Non-linear regression models for imputing longitudinal missing data

The state-of-the-art literature has largely accepted multivariate imputation techniques such as multiple imputation using chained equations (MICE) [1], [2]. The MICE model is primarily proposed to impute missing values in cross-sectional data. However, the time varying nature of longitudinal data has not been fully modeled in traditional imputation methods [3], [4]. We have speculated two issues with MICE model and proposed a new approach to address these issues. First, the chained equations used in MICE are linear regression models. The performance of non-linear regression models has not been well sought in the literature. Second, the regression models of MICE may yield estimates of missing values that are out of bounds or range of normalization. This phenomenon eventually affects the overall imputation performance. In this study, we propose three methods for imputing longitudinal data: 1) an unsupervised method using piece-wise interpolation, 2) supervised non-linear regression models, and 3) an integration of the proposed unsupervised and supervised methods in a hybrid imputation pipeline.