Cluster Analysis on Longitudinal Data of Patients with Kidney Dialysis using a Smoothing Cubic B-Spline Model

Abstract

Longitudinal data analysis is gaining prominence, particularly in medicine and economics. This research centers on collecting and analyzing longitudinal data, specifically cluster analysis. The thesis emphasizes the nonparametric cubic B-spline model, known for its smoothness, flexibility, and ability to capture intricate patterns and data fluctuations due to the continuity of its derivatives. The penalization method was employed to accomplish clustering. It categorizes longitudinally balanced data by penalizing the pairwise distances between cubic B-spline model coefficients using a penalization function, such as the recently devised concave penalization function. The cubic spline penalty CSP, part of the pair distance penalty, employs the nonparametric pairwise grouping (NPG) method. Model selection criteria, like Bayesian Information Criteria (BIC), help determine the number of clusters. Optimization methods, including the alternative direction method of the multiplier ADMM algorithm, are applied to approximate solutions within the R statistical program. A simulation study generated balanced longitudinal data for 60 and 100 subjects with ten replicates each. The experiments demonstrated the effectiveness of the CSP penalty function in the clustering process. For practical application, the study involved the analysis of data from kidney failure patients collected from Ibn Sina Teaching Hospital for Dialysis in Mosul over seven consecutive months in 2023. The NPG aggregation method and CSP penalty functions were used, resulting in two groups based on the glomerular filtration rate of the kidneys. According to medical criteria, this rate determines the required dialysis frequency twice a week or thrice.