A new survival model with surviving fraction: An application to colorectal cancer data

We propose a new survival model for lifetime data in the presence of surviving fraction and obtain some of its properties. Its genesis is based on extensions of the promotion time cure model, where an extra parameter controls the heterogeneity or dependence of an unobserved number of lifetimes. We construct a regression model to evaluate the effects of covariates in the cured fraction. We discuss inference aspects for the proposed model in a classical approach, where some maximum likelihood tools are explored. Further, an expectation maximization algorithm is developed to calculate the maximum likelihood estimates of the model parameters. We also perform an empirical study of the likelihood ratio test in order to compare the promotion time cure and the proposed models. We illustrate the usefulness of the new model by means of a colorectal cancer data set.