Density-based spatial clustering (DBSC) algorithm

This repository contains the Supplementary Material and R code to fit the models described in the paper entitled "Dealing with risk discontinuities to estimate cancer mortality risks when the number of small areas is large" (Santafé et al., 2021)

Table of contents

• Supplementary Material
• R code
• References

Supplementary Material

Figures S1-S9 contains some results of the simulation study described in Santafé et al. (2021).

Scenario 1

• Figure S1: True risks and average values of the relative risk posterior median estimates for the simulation study of Scenario 1A for LCAR, AHC and DBSC models.
• Figure S2: True risks and average values of the relative risk posterior median estimates for the simulation study of Scenario 1B for LCAR, AHC and DBSC models.
• Figure S3: True risks and average values of the relative risk posterior median estimates for the simulation study of Scenario 1C for LCAR, AHC and DBSC models.

Scenario 2

• Figure S4: True risks and average values of the relative risk posterior median estimates for the simulation study of Scenario 2A for LCAR, AHC and DBSC models.
• Figure S5: True risks and average values of the relative risk posterior median estimates for the simulation study of Scenario 2B for LCAR, AHC and DBSC models.
• Figure S6: True risks and average values of the relative risk posterior median estimates for the simulation study of Scenario 2C for LCAR, AHC and DBSC models.

Scenario 3

• Figure S7: True risks and average values of the relative risk posterior median estimates for the simulation study of Scenario 3A for LCAR, AHC and DBSC models.
• Figure S8: True risks and average values of the relative risk posterior median estimates for the simulation study of Scenario 3B for LCAR, AHC and DBSC models.
• Figure S9: True risks and average values of the relative risk posterior median estimates for the simulation study of Scenario 3C for LCAR, AHC and DBSC models.

Figures S10-S13 contains some results of the motivating application described in Santafé et al. (2021).

• Figure S10: Maps of posterior median estimates for stomach cancer mortality risks in the municipalities of Spain for male population during the period 2011-2015.

• Figure S11: Maps of posterior exceedence probabilities of stomach cancer mortality risks in the municipalities of Spain for male population during the period 2011-2015.

• Figure S12: Maps of posterior median estimates for stomach cancer mortality risks in the municipalities of Spain for female population during the period 2011-2015.

• Figure S13: Maps of posterior exceedence probabilities of stomach cancer mortality risks in the municipalities of Spain for female population during the period 2011-2015.

R code

R code to fit the following spatial disease mapping models

• LCAR model (Leroux et al., 1999)
• AHC model (Adin et al., 2019)
• DBSC model (Santafé et al., 2021)

has been included here.

Acknowledgements

This work has been supported by the Spanish Ministry of Economy and Competitiveness (project MTM2014-51992-R), by the Spanish Ministry of Economy, Industry, and Competitiveness (project MTM2017-82553-R, AEI/FEDER, UE), and by the UK Medical Research Council (Grant number MR/L022184/1).

References

Adin, A., Lee, D., Goicoa, T., and Ugarte, M.D. (2019). A two-stage approach to estimate spatial and spatio-temporal disease risks in the presence of local discontinuities and clusters. Statistical Methods in Medical Research, 28(9), 2595-2613.

Leroux, B.G., Lei, X., and Breslow, N. (1999). Estimation of disease rates in small areas: A new mixed model for spatial dependence. In Halloran, M. and Berry, D. (eds), Statistical Models in Epidemiology, the Environment, and Clinical Trials, pp. 179-191. Springer-Verlag: New York.

Santafé, G., Adin, A., Lee, D., and Ugarte, M.D. (2021). Dealing with risk discontinuities to estimate cancer mortality risks when the number of small areas is large. Statistical Methods in Medical Research, 30(1), 6-21.