Multiple imputation for longitudinal data: A tutorial (2404.06967v1)

Abstract: Longitudinal studies are frequently used in medical research and involve collecting repeated measures on individuals over time. Observations from the same individual are invariably correlated and thus an analytic approach that accounts for this clustering by individual is required. While almost all research suffers from missing data, this can be particularly problematic in longitudinal studies as participation often becomes harder to maintain over time. Multiple imputation (MI) is widely used to handle missing data in such studies. When using MI, it is important that the imputation model is compatible with the proposed analysis model. In a longitudinal analysis, this implies that the clustering considered in the analysis model should be reflected in the imputation process. Several MI approaches have been proposed to impute incomplete longitudinal data, such as treating repeated measurements of the same variable as distinct variables or using generalized linear mixed imputation models. However, the uptake of these methods has been limited, as they require additional data manipulation and use of advanced imputation procedures. In this tutorial, we review the available MI approaches that can be used for handling incomplete longitudinal data, including where individuals are clustered within higher-level clusters. We illustrate implementation with replicable R and Stata code using a case study from the Childhood to Adolescence Transition Study.

• The paper demonstrates that multiple imputation methods, including joint modelling and FCS, effectively manage missing data in longitudinal studies.
• It highlights the need to align imputation models with analysis models to correctly address non-linearities and interactions.
• The study uses practical R and Stata examples to compare standard and advanced MI approaches, detailing computational challenges in hierarchical data.

Analyzing Multiple Imputation Techniques for Longitudinal Data

The paper "Multiple Imputation for Longitudinal Data: A Tutorial" by Wijesuriya et al. offers a thorough overview of methodologies applicable for handling missing data in longitudinal studies. The authors address the specific challenges posed by correlated data across time points and demonstrate both established and cutting-edge multiple imputation (MI) approaches using case studies programmed in R and Stata.

Longitudinal studies collect data over several waves from the same subjects, which typically results in correlated observations within individuals. A major complication in such research designs is the management of missing data, particularly as participation often dwindles over time. MI, which employs a process of replacing missing values through predictions based on observed data, is a prevalent method for addressing this problem. Properly executed, it accounts for the correlation within individuals while remaining compatible with the subsequent substantive analysis.

The authors review traditional methods such as Joint Modelling (JM) and Fully Conditional Specification (FCS), as well as complex new strategies that consider clustering at multiple levels (e.g., individuals within schools). Special attention is paid to how imputation aligns with the analysis model to ensure valid inferences, especially when handling non-linear terms or interactions.

In terms of practical recommendations, the paper brings to light several MI approaches:

• Standard JM and FCS: These approaches handle missing values under the assumption that the propensity to miss does not depend on unobserved data, frequently facilitating unbiased estimates when conditions such as the missing at random (MAR) assumption hold. JM models missing variables jointly while FCS sequentially fills in missing data.
• LMM-based Approaches: Useful for unbalanced datasets, these methods involve modeling the covariance structure of data via linear mixed models (LMMs), explicitly accounting for both time-varying and time-fixed variables. However, these methods necessitate parametric assumptions about distribution, which can be risky if inaccurately specified.
• Extensions to Handle Clustering: The growth of longitudinal studies involving hierarchical data structures prompts the need for methods such as Dummy Indicator (DI) or further LMM integrations, which manage data correlation at additional cluster levels, like schools or other groupings.

Simulation studies underscore that while techniques like JM-1L-wide and FCS-1L-wide maintain reliable estimates under typical scenarios, convergence issues can arise when datasets have high proportions of missing data or high inter-variable correlation. Moreover, methods that extend DI and LMM to interactive or complex settings — like those with random slopes — expose potential biases under certain configurations, calling for cautious use or the adoption of Substantive Model Compatible (SMC) MI approaches.

The paper contributes significantly to longitudinal data analysis by mapping out the myriad avenues and considerations involved in MI, particularly for researchers seeking accurate model-data compatibility. Looking forward, future improvements in MI methodologies, especially those available in mainstream statistical software, will likely focus on improving computational efficiency, robustness, and more intuitive error checking or warnings.

Through precise code illustrations and comprehensive reviews, this paper serves as both a guide and an impetus for further research and uptake of MI techniques among data analysts and statisticians working with longitudinal datasets.