Multiple imputation methods for handling incomplete longitudinal and clustered data where the target analysis is a linear mixed effects model

Abstract

Multiple imputation (MI) is increasingly popular for handling multivariate missing data. Two general approaches are available in standard computer packages: MI based on the posterior distribution of incomplete variables under a multivariate (joint) model, and fully conditional specification (FCS), which imputes missing values using univariate conditional distributions for each incomplete variable given all the others, cycling iteratively through the univariate imputation models. In the context of longitudinal or clustered data, it is not clear whether these approaches result in consistent estimates of regression coefficient and variance component parameters when the analysis model of interest is a linear mixed effects model (LMM) that includes both random intercepts and slopes with either covariates or both covariates and outcome contain missing information. In the current paper, we compared the performance of seven different MI methods for handling missing values in longitudinal and clustered data in the context of fitting LMMs with both random intercepts and slopes. We study the theoretical compatibility between specific imputation models fitted under each of these approaches and the LMM, and also conduct simulation studies in both the longitudinal and clustered data settings. Simulations were motivated by analyses of the association between body mass index (BMI) and quality of life (QoL) in the Longitudinal Study of Australian Children (LSAC). Our findings showed that the relative performance of MI methods vary according to whether the incomplete covariate has fixed or random effects and whether there is missingnesss in the outcome variable. We showed that compatible imputation and analysis models resulted in consistent estimation of both regression parameters and variance components via simulation. We illustrate our findings with the analysis of LSAC data.

Evaluation of approaches for multiple imputation of three-level data

“…However, our results are consistent with those from similar studies conducted in a two-level setting. In particular, Huque et al (2018) and Huque et al(2019) showed that the single-level JM and FCS approaches which impute the repeated measures in wide format to account for the clustering of repeated measures (labelled JM-mvni and FCS-standard in their study) performed well compared to several generalized linear mixed model (GLMM) based approaches for handling incomplete longitudinal data [47,57]. Our results are also consistent with the simulations result of , who showed that the two-level MI application in Blimp resulted in regression coefficients with negligible bias even in small samples with large proportions of missing data and minimal bias for the variance component estimates for a random intercept model [30].…”

“…However, caution should be taken when generalizing these results to more complex analysis models, for example multilevel analysis models with random slopes and/or interaction terms. It would be interesting to compare the possible approaches in the context of a random slope model because it is likely that the performance of these approaches are quite different [57]. With random slopes, the single-and two-level imputation models with extensions, particularly those which use DIs, might lead to biased estimates and can often be infeasible with a large number of clusters [58].…”

Imputation of missing values for electronic health record laboratory data

“…When comparing monotone to FCS imputation with the Monte Carlo iterative procedure, we always observed better performance with FCS. We also compared the cross-sectional imputation (PMM) to multi-level multivariate imputation such as 2l.pan (FCS-LMM) or 2 l.norm (FCS-LMM-het), which was based on an assumption of homogenous or heterogeneous within-group variances respectively 18 , 29 . Our analysis showed that when the imputed data was out of the normal range, higher variation may have increased the within- and between -imputation variance but did not improve the prediction accuracy.…”

Using linear and natural cubic splines, SITAR, and latent trajectory models to characterise nonlinear longitudinal growth trajectories in cohort studies

“…With incomplete covariates, bias can occur when the probability of excluding an individual with missing covariate data is related to the outcome. Regardless of bias, excluding individuals with missing covariate information will often mean discarding useful observed data, leading to imprecision [64].…”