Proportional Hazards and Frailty Models for Analysis of Spatial Survival Data

One of the most widely used models for fitting survival data is Cox proportional hazards model that is based on homogeneity, independence and equi-distributed of survival data. But in many cases hazards of statistical units are different and the assumption of population homogeneity is not established. One of the reasons for such deference is the unknown or unobserved risk factors which may lead to some misleading models if there is no concern for them or some models such as Cox proportional hazard models have to be implemented. In such cases, regarding the unknown risk factors, frailty models are used. In this paper the performances of the Cox and frailty models for survival and spatial survival data with unknown risk factors are considered. The efficiency of these models whilst the source of unknown risk factors is the spatial correlation of survival data is also examined.