A new regression model under informative censoring mechanism with applications

The choice of the censoring mechanism is very important when we are analyzing survival data because, in some practical situations, there is a dependence between the failure and censoring times, contradicting the assumption of non informative censoring. The present article proposes a censored-data regression in the presence of informative censoring based on the generalized odd log-logistic family of distributions under two systematic components. The proposed model is based on the assumption that failure and censoring times are conditionally independent given a frailty. The choice of the widespread odd log-logistic family for failure and censoring times is justified by the fact that it generalizes some distributions already consolidated in the area of survival and, concomitantly, by the fact that it offers great flexibility in data modeling in practice, in addition to the capacity to present various forms of the risk function, among them, bimodal. The maximum likelihood method is used to estimate the model parameters. For different parameter configurations and sample sizes, some simulations are performed to analyze the behavior of the maximum likelihood estimates. Two real data applications illustrate the usefulness of the proposed survival regression with informative censoring.