The Log-New Generalized Odd Fréchet-Weibull Distribution: Theory, Survival Regression, and Applications to Cervical Cancer and Radiation Data

Abstract

Radiation-response and cancer-survival data often exhibit skewness, complex hazard structures, and heterogeneous covariate effects that may not be adequately represented by conventional lifetime distributions. This study develops the Log-New Generalized Odd Fréchet-Weibull (log-NGOF-W) distribution and its survival regression extension, the log-NGOF-Weibull survival regression (log-NGOF-WSR) model, to provide a flexible framework for modelling such data. The mathematical contribution is the formulation and investigation of a new log-transformed lifetime distribution and its regression structure, including their inferential and diagnostic properties. The proposed distribution is applied to three radiation datasets: F1 adult counts in peppermint packets, F1 adult susceptibility index, and feeding duration of Stegobium paniceum. The model provides competitive fits across the datasets, although the best-fitting distribution varies by dataset. For cervical cancer, survival data from 347 patients treated at Ahmadu Bello University Teaching Hospital, Zaria, were analysed using the log-NGOF-WSR, log-NGOF-Et-WSR, and log-WSR models. The log-NGOF-WSR model had the lowest AIC (348.63) and BIC (460.26), compared with 449.62 and 565.10 for log-NGOF-Et-WSR and 366.52 and 466.61 for log-WSR, respectively. At the 5% significance level, smoking history, family history, miscarriage, visitation, chemotherapy courses, treatment type, cancer stage, and age showed statistically significant associations with survival in the fitted model. These findings represent statistical associations rather than causal effects. The proposed framework provides a useful parametric alternative for lifetime and survival modelling, while its fully parametric assumptions, sensitivity to model specification and estimation, and validation on additional datasets warrant further investigation.