed method achieves the state-of-the-art performance. The relationship between morphological features and cognitive abilities is also analyzed.

Longitudinal atopic dermatitis control and persistence vary with timing of disease onset in children: A cohort study

Wide variation exists in the timing of atopic dermatitis (AD) disease onset among children. Distinct trajectories of early-onset, mid-onset, and late-onset AD have been previously described. To evaluate longitudinal disease control and persistence with respect to age at onset of AD. A cohort study was performed using the Pediatric Eczema Elective Registry, a prospective observational cohort of subjects with childhood-onset AD. AD control and persistence were assessed biannually for up to 10years. A total of 8015 subjects with 41,934 person-years of follow-up were included. In longitudinal analyses using generalized linear latent and mixed modeling, older age at onset of AD was associated with better disease control and less-persistent AD. For each additional year of age at onset of AD, the adjusted odds ratios for poorer AD control and for persistent AD were 0.93 (95% confidence interval, 0.91-0.94) and 0.84 (95% confidence interval, 0.80-0.88), respectively. Differences in AD control and persistence among subjects with early-, mid-, and late-onset AD were most pronounced from early adolescence onward. Misclassification bias may arise from using self-reported data on age at onset. Attrition and missing data in longitudinal studies may introduce bias. Early-, mid-, and late-onset pediatric AD appear to be clinically distinct subtypes of the disease.

A comparison of multiple imputation methods for missing data in longitudinal studies

BackgroundMultiple imputation (MI) is now widely used to handle missing data in longitudinal studies. Several MI techniques have been proposed to impute incomplete longitudinal covariates, including standard fully conditional specification (FCS-Standard) and joint multivariate normal imputation (JM-MVN), which treat repeated measurements as distinct variables, and various extensions based on generalized linear mixed models. Although these MI approaches have been implemented in various software packages, there has not been a comprehensive evaluation of the relative performance of these methods in the context of longitudinal data.MethodUsing both empirical data and a simulation study based on data from the six waves of the Longitudinal Study of Australian Children (N = 4661), we investigated the performance of a wide range of MI methods available in standard software packages for investigating the association between child body mass index (BMI) and quality of life using both a linear regression and a linear mixed-effects model.ResultsIn this paper, we have identified and compared 12 different MI methods for imputing missing data in longitudinal studies. Analysis of simulated data under missing at random (MAR) mechanisms showed that the generally available MI methods provided less biased estimates with better coverage for the linear regression model and around half of these methods performed well for the estimation of regression parameters for a linear mixed model with random intercept. With the observed data, we observed an inverse association between child BMI and quality of life, with available data as well as multiple imputation.ConclusionBoth FCS-Standard and JM-MVN performed well for the estimation of regression parameters in both analysis models. More complex methods that explicitly reflect the longitudinal structure for these analysis models may only be needed in specific circumstances such as irregularly spaced data.

Comparison of maximum likelihood approach, Diggle–Kenward selection model, pattern mixture model with MAR and MNAR dropout data

In longitudinal studies, missing data are ubiquitous. This article made a comparison of three model-based techniques for handling different types of missing data (i.e., missing at random (MAR)-based maximum likelihood (ML) approach, missing not at random (MNAR)-based Diggle–Kenward (DK) selection model and MNAR-based pattern mixture (PM) model) in longitudinal studies through a Monte Carlo simulation study. Two influential factors were considered: the dropout rates (5%, 10%, 20%, and 40%) and the sample sizes (100, 300, 500, and 1000) under MAR and MNAR missingness mechanisms respectively. The results indicated that the model selection was a crucial issue when researchers were dealing with missing data in longitudinal studies because under MNAR mechanism, DK method outperformed MAR-based ML approach, but PM method performed worse than MAR-based method did. The differences of the parameter estimation among three methods became more significant as the sample size and the dropout rate increased.

Emerging Methodologies in Pediatric Palliative Care Research: Six Case Studies.

Given the broad focus of pediatric palliative care (PPC) on the physical, emotional, and spiritual needs of children with potentially life-limiting illnesses and their families, PPC research requires creative methodological approaches. This manuscript, written by experienced PPC researchers, describes issues encountered in our own areas of research and the novel methods we have identified to target them. Specifically, we discuss potential approaches to: assessing symptoms among nonverbal children, evaluating medical interventions, identifying and treating problems related to polypharmacy, addressing missing data in longitudinal studies, evaluating longer-term efficacy of PPC interventions, and monitoring for inequities in PPC service delivery.

MISSING DATA IN LONGITUDINAL STUDIES OF AGING: THE GOOD, THE BAD, AND THE UGLY

In longitudinal studies of aging, missing data are inevitable. In the literature on the association between grip strength and survival time in older persons, the methods used to deal with missing values are generally not even mentioned. The default in standard statistical software is listwise deletion - removing all observations with any missing data. Missing data have been classified into three types: missing completely at random (the good), missing at random (the bad) and missing not at random (the ugly). Depending on the type of missing data, listwise deletion may produce biased results.The objectives of this presentation are: 1) To identify different types of missing data that may arise within a longitudinal study of aging and 2) To assess the estimates of the association between grip strength and mortality that result from applying different methods for handling missing data.Using data from the Cardiovascular Health Study, a longitudinal study of 5,201 older persons, we: 1) examined the types of missing data; 2) investigated the association between grip strength and survival time, applying three common methods of handling missing data: listwise deletion, last value carried forward (LOCF), and multiple imputation (MI). We identified all three types of missing data in the CHS. Compared to the method of listwise deletion, estimates of the association between grip strength and survival were weaker when applying LOCF, and stronger with MI. Methods of handling missing data in longitudinal studies of aging should be considered carefully in order to limit the potential for biased results.

Power calculations for delta-adjusted pattern-mixture models.

Pattern-mixture models provide a general and flexible framework for sensitivity analyses of nonignorable missing data in longitudinal studies. The delta-adjusted pattern-mixture models handle missing data in a clinically interpretable manner and have been used as sensitivity analyses addressing the effectiveness hypothesis, while a likelihood-based approach that assumes data are missing at random is often used as the primary analysis addressing the efficacy hypothesis. We describe a method for power calculations for delta-adjusted pattern-mixture model sensitivity analyses in confirmatory clinical trials. To apply the method, we only need to specify the pattern probabilities at postbaseline time points, the expected treatment differences at postbaseline time points, the conditional covariance matrix of postbaseline measurements given the baseline measurement, and the delta-adjustment method for the pattern-mixture model. We use an example to illustrate and compare various delta-adjusted pattern-mixture models and use simulations to confirm the analytic results.

A Flexible Bayesian Approach to Monotone Missing Data in Longitudinal Studies With Nonignorable Missingness With Application to an Acute Schizophrenia Clinical Trial

We develop a Bayesian nonparametric model for a longitudinal response in the presence of nonignorable missing data. Our general approach is to first specify a working model that flexibly models the missingness and full outcome processes jointly. We specify a Dirichlet process mixture of missing at random (MAR) models as a prior on the joint distribution of the working model. This aspect of the model governs the fit of the observed data by modeling the observed data distribution as the marginalization over the missing data in the working model. We then separately specify the conditional distribution of the missing data given the observed data and dropout. This approach allows us to identify the distribution of the missing data using identifying restrictions as a starting point. We propose a framework for introducing sensitivity parameters, allowing us to vary the untestable assumptions about the missing data mechanism smoothly. Informative priors on the space of missing data assumptions can be specified to combine inferences under many different assumptions into a final inference and accurately characterize uncertainty. These methods are motivated by, and applied to, data from a clinical trial assessing the efficacy of a new treatment for acute schizophrenia. Supplementary materials for this article are available online.

Using multiple imputation to deal with missing data and attrition in longitudinal studies with repeated measures of patient-reported outcomes.

ObjectiveMissing data is a ubiquitous problem in studies using patient-reported measures, decreasing sample sizes and causing possible bias. In longitudinal studies, special problems relate to attrition and death during follow-up. We describe a methodological approach for the use of multiple imputation (MI) to meet these challenges.MethodsIn a cohort of patients treated with percutaneous coronary intervention followed with use of repetitive questionnaires and information from national registers over 3 years, only 417 out of 1,726 patients had complete data on all measure points and covariates. We suggest strategies for use of MI and different methods for dealing with death along with sensitivity analysis of deviations from the assumption of missing at random, all with the use of standard statistical software. The Mental Component Summary from Short Form 12-item survey was used as an example.ConclusionIgnoring missing data may cause bias of unknown size and direction in longitudinal studies. We have illustrated that MI is a feasible method to try to deal with bias due to missing data in longitudinal studies, including attrition and nonresponse, and should be considered in combination with analysis of sensitivity in longitudinal studies. How to handle dropout due to death is still open for debate.

An extension of the placebo‐based pattern‐mixture model

Pattern-mixture models provide a general and flexible framework for sensitivity analyses of nonignorable missing data in longitudinal studies. The placebo-based pattern-mixture model handles missing data in a transparent and clinically interpretable manner. We extend this model to include a sensitivity parameter that characterizes the gradual departure of the missing data mechanism from being missing at random toward being missing not at random under the standard placebo-based pattern-mixture model. We derive the treatment effect implied by the extended model. We propose to utilize the primary analysis based on a mixed-effects model for repeated measures to draw inference about the treatment effect under the extended placebo-based pattern-mixture model. We use simulation studies to confirm the validity of the proposed method. We apply the proposed method to a clinical study of major depressive disorders.

An analytic method for the placebo‐based pattern‐mixture model

Pattern-mixture models provide a general and flexible framework for sensitivity analyses of nonignorable missing data. The placebo-based pattern-mixture model (Little and Yau, Biometrics 1996; 52:1324-1333) treats missing data in a transparent and clinically interpretable manner and has been used as sensitivity analysis for monotone missing data in longitudinal studies. The standard multiple imputation approach (Rubin, Multiple Imputation for Nonresponse in Surveys, 1987) is often used to implement the placebo-based pattern-mixture model. We show that Rubin's variance estimate of the multiple imputation estimator of treatment effect can be overly conservative in this setting. As an alternative to multiple imputation, we derive an analytic expression of the treatment effect for the placebo-based pattern-mixture model and propose a posterior simulation or delta method for the inference about the treatment effect. Simulation studies demonstrate that the proposed methods provide consistent variance estimates and outperform the imputation methods in terms of power for the placebo-based pattern-mixture model. We illustrate the methods using data from a clinical study of major depressive disorders.

Multiple imputation of missing values was not necessary before performing a longitudinal mixed-model analysis

Background and ObjectivesAs a result of the development of sophisticated techniques, such as multiple imputation, the interest in handling missing data in longitudinal studies has increased enormously in past years. Within the field of longitudinal data analysis, there is a current debate on whether it is necessary to use multiple imputations before performing a mixed-model analysis to analyze the longitudinal data. In the current study this necessity is evaluated. Study Design and SettingThe results of mixed-model analyses with and without multiple imputation were compared with each other. Four data sets with missing values were created—one data set with missing completely at random, two data sets with missing at random, and one data set with missing not at random). In all data sets, the relationship between a continuous outcome variable and two different covariates were analyzed: a time-independent dichotomous covariate and a time-dependent continuous covariate. ResultsAlthough for all types of missing data, the results of the mixed-model analysis with or without multiple imputations were slightly different, they were not in favor of one of the two approaches. In addition, repeating the multiple imputations 100 times showed that the results of the mixed-model analysis with multiple imputation were quite unstable. ConclusionIt is not necessary to handle missing data using multiple imputations before performing a mixed-model analysis on longitudinal data.

Linear mixed-effects modeling approach to FMRI group analysis

Conventional group analysis is usually performed with Student-type t-test, regression, or standard AN(C)OVA in which the variance-covariance matrix is presumed to have a simple structure. Some correction approaches are adopted when assumptions about the covariance structure is violated. However, as experiments are designed with different degrees of sophistication, these traditional methods can become cumbersome, or even be unable to handle the situation at hand. For example, most current FMRI software packages have difficulty analyzing the following scenarios at group level: (1) taking within-subject variability into account when there are effect estimates from multiple runs or sessions; (2) continuous explanatory variables (covariates) modeling in the presence of a within-subject (repeated measures) factor, multiple subject-grouping (between-subjects) factors, or the mixture of both; (3) subject-specific adjustments in covariate modeling; (4) group analysis with estimation of hemodynamic response (HDR) function by multiple basis functions; (5) various cases of missing data in longitudinal studies; and (6) group studies involving family members or twins. Here we present a linear mixed-effects modeling (LME) methodology that extends the conventional group analysis approach to analyze many complicated cases, including the six prototypes delineated above, whose analyses would be otherwise either difficult or unfeasible under traditional frameworks such as AN(C)OVA and general linear model (GLM). In addition, the strength of the LME framework lies in its flexibility to model and estimate the variance-covariance structures for both random effects and residuals. The intraclass correlation (ICC) values can be easily obtained with an LME model with crossed random effects, even at the presence of confounding fixed effects. The simulations of one prototypical scenario indicate that the LME modeling keeps a balance between the control for false positives and the sensitivity for activation detection. The importance of hypothesis formulation is also illustrated in the simulations. Comparisons with alternative group analysis approaches and the limitations of LME are discussed in details.

A Hot-Deck Multiple Imputation Procedure for Gaps in Longitudinal Recurrent Event Histories

We propose a regression-based hot-deck multiple imputation method for gaps of missing data in longitudinal studies, where subjects experience a recurrent event process and a terminal event. Examples are repeated asthma episodes and death, or menstrual periods and menopause, as in our motivating application. Research interest concerns the onset time of a marker event, defined by the recurrent event process, or the duration from this marker event to the final event. Gaps in the recorded event history make it difficult to determine the onset time of the marker event, and hence, the duration from onset to the final event. Simple approaches such as jumping gap times or dropping cases with gaps have obvious limitations. We propose a procedure for imputing information in the gaps by substituting information in the gap from a matched individual with a completely recorded history in the corresponding interval. Predictive mean matching is used to incorporate information on longitudinal characteristics of the repeated process and the final event time. Multiple imputation is used to propagate imputation uncertainty. The procedure is applied to an important data set for assessing the timing and duration of the menopausal transition. The performance of the proposed method is assessed by a simulation study.

Missing Data? Plan on It!

Longitudinal study designs are indispensable for investigating age-related functional change. There now are well-established methods for addressing missing data in longitudinal studies. Modern missing data methods not only minimize most problems associated with missing data (e.g., loss of power and biased parameter estimates), but also have valuable new applications such as research designs that use modern missing data methods to plan missing data purposefully. This article describes two state-of-the-art statistical methodologies for addressing missing data in longitudinal research: growth curve analysis and statistical measurement models. How the purposeful planning of missing data in research designs can reduce subject burden, improve data quality and statistical power, and manage costs is then described.

Why Missing Data Matter in the Longitudinal Study of Adolescent Development: Using the 4-H Study to Understand the Uses of Different Missing Data Methods

The study of adolescent development rests on methodologically appropriate collection and interpretation of longitudinal data. While all longitudinal studies of adolescent development involve missing data, the methods to treat missingness that have been recommended most often focus on missing data from cross-sectional studies. The problems of missing data in longitudinal studies are not described well, there are not many statistical software programs developed for researchers to use, and there are no longitudinal empirical examples involving adolescent development that show the extent to which different missing data procedures can yield different results. Data from the first three waves of the 4-H Study of Positive Youth Development were used to provide such an illustration. The sample contains 2,265 participants (56.7% females) who were in Grade 5 at Wave 1, in Grade 6 at Wave 2, and in Grade 7 at Wave 3, and varied in race, ethnicity, socioeconomic status, family structure, rural-urban location, and geographic region. The results showed that three missing data techniques, i.e., listwise deletion, direct maximum likelihood (DirML), and multiple imputation (MI), did not yield comparable results for research questions assessing different aspects of development (i.e., change over time or prediction effects). The results indicated also that listwise deletion should not be used. Instead, both DirML and MI methods should be used to determine if and how results change when these procedures are employed.