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All Journal CAUCHY: Jurnal Matematika Murni dan Aplikasi
Deby Victoria
Universitas Airlangga
Mathematics

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Two-Parameter Exponential Estimation via EM Algorithm: Uterine Leiomyosarcoma Survival Risk Analysis Ardi Kurniawan; Deby Victoria; Christabel Lee Angie Sugianto
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 1 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i1.41855

Abstract

Accurate survival prognosis is critical for clinical decision-making, yet analyzing censored on cological data remains a statistical challenge. This study aims to implement the Expectation Maximization (EM) algorithm for the two-parameter exponential distribution to estimate parameters and forecast extreme survival risks in uterine leiomyosarcoma (uLMS). Using clinical data from 122 patients, the EM algorithm achieved rapid convergence after 19 it erations, yielding a scale parameter of 68.7037 months and a 2-month survival threshold. Statistical validity was confirmed by a Kolmogorov-Smirnov test (p = 0.2084) and a 94.5% coverage probability from Monte Carlo simulations. A key contribution of this research is the integration of Value-at-Risk (VaR) and Tail Value-at-Risk (TVaR) metrics, which identified a 95% survival threshold of 207.82 months. Sensitivity analysis further demonstrated the es timator’s structural stability across varying censoring proportions. These results signify that the proposed framework provides a robust and reliable tool for quantifying extreme survival probabilities, offering clinicians a sophisticated method for long-term risk management and personalized patient prognosis.
Co-Authors Ardi Kurniawan Christabel Lee Angie Sugianto