Promotion time cure model with generalized Poisson-Inverse Gaussian Distribution

In the survival data with Long-term survivors the event has not occurred for all the patients despite long-term follow-up, so the survival time for a certain percent is censored at the end of the study. Mixture cure model was introduced by Boag, 1949 for reaching a more efficient analysis of this set of data. Because of some disadvantages of this model non-mixture cure model was introduced by Chen, 1999, which became well-known promotion time cure model. This model was based on the latent variable distribution of N. Non mixture cure models has obtained much attention after the introduction of the latent activating Scheme of Cooner, 2007, in recent decades, and diverse distributions have been introduced for latent variable.
Methods & Materials: In this article, generalized Poisson- inverse Gaussian distribution (GPIG) will be presented for the latent variable of N, and the novel model which is obtained will be utilized in analyzing long-term survival data caused by skin cancer. To estimate the model parameters with Bayesian approach, numerical methods of Monte Carlo Markov chain will be applied. The comparison drawn between the models is on the basis of deviance information criteria (DIC). The model with the least DIC will be selected as the best model.
The introduced model with GPIG, with deviation criterion of 411.775, had best fitness than Poisson and Poisson-inverse Gaussian distribution with deviation criterion of 426.243 and 414.673, respectively.
In the analyzing long-term survivors, to overcome high skewness and over dispersion using distributions that consist of parameters to estimate these statistics may improve the fitness of model. Using distributions which are converted to simpler distributions in special occasions, can be applied as a criterion for comparing other models.