On the computational Bayesian survival spatial dengue hemorrhagic fever (DHF) modeling with double-exponential CAR frailty

In statistics, there are many types of data. Some data carry information about the location where observations occur, so that they can have a spatial effect. Dengue hemorrhagic fever (DHF) data which is easily transmitted, will be consequently has a spatial effect on its patient survival. In this study, we included DHF patient recovery time as a response variable, and several other variables as covariates considered to influence the patient's recovery time. Our aim in this study is to model how these variables affect the recovery rate for DHF patients with the accompanying patient residence as the spatial effects. Survival analysis is the best method for modeling the recovery rate for DHF patients. A conditional autoregressive (CAR) model is given to explain the relationship between adjacent locations, which is not explained in the general survival analysis. Several researchers have used the Cox model coupled with the Normal CAR. In this study, we used the Cox model using Normal CAR and compared it with the Double-Exponential (DE) CAR. To estimate the regression parameters of the Cox model, we used the Stan software. The advantage of Stan compared to the other Bayesian software such as BUGS and JAGS is the creativity of the researcher in writing the distribution as user-defined, as well as writing the CAR model in the Stan. Based on the WAIC value, modeling the DHF data using the Cox model coupled with the DE CAR is better than coupled with the Normal CAR. Based on the best model, variables that affect the recovery rate of DHF patients are age, the high schools in last education, unemployed in the type of occupations, the stadium II in severity level, pulse, temperature, and leukocytes.