On Generalized Log‐Logistic Model for Censored Survival Data

In the analysis of survival data with parametric models, it is well known that the Weibull model is not suitable for modeling cases where the hazard rate is non‐monotonic. For such cases, log‐logistic model is frequently used. However, due to the symmetric property of the log‐logistic model, it may be poor for the cases where the hazard rate is skewed or heavily tailed. In this paper, we suggest a generalization of the log‐logistic model by introducing a shape parameter. This generalized model is then applied to fit the lung cancer data of Prentice (1973). The results seem to improve over those obtained by using the log‐logistic model.