Poisson-Exponential Distribution Approach to Survival Analysis of Right-Censored Data of Lung Cancer Patients

Survival analysis of lung cancer patients is essential for understanding the dynamics of their survival probabilities over time. The Poisson–Exponential (PE) distribution is particularly relevant for data involving complementary risks and right-censoring, and it provides a framework for comparing different parameter estimation approaches. This study aims to estimate the parameters of the PE distribution for the survival times of lung cancer patients treated at Dr. Wahidin Sudirohusodo Hospital, Makassar, in 2015, and to compare the performance of two estimation methods: Maximum Likelihood Estimation (MLE) and Maximum Product Spacing (MPS). Parameter estimation was conducted numerically using the Newton–Raphson algorithm, resulting in and . The survival probabilities decline as survival time increases, and both the PE–MLE and PE–MPS curves closely follow the Kaplan–Meier estimator. All information criteria indicate that MPS outperforms MLE, as reflected by a higher log-likelihood and lower AIC, AICc, and CAIC values. These findings demonstrate that the PE distribution is suitable for modeling the survival dynamics of lung cancer patients, with MPS identified as the most appropriate parameter estimation method for the analyzed dataset.