Arctan-type Chen-Inspired Probability Distribution for Survival and Reliability Modelling: Bayesian and Classical Approaches with Applications to Cancer Remission Data

Abstract

This study introduces an Arctan-type Chen-inspired probability distribution (ATCI) by incorporating a new shape parameter  δ to increase the flexibility of survival/reliability modeling. Both Bayesian and classical analysis with MCMC sampling (8 chains and 150000 iterations) are applied. The model is applied to a real dataset of 128 remission-time observations from bladder cancer patients and demonstrates significant improvements over the Chen and Lomax distribution with a WAIC = 824.52, representing a reduction of 6.42 compared to Exponential (830.97) and a reduction of 8.59 compared to Log-Normal (835.17). The proposed model handles tied events (5% duplicate events), effectively capturing non-monotonic hazard rates, and is validated under 14 diagnostic plots. Results indicate that ATCI provides a close fit to empirical data, yielding a mean survival time (MST) of 9.50 months (95% CI: 7.78 - 11.62) and Kaplan-Meier median survival time (MST50) of 6.39 months, highlighting its clinical interpretability. The ATCI model also shows strong posterior predictive checks (KS = 0.099, p-value = 0.155). Reliable parameter convergence (\(\hat{R} < 1.01\); E \(> 1689\)) confirms model stability, and comparison with the Kaplan-Meier survival curve confirms the validity of the proposed model. ATCI model offers prognostic insights and maintenance scheduling in engineering and warranty analysis are among its practical applications, making it a suitable model for systems or populations exhibiting time-dependent event mechanisms. Open-source R and JAGS are used for analysis. MCMC with 8 chains of 150K iterations converged in ~47 min (ESS >1689, \(\hat{R} < 1.01\)) on standard hardware.