Use of Bayesian Mixture Models in Analyzing Heterogeneous Survival Data: A Simulation Study

One of the statistical methods used to analyze the time-to-event medical data is survival analysis. In survival models, the response variable is time to the occurrence of an event. The main characteristic of survival data is the existence of censored data. When we have the distribution of survival time, we can use parametric methods. Among the important and popular distributions that can be used, we can mention the Weibull distribution. If the data derives from a heterogeneous population, simple parametric models (such as Weibull) would not fit the data appropriately. One of the methods which have been introduced to overcome this problem is the use of mixture models.

To assess the validity of the two-component Weibull mixture model, we use a simulation method on heterogeneous survival data. For this purpose, data with different sample sizes were produced in a batch of 1000. Then, the validity of the model is checked using root mean square error (RMSE) criterion

It is obtained that increasing the sample size would decrease the RMSE in the parameters. However the maximum observed RMSE in all the parameters was negligible.

The Bayesian Weibull mixture model was a proper fit for the heterogeneous survival data.