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Mixture of multivariate t nonlinear mixed models for multiple longitudinal data with heterogeneity and missing values

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Abstract

The multivariate t nonlinear mixed-effects model (MtNLMM) has been shown to be effective for analyzing multi-outcome longitudinal data following nonlinear growth patterns with fat-tailed noises or potential outliers. This paper considers the problem of clustering heterogeneous longitudinal profiles in a mixture framework of MtNLMM. A finite mixture of multivariate t nonlinear mixed model is proposed, and this new model allows accommodating more complex features of longitudinal data. Intermittent missing values frequently occur in the data collection process of multiple repeated measures. Under a missing at random mechanism, a pseudo-data version of the alternating expectation-conditional maximization algorithm is developed to carry out maximum likelihood estimation and impute missing values simultaneously. The techniques for clustering of incomplete multiple trajectories, recovery of missing responses, and allocation of future subjects are also investigated. The practical utility is demonstrated through a real data example coming from a study of 124 normal and 37 abnormal pregnant women. Simulation studies are provided to validate the proposed approach.

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Acknowledgements

The author would like to express her deepest gratitude to the Co-Editor, the Associate Editor and two anonymous reviewers for their insightful comments and suggestions that greatly improved this paper. This research was supported by MOST 107-2628-M-035-001-MY3 awarded by the Ministry of Science and Technology of Taiwan.

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  1. Department of Statistics, Graduate Institute of Statistics and Actuarial Science, Feng Chia University, Taichung, 40724, Taiwan

    Wan-Lun Wang

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Correspondence to Wan-Lun Wang.

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Wang, WL. Mixture of multivariate t nonlinear mixed models for multiple longitudinal data with heterogeneity and missing values. TEST 28, 196–222 (2019). https://doi.org/10.1007/s11749-018-0612-4

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