Poisson-Gamma Trigonometric Families of Cure Fraction Models: Estimation and Analysis of Cancer Data

Abstract

Sustainable Development Goal 3 has established clear targets to combat noncommunicable diseases (NCDs) such as cancer and cardiovascular diseases among others by the year 2030. A handy technique to study cancer progression is to analyze patient survival over time to obtain precise results to enable for the establishment of cancer control mechanisms. The use of cure rate models for analyzing survival data with cured elements is more desirable than the standard survival analysis models. This study formulated the Poisson-gamma trigonometric families of cure rate models under the competing risks setup based on the Poisson-gamma cure rate model and the trigonometric families of distributions. Four special models are obtained from the proposed families. Maximum likelihood estimation technique was utilized for estimating the parameters of the developed families. The cure rate families are parameterized in terms of the cure term and diverse link functions such as logit, cauchit, Aranda-Ordaz, and skewed logit are utilized to determine the effects of covariates. Monte Carlo simulation study was conducted to determine the behavior of the maximum likelihood estimator. The applications of the proposed models were finally established using myeloma and acute myeloid leukemia datasets. The study revealed that the proposed cure rate models provided better fit to the cancer datasets compared with the candidate models.