Bayesian and Frequentist Approach for the Mixture Cure Models with Generalized Log-logistic Baseline: An Application to Cancer Data

Abstract

Most event-data studies assume that everybody involved in the study will eventually encounter an instance of interest; nevertheless, it is anticipated that some of these participants will be exposed to the event. Cure models are frequently employed in time-to-event analysis to handle this data type. In mixed cure models, the target population is considered a mix of susceptible and non-susceptible individuals. The statistical analysis of these models provides the probability of cure (incidence model) and time-to-event in the vulnerable sub- population (delay model). This research presented a maximum likelihood estimate (MLE) and a Bayesian analysis for the six-parameter Generalized Log-Logistic (GLL) mixture cure model with cured, censored, and covariate variables. A mixture cure model with a GLL baseline is proposed to account for the rate of cured participants in the analysis. To apply various parametric hazard-based regression models, we recommend the GLL baseline distribution, which is based on a reasonable baseline hazard. The recommended model performs well on real-world data sets, highlighting the need for adaptive parametric regression formulations with time-dependent and time-independent covariates to assess hazard function and rate across time. Bayesian survival analysis with a non-informative prior outperformed the MLE method in terms of simulation parameter bias. The Generalized Log-Logistic model fits real cancer data better than the other survival models.