Bayesian spatial survival models for HIV/AIDS event processes in East Java

Survival analysis can be defined as a statistical analysis of the duration of time of an event happen as a response that can also be influenced by several influencing covariates. This paper would elaborate this analysis to understand the survival rate of HIV-AIDS patients in East Java province, Indonesia. The spread of HIV-AIDS infection which affects the human immune system caused by some factors, i.e. the level of reproductive health education in the area, imported cases, the number of people at risk in the area. An incidence of HIV infection from one area will be suspected to affect the others. Modelling of spatial survival, therefore, will be suitable for this case. A model that includes the spatial random effect of Conditionally Autoregressive (CAR) was used to adjust unexplainable spatial dependent in the model. The weighted matrix Queen’s contiguity is employed and the Moran’s I statistical test is used to detect the existence of an effect of between-districts/cities toward the incidence rate of HIV-AIDS cases are exist. The preliminary analysis to the data show that there is a significant effect of space (spatial) to the HIV-AIDS incidence in every districts/city in East Java province, and the distribution of the survival time of HIV-AIDS patients is following the 3-parameter Lognormal. The work of the approach demonstrates that the survival function of HIV-AIDS patients reduced as the more extended treatment time while hazard function increased, and additionally all districts/cities had different survival rate.