Comparison of Missing Value Imputation Methods for Longitudinal Data: Mathematical Formulations and Simulation Performance

Longitudinal studies frequently suffer from missing data due to attrition, missed visits, or unmeasured events. Standard complete-case analysis compromises statistical power and introduces severe parameter bias under non-random missingness. This paper provides a rigorous mathematical framework and experimental evaluation comparing six imputation approaches for longitudinal numerical data: Last Observation Carried Forward (LOCF), Linear Interpolation, Mean Imputation, K-Nearest Neighbors (KNN), Expectation-Maximization (EM) using multivariate normal parameters, and Multiple Imputation by Chained Equations (MICE) with linear mixed-effects modeling. We formalize each method mathematically within a repeated-measures context and evaluate performance across Missing Completely at Random (MCAR) and Missing at Random (MAR) mechanisms at missingness rates of 10%, 25%, and 40%. Performance is benchmarked using Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), Bias, and Coverage Probability of the fixed-effects trajectory parameters in a linear mixed model (LMM). A fully reproducible simulation script written in R is provided to execute the benchmark and visualize parameter recovery.

Longitudinal Data Analysis, Missing Data, Multiple Imputation, MICE, Linear Mixed-Effects Models, Expectation-Maximization, Simulation Benchmark.

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