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Nonparametric Bayesian modeling for hazard functions in spatial survival data
Journal of the Korean Data & Information Science Society 2022;33:1163-74
Published online November 30, 2022;
© 2022 Korean Data and Information Science Society.

Yena Jeon1 · Yongku Kim2

12Department of Statistics, Kyungpook National University
Correspondence to: This research was supported by the Research Grants of Korea Forest Service (Korea Forestry Promotion Institute) project (No.2019149B10-2223-0301).
1 Graduate student, Department of Statistics, Kyungpook National University, Daegu 41566, Korea
2 Professor, Department of Statistics, Kyungpook National University, Daegu 41566, Korea. E-mail:
Received October 14, 2022; Revised October 25, 2022; Accepted October 26, 2022.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License ( which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
Survival analysis is a collection of statistical procedures for data analysis where the outcome variable of interest is time until an event occurs. The Cox proportional hazard is the most widely used in survival analysis as it takes advantage that it accounts for the proportionate risk of covariates without estimating baseline hazards. However, it is necessary to obtain the baseline hazard function as well as regression parameters to describe the exact hazards of a study population. When data is collected by clinical sites or geographical regions, we should reflect the spatial structures into the model. In this paper we adopted a nonparametric Bayesian hierarchical model to estimate the hazard function in spatial survival data. We assume the cumulative baseline hazard function as a monotone step function, considering flexible priors called stick-breaking priors. We provide modeling for the hazard function that can describe spatial structure, and apply it to survival data which is observed in 24 administrative districts in the northwest of England.
Keywords : Cox proportional hazard regression, baseline hazard function, nonparametric Bayesian, spatial survival data