On Maximum Likelihood Estimation of Mixed Cure Fraction Model Assuming Stable Distribution
In the analysis of survival data, the models used to estimate the cure rate of many diseases (especially cancer diseases) and the survival time distribution of uncured patients are called the cure rate models. In these models, few people will encounter special situations that involve the problem of model assumptions, especially the extreme values and censoring rate during the study period. Therefore, this paper proposes a method that can use a stable distribution family, namely "log-Cauchy" as an alternative cure rate model for right-censored survival data, which is different from the commonly studied exponential, Gamma, Weibull, and Lognormal distributions.
The maximum likelihood method estimates the model parameters in the log Cauchy mixed cure rate model. The simulation results and the analysis results of the breast cancer data set show that when the censoring rate is high, the log-Cauchy distribution is the best in parameter estimation and model fitting.
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