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Background Multiple 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. Method Using 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. Results In 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. Conclusion Both 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.

Missing data are ubiquitous in clinical epidemiological research. Individuals with missing data may differ from those with no missing data in terms of the outcome of interest and prognosis in general. Missing data are often categorized into the following three types: missing completely at random (MCAR), missing at random (MAR), and missing not at random (MNAR). In clinical epidemiological research, missing data are seldom MCAR. Missing data can constitute considerable challenges in the analyses and interpretation of results and can potentially weaken the validity of results and conclusions. A number of methods have been developed for dealing with missing data. These include complete-case analyses, missing indicator method, single value imputation, and sensitivity analyses incorporating worst-case and best-case scenarios. If applied under the MCAR assumption, some of these methods can provide unbiased but often less precise estimates. Multiple imputation is an alternative method to deal with missing data, which accounts for the uncertainty associated with missing data. Multiple imputation is implemented in most statistical software under the MAR assumption and provides unbiased and valid estimates of associations based on information from the available data. The method affects not only the coefficient estimates for variables with missing data but also the estimates for other variables with no missing data.

Background Missing data are common in randomised controlled trials (RCTs) and can bias results if not handled appropriately. A statistically valid analysis under the primary missing-data assumptions should be conducted, followed by sensitivity analysis under alternative justified assumptions to assess the robustness of results. Controlled Multiple Imputation (MI) procedures, including delta-based and reference-based approaches, have been developed for analysis under missing-not-at-random assumptions. However, it is unclear how often these methods are used, how they are reported, and what their impact is on trial results. This review evaluates the current use and reporting of MI and controlled MI in RCTs. Methods A targeted review of phase II-IV RCTs (non-cluster randomised) published in two leading general medical journals (The Lancet and New England Journal of Medicine) between January 2014 and December 2019 using MI. Data was extracted on imputation methods, analysis status, and reporting of results. Results of primary and sensitivity analyses for trials using controlled MI analyses were compared. Results A total of 118 RCTs (9% of published RCTs) used some form of MI. MI under missing-at-random was used in 110 trials; this was for primary analysis in 43/118 (36%), and in sensitivity analysis for 70/118 (59%) (3 used in both). Sixteen studies performed controlled MI (1.3% of published RCTs), either with a delta-based ( n  = 9) or reference-based approach ( n  = 7). Controlled MI was mostly used in sensitivity analysis ( n  = 14/16). Two trials used controlled MI for primary analysis, including one reporting no sensitivity analysis whilst the other reported similar results without imputation. Of the 14 trials using controlled MI in sensitivity analysis, 12 yielded comparable results to the primary analysis whereas 2 demonstrated contradicting results. Only 5/110 (5%) trials using missing-at-random MI and 5/16 (31%) trials using controlled MI reported complete details on MI methods. Conclusions Controlled MI enabled the impact of accessible contextually relevant missing data assumptions to be examined on trial results. The use of controlled MI is increasing but is still infrequent and poorly reported where used. There is a need for improved reporting on the implementation of MI analyses and choice of controlled MI parameters.

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

Background The multiple imputation by chained equations (MICE) is a widely used approach for handling missing data. However, its robustness, especially for high missing proportions in health indicators, is under-researched. The study aimed to provide a preliminary guideline for the choice of the extent of missing proportion to impute longitudinal health-related data using the MICE method. Methods The study obtained complete data on five mortality-related health indicators of 100 countries (2015–2019) from the Global Health Observatory. Nine incomplete datasets with missing rates from 10 to 90% were generated and imputed using MICE. The robustness of MICE was assessed through three approaches: comparison of means using the Repeated Measures- Analysis of variance, estimation of evaluation metrics (Root mean square error, mean absolute deviation, Bias, and proportionate variance), and visual inspection of box plots of imputed and non-imputed data. Results The Repeated Measures- Analysis of variance revealed significant differences between complete and imputed data, primarily in imputed data with over 50% missing proportions. Evaluation metrics exhibited ‘high performance’ for the dataset with a 50% missing proportion for various health indicators However, with missing proportions exceeding 70%, the majority of indicators demonstrated a ‘low’ performance level in terms of most evaluation metrics. The visual inspection of the box plot revealed severe variance shrinkage in imputed datasets with missing proportions beyond 70%, corroborating the findings from the evaluation metrics. Conclusion It demonstrates high robustness up to 50% missing values, with marginal deviations from complete datasets. Caution is warranted for missing proportions between 50 and 70%, as moderate alterations are observed. Proportions beyond 70% lead to significant variance shrinkage and compromised data reliability, emphasizing the importance of acknowledging imputation limitations for practical decision-making.

Background Three-level data arising from repeated measures on individuals who are clustered within larger units are common in health research studies. Missing data are prominent in such longitudinal studies and multiple imputation (MI) is a popular approach for handling missing data. Extensions of joint modelling and fully conditional specification MI approaches based on multilevel models have been developed for imputing three-level data. Alternatively, it is possible to extend single- and two-level MI methods to impute three-level data using dummy indicators and/or by analysing repeated measures in wide format. However, most implementations, evaluations and applications of these approaches focus on the context of incomplete two-level data. It is currently unclear which approach is preferable for imputing three-level data. Methods In this study, we investigated the performance of various MI methods for imputing three-level incomplete data when the target analysis model is a three-level random effects model with a random intercept for each level. The MI methods were evaluated via simulations and illustrated using empirical data, based on a case study from the Childhood to Adolescence Transition Study, a longitudinal cohort collecting repeated measures on students who were clustered within schools. In our simulations we considered a number of different scenarios covering a range of different missing data mechanisms, missing data proportions and strengths of level-2 and level-3 intra-cluster correlations. Results We found that all of the approaches considered produced valid inferences about both the regression coefficient corresponding to the exposure of interest and the variance components under the various scenarios within the simulation study. In the case study, all approaches led to similar results. Conclusion Researchers may use extensions to the single- and two-level approaches, or the three-level approaches, to adequately handle incomplete three-level data. The two-level MI approaches with dummy indicator extension or the MI approaches based on three-level models will be required in certain circumstances such as when there are longitudinal data measured at irregular time intervals. However, the single- and two-level approaches with the DI extension should be used with caution as the DI approach has been shown to produce biased parameter estimates in certain scenarios.

The life course paradigm emphasizes the need to study not only the situation at a given point in time, but also its evolution over the life course in the medium and long term. These trajectories are often represented by categorical data. This article aims to provide a comprehensive review of the multiple imputation methods proposed so far in the context of univariate categorical data and to assess their practical relevance through a simulation study based on real data. The primary goal is to provide clear methodological guidelines and improve the handling of missing data in life course research. In parallel, we develop the MICT-timing algorithm, which is an extension of the MICT algorithm. This innovative multiple imputation method improves the quality of imputation in trajectories subject to time-varying transition rates, a situation often encountered in life course data.

Background Incomplete data are of particular important influence in mental measurement questionnaires. Most experts, however, mostly focus on clinical trials and cohort studies and generally pay less attention to this deficiency. We aim is to compare the accuracy of four common methods for handling items missing from different psychology questionnaires according to the items non-response rates. Method All data were drawn from the previous studies including the self-acceptance scale (SAQ), the activities of daily living scale (ADL) and self-esteem scale (RSES). SAQ and ADL dataset, simulation group, were used to compare and assess the ability of four imputation methods which are direct deletion, mode imputation, Hot-deck (HD) imputation and multiple imputation (MI) by absolute deviation, the root mean square error and average relative error in missing proportions of 5, 10, 15 and 20%. RSES dataset, validation group, was used to test the application of imputation methods. All analyses were finished by SAS 9.4. Results The biases obtained by MI are the smallest under various missing proportions. HD imputation approach performed the lowest absolute deviation of standard deviation values. But they got the similar results and the performances of them are obviously better than direct deletion and mode imputation. In a real world situation, the respondents’ average score in complete data set was 28.22 ± 4.63, which are not much different from imputed datasets. The direction of the influence of the five factors on self-esteem was consistent, although there were some differences in the size and range of OR values in logistic regression model. Conclusion MI shows the best performance while it demands slightly more data analytic capacity and skills of programming. And HD could be considered to impute missing values in psychological investigation when MI cannot be performed due to limited circumstances.

Background Missing data is a pervasive problem in longitudinal data analysis. Several single-imputation (SI) and multiple-imputation (MI) approaches have been proposed to address this issue. In this study, for the first time, the function of the longitudinal regression tree algorithm as a non-parametric method after imputing missing data using SI and MI was investigated using simulated and real data. Method Using different simulation scenarios derived from a real data set, we compared the performance of cross, trajectory mean, interpolation, copy-mean, and MI methods (27 approaches) to impute missing longitudinal data using parametric and non-parametric longitudinal models and the performance of the methods was assessed in real data. The real data included 3,645 participants older than 18 years within six waves obtained from the longitudinal Tehran cardiometabolic genetic study (TCGS). The data modeling was conducted using systolic and diastolic blood pressure (SBP/DBP) as the outcome variables and included predictor variables such as age, gender, and BMI. The efficiency of imputation approaches was compared using mean squared error (MSE), root-mean-squared error (RMSE), median absolute deviation (MAD), deviance, and Akaike information criteria (AIC). Results The longitudinal regression tree algorithm outperformed based on the criteria such as MSE, RMSE, and MAD than the linear mixed-effects model (LMM) for analyzing the TCGS and simulated data using the missing at random (MAR) mechanism. Overall, based on fitting the non-parametric model, the performance of the 27 imputation approaches was nearly similar. However, the SI traj-mean method improved performance compared with other imputation approaches. Conclusion Both SI and MI approaches performed better using the longitudinal regression tree algorithm compared with the parametric longitudinal models. Based on the results from both the real and simulated data, we recommend that researchers use the traj-mean method for imputing missing values of longitudinal data. Choosing the imputation method with the best performance is widely dependent on the models of interest and the data structure.

Background Multiple imputation is frequently used to address missing data when conducting statistical analyses. There is a paucity of research into the performance of multiple imputation when the prevalence of missing data is very high. Our objective was to assess the performance of multiple imputation when estimating a logistic regression model when the prevalence of missing data for predictor variables is very high. Methods Monte Carlo simulations were used to examine the performance of multiple imputation when estimating a multivariable logistic regression model. We varied the size of the analysis samples ( N  = 500, 1,000, 5,000, 10,000, and 25,000) and the prevalence of missing data (5–95% in increments of 5%). Results In general, multiple imputation performed well across the range of scenarios. The exceptions were in scenarios when the sample size was 500 or 1,000 and the prevalence of missing data was at least 90%. In these scenarios, the estimated standard errors of the log-odds ratios were very large and did not accurately estimate the standard deviation of the sampling distribution of the log-odds ratio. Furthermore, in these settings, estimated confidence intervals tended to be conservative. In all other settings (i.e., sample sizes > 1,000 or when the prevalence of missing data was less than 90%), then multiple imputation allowed for accurate estimation of a logistic regression model. Conclusions Multiple imputation can be used in many scenarios with a very high prevalence of missing data.