Bayesian Mixture Generalized Extreme Value Regression with Double-Exponential CAR Frailty for Dengue Haemorrhagic Fever in Pamekasan, East Java, Indonesia

There is a lot of research on infectious diseases. One of the dangers is caused by dengue hemorrhagic fever (DHF) viruses. Almost all the world there are dengue viruses that spread. In health science, this research continues to increase over time. It has been widely studied by medical circles, but from a statistical point of view, patient survival can be investigated probabilistically. The survival time of DHF patients could refer to the time of arrival of DHF patients to the hospital with all the health conditions of the patient to be discharged from the hospital. It is because the patient has been declared medically cured or further improved from the initial hospital admission. In this case, survival analysis will be appropriate to be implemented, where the event of the study is DHF patients who are discharged from the hospital due to recovery. DHF patient survival data is found following the multimodal Generalized Extreme Value distribution so that a mixture model would be employed. There is a lot of transmission media for diseases transmitted by the DHF virus, but the fastest transmission medium occurs in a short time, called the Aedes Aegypti Mosquito. This transmission of the DHF virus by mosquitoes can occur between adjacent neighboring regions. This article brings together two fields of research, namely survival models with spatial random effects. The Bayesian analysis will be used as a model parameter estimation approach, whereby unmeasured autocorrelations between intersecting regions will be captured through the conditional autoregressive (CAR). Two different distributions approach for these unmeasured autocorrelations will be given, i.e. the Normal CAR and the Double Exponential CAR. Four predictor variables, namely sex, age, hematocrit level, and platelet count in each DHF patient are used to explain the variability of the survival. The Cox Proportional Hazard regression is employed to find out the significant influence of those variables on the survival spatial DHF model. The result shows that the two-component mixture Generalized Extreme Value regression model coupled with a random Double Exponential CAR effect is the best model. Based on the best model obtained, the significant predictor variables for the DHF spatial survival model are sex, hematocrit level, and platelet count.