BAREKENG: Jurnal Ilmu Matematika dan Terapan
Vol 20 No 4 (2026): BAREKENG: Journal of Mathematics and Its Application

SURVIVAL TIME MODELING IN HEMODIALYSIS PATIENTS USING A WEIBULL MIXTURE PROPORTIONAL HAZARDS MODEL

Rahida Rihhadatul Aisy (Department of Statistics, Faculty of Science and Data Analytics, Institut Teknologi Sepuluh Nopember, Indonesia)
Nur Iriawan (Department of Statistics, Faculty of Science and Data Analytics, Institut Teknologi Sepuluh Nopember, Indonesia)
Shofi Andari (Department of Statistics, Faculty of Science and Data Analytics, Institut Teknologi Sepuluh Nopember, Indonesia)
Mayta Rithmala (Jemursari Islamic Hospital, Indonesia)
Yani Sumartin (Jemursari Islamic Hospital, Indonesia)



Article Info

Publish Date
24 Aug 2026

Abstract

Hemodialysis is a critical treatment for patients with end-stage chronic kidney disease (CKD). Although it is associated with a higher risk of mortality and complications compared to other renal treatment choices, many patients prefer hemodialysis as their renal replacement therapy. Traditional parametric survival models often struggle to capture the complexity of the distribution due to multimodal survival data in heterogeneous populations, such as hemodialysis patients. To overcome this, mixture models provide greater flexibility by combining several distributions to better reflect latent survival patterns. This study investigates mortality risk factors by applying a Bayesian Weibull mixture proportional hazards model to 151 hemodialysis patients from one hospital in Surabaya, Indonesia, in 2024, with data extracted from medical hospital records. The Expectation-Maximization and No-U-Turn Sampler (EM-NUTS) approach was used to estimate model parameters and latent class memberships. The Expectation-Maximization (EM) approach, originally developed for control charts and time series, was adapted for survival analysis to address latent heterogeneity. Exploratory analysis reveals multimodal survival distributions, suggesting distinct risk groups. Model selection using the Bayesian Information Criterion and the Akaike Information Criterion identified two latent groups with distinct risk profiles. In the first group, male gender and diabetes significantly increased mortality risk, while hypertension had a smaller effect. In the second group, hypertension was the dominant risk factor, with less influence from gender and diabetes. These findings emphasize the importance of accounting for population heterogeneity in the survival analysis of hemodialysis patients. The use of advanced Bayesian mixture models with EM-NUTS estimation provides robust tools for uncovering hidden subgroups and improving risk stratification, allowing for more personalized treatment strategies in CKD care.

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Journal Info

Abbrev

barekeng

Publisher

Subject

Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Energy Engineering Mathematics Mechanical Engineering Physics Transportation

Description

BAREKENG: Jurnal ilmu Matematika dan Terapan is one of the scientific publication media, which publish the article related to the result of research or study in the field of Pure Mathematics and Applied Mathematics. Focus and scope of BAREKENG: Jurnal ilmu Matematika dan Terapan, as follows: - Pure ...