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All Journal Journal of Mathematics and Scientific Computing With Applications
Idrus Syahzaqi
Department of Mathematics, Universitas Airlangga, Surabaya, Indonesia
Mathematics

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PARAMETRIC SURVIVAL ANALYSIS OF TESTICULAR CANCER USING AN EXPONENTIAL MODEL WITH TYPE I CENSORED DATA Idrus Syahzaqi; Ardi Kurniawan; Valerina Marischa Usmarasima; Aurora Gie Nur Wahyudi; Muhamad Zaky Ramadhani; Nuzzulia Calvina Izumy
Journal of Mathematics and Scientific Computing With Applications Vol. 7 No. 1 (2026)
Publisher : Pena Cendekia Insani

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.53806/jmscowa.v7i1.1509

Abstract

Quantitative prognostic evaluation is essential for testicular cancer, yet standard analyses often overlook model assumptions. This study evaluates patient survival times using a parametric exponential model under a type I censoring structure (n = 134, from cBioPortal). Parameter estimation via Maximum Likelihood Estimation yielded 82 uncensored and 52 censored observations. The Anderson-Darling test (p = 0.067) indicated statistical adequacy for the exponential distribution while the Weibull distribution was rejected (p < 0,010), confirming the assumption of a constant hazard, estimating a Mean Time to Failure of 64,54 months with a constant hazard rate of 0.0155 per month. However, these model-based estimates face critical clinical limitations. The small sample size and the rigid assumption of a constant hazard fail to capture the dynamic, time-varying biological progression of cancer. While this parametric approach provides a simplified baseline, clinical conclusions must be drawn cautiously; future research requires larger cohorts and flexible, non-constant hazard models to ensure actual clinical generalizability.
TYPE II CENSORED EXPONENTIAL DISTRIBUTION FOR ESTIMATING SURVIVAL AND LIFE EXPECTANCY IN BLADDER CANCER PATIENTS Idrus Syahzaqi; Ardi Kurniawan; Nazwa Salsabila; Dinar Rahma Fauzia; Diah Ayu Nofitasari
Journal of Mathematics and Scientific Computing With Applications Vol. 7 No. 1 (2026)
Publisher : Pena Cendekia Insani

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.53806/jmscowa.v7i1.1600

Abstract

Bladder cancer incidence and mortality continue to rise, yet global studies on bladder cancer survival prediction remain dominated by nomogram and Cox regression-based approaches overlooking Type II censoring. Using secondary data from 80 bladder cancer patients (48 uncensored, 32 Type II censored) from a public cBioPortal repository, this study applied the Type II censored exponential distribution, selected for its memoryless property and constant hazard rate, to estimate the survival function, hazard function, confidence interval, and Mean Time to Failure (MTTF). Descriptive statistics, a goodness-of-fit test, and maximum likelihood estimation were applied. The data followed an exponential distribution with a mean survival time of 33.95 months, an estimated parameter of 38.01 months, a hazard rate of 0.026, and an MTTF of 38.02 months, with a 95% CI of 29.35-51.56 months. These findings offer preliminary insight relevant to clinical decision-making and SDG Target 3.4 on reducing premature mortality from non-communicable diseases.
Co-Authors Ardi Kurniawan Aurora Gie Nur Wahyudi Diah Ayu Nofitasari Dinar Rahma Fauzia Muhamad Zaky Ramadhani Nazwa Salsabila Nuzzulia Calvina Izumy Valerina Marischa Usmarasima