A flexible bimodal model with long-term survivors and different regression structures

Abstract

The cure fraction models are useful to model lifetime data with long-term survivors. In this paper, we introduce a flexible cure rate survival model where the model parameters are related to covariates in different regression structures. The regression model allows to model jointly the location, scale and shape effects. The maximum likelihood method is employed to estimate the model parameters. We provide Monte Carlo simulation experiments to verify the performance of the maximum likelihood estimates for different sample sizes and cure rate percentages. Furthermore, some diagnostic measures to assess departures from model assumptions as well as to detect outlying observations are also considered. Finally, applications to real data are presented to show the usefulness of the new cure rate model.

Keywords:

• Bi-modality
• Cure rate models
• Parametric inference
• Residual analysis
• Sensitivity analysis

Acknowledgments

The authors acknowledge the financial support from the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq/Brazil). We are very grateful to two anonymous reviewers for their helpful comments.