Abstarct: Analysis of time-to-event data has many applications in medicine, engineering, and other sciences. Such data have different real events, such as the death of a human being, in medicine, which relates to survival analysis, and the failure of a mechanical component in engineering, from which it is considered reliability. In this thesis, we aim to analyze the survival data of multiple cancers. Proportional hazards and proportional odds models, along with the homogeneity assumption of the population, are the most used survival models. However, in many cases, due to the presence of unknown or unobserved factors, this assumption does not hold and there is a kind of heterogeneity in the data. The usual approach for considering this heterogeneity is to use frailty models. The frailty models in survival analysis are a subcategory of random effects models. If we also have geographical information of the data, the inhomogeneity of data can be due to the structure of spatial dependence between survival data. Such data are called spatial survival data. In this situation, the spatial effect is usually introduced into the modeling as a Gaussian (Markov) random field. In addition, in this thesis, we use parametric and nonparametric versions of the proportional hazards and proportional odds models for the baxseline hazard function. We also show the application of the proposed models in a semiparametric version for analyzing a leukemia data set. Due to the complexity of the models, we choose a Bayesian approach for extracting related statistical inference.