Non-proportional hazards model with a frailty term: Application with a melanoma dataset - Rosa, Karen Cristine Ferreira (2021)
In the modeling of survival data, commonly, the traditional semiparametric Cox regression model is fitted to the dataset due to its ease of interpretation, as long as the hazard rates for two individuals do not vary over time. However, in some situations, the proportionality assumption of the hazards can not be valid. In medical studies, it is expected that a fraction of units do not become susceptible to the event of interest (death or recurrence), even if a sufficiently large time was accompanied, e.g., the so-called long-term survivors. There are several cure rate models available in the literature. Here, we propose the generalized time-dependent complement log-log (CLL) model with a power variance function (PVF) frailty term introduced in the hazard function to control the amount of unobservable heterogeneity in the sample the possibility of long-term survivors. The maximum likelihood estimation procedure reaches the parameter estimation, and we evaluate the performance of the proposed models using Monte Carlo simulation studies. The proposed models practical relevance is illustrated by applying a dataset on patients diagnosed with skin cancer in the state of São Paulo, Brazil.