On the Computational Bayesian Survival Spatial Dengue Hemorrhagic Fever (DHF) Modelling with Fernandez-Steel Skew Normal Conditional Autoregressive (FSSN CAR) Frailty

Generally, infectious disease data has a spatial effect, meaning that areas that are close together affect each other. One of the infectious diseases is dengue hemorrhagic fever (DHF). The recovery time of DHF patients is interesting to study. In this research, DHF data in eastern Surabaya was used. The recovery time of this DHF patient can be modeled using one of the statistical methods, namely survival analysis. This recovery time data follows the Weibull distribution. On the data indicated spatial effect, the conditional autoregressive (CAR) model can be used to express dependencies between adjacent areas. Spatial random effects in the survival model were modeled with Normal CAR, Double-Exponential (DE) CAR, and Fernandez-Steel skew Normal (FSSN) CAR. In this research, Cox regression was used and parameter estimation was performed using the Bayesian analysis with Hamiltonian Monte Carlo (HMC) algorithm using the Stan programming language. Based on the comparison of the Watanabe-Akaike information criterion (WAIC), the spatial random effects on the Weibull Cox regression model are best modeled with the FSSN CAR. This is because the FSSN CAR is able to capture error patterns both symmetrical and asymmetrical, not with Normal CAR and DE CAR which can only capture symmetrical error patterns. In this research, several variables that allegedly affect the recovery rate of DHF patients are given. Then, based on the best model, variables that significantly affect the patient's recovery rate are age, the high schools in last education, housewife in the type of occupation, stadium-II in severity level, fever days before entering the hospital, pulse, temperature, and leukocytes.