MIFuzzy Clustering for Incomplete Longitudinal Data in Smart Health

Abstract

Missing data are common in longitudinal observational and randomized controlled trials in smart health studies. Multiple-imputation based fuzzy clustering is an emerging non-parametric soft computing method, used for either semi-supervised or unsupervised learning. Multiple imputation (MI) has been widely-used in missing data analyses, but has not yet been scrutinized for unsupervised learning methods, although they are important for explaining the heterogeneity of treatment effects. Built upon our previous work on MIfuzzy clustering, this paper introduces the MIFuzzy concepts and performance, theoretically, empirically and numerically demonstrate how MI-based approach can reduce the uncertainty of clustering accuracy in comparison to non- and single-imputation based clustering approach. This paper advances our understanding of the utility and strength of MIFuzzy clustering approach to processing incomplete longitudinal behavioral intervention data.

Keywords: Fuzzy clustering; MIFuzzy; Missing values; Multiple imputation; longitudinal data.

Fig. 1

Conceptual diagram of MI-Fuzzy procedure

Fig. 2

An illustration of mean-imputation

Fig. 3

Clustering accuracy of single regression imputation

Fig. 4

Clustering accuracy of single hotdeck imputation

Fig. 5

Clustering accuracy of multiple imputation

Fig. 6

Performance of MI-, SI- and NI-clustering on TDTA data

Fig. 7

Performance of MI-, SI- and NI-clustering on QP data

Fig. 8

MI- vs. SI- and NI-clustering under MCAR

Fig. 9

MI- vs. SI- and NI-clustering under MAR

Fig. 10

MI- vs. SI- and NI-clustering under MNAR