Abstract
BackgroundMissing data is a common problem in epidemiological studies, and is particularly prominent in longitudinal data, which involve multiple waves of data collection. Traditional multiple imputation (MI) methods (fully conditional specification (FCS) and multivariate normal imputation (MVNI)) treat repeated measurements of the same time-dependent variable as just another ‘distinct’ variable for imputation and therefore do not make the most of the longitudinal structure of the data. Only a few studies have explored extensions to the standard approaches to account for the temporal structure of longitudinal data. One suggestion is the two-fold fully conditional specification (two-fold FCS) algorithm, which restricts the imputation of a time-dependent variable to time blocks where the imputation model includes measurements taken at the specified and adjacent times. To date, no study has investigated the performance of two-fold FCS and standard MI methods for handling missing data in a time-varying covariate with a non-linear trajectory over time – a commonly encountered scenario in epidemiological studies.MethodsWe simulated 1000 datasets of 5000 individuals based on the Longitudinal Study of Australian Children (LSAC). Three missing data mechanisms: missing completely at random (MCAR), and a weak and a strong missing at random (MAR) scenarios were used to impose missingness on body mass index (BMI) for age z-scores; a continuous time-varying exposure variable with a non-linear trajectory over time. We evaluated the performance of FCS, MVNI, and two-fold FCS for handling up to 50% of missing data when assessing the association between childhood obesity and sleep problems.ResultsThe standard two-fold FCS produced slightly more biased and less precise estimates than FCS and MVNI. We observed slight improvements in bias and precision when using a time window width of two for the two-fold FCS algorithm compared to the standard width of one.ConclusionWe recommend the use of FCS or MVNI in a similar longitudinal setting, and when encountering convergence issues due to a large number of time points or variables with missing values, the two-fold FCS with exploration of a suitable time window.
Highlights
Introduction of missing dataFor each simulated dataset, bmiz measures were assigned to missing so by wave 5, 25% and 50% of these were missing
The root mean square error increased with the proportion of missingness, and for missing at random (MAR) compared with missing completely at random (MCAR), and multiple imputation (MI) methods showed a gain in root mean square error under the strong MAR scenario with 50% missing data
We evaluated the performance of MI methods, Multivariate normal imputation (MVNI), Fully conditional specification (FCS) and two-fold FCS, and complete case analysis for handling up to 50% missing data in a longitudinal exposure variable which had a non-linear association with time, using a simulation study designed based on the Longitudinal Study of Australian Children (LSAC) child cohort
Summary
Introduction of missing dataFor each simulated dataset, bmiz measures were assigned to missing so by wave 5, 25% and 50% of these were missing (keeping bmiz at wave 1 as complete). Epidemiological research has witnessed a major shift towards life-course studies which investigate how biological, behavioural, and physical exposures during gestation, childhood and adolescence are related to the development of disease in adulthood [1, 2] Such studies involve following up individuals over a long period of time, with multiple waves of data collection, and missing data are a major problem [3]. Common approaches include complete case analyses and multiple imputation (MI) [5] Another approach for longitudinal data is last observation carried forward; this method has been shown to result in biased inference [6,7,8]. MI enables all participants to be included in the analysis and may reduce bias and improve precision of the parameter estimates compared to a complete case analysis [9, 11]
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