Evaluating recent methods to overcome spatial confounding

This repository contains the R code to implement the methods described in the paper entitled "Evaluating recent methods to overcome spatial confounding" (Urdangarin et al., 2023) as well as the R code to create the figures and tables presented in the paper.

Table of contents

• Data
• Simulated data
• R code
• References

Data

Dowry deaths data in Uttar Pradesh in 2001 (Vicente et al., 2020)

The Dowry_death_2001.Rdata file contains the following objects:

• Data: contains the data set used. It is a data.frame object with the following variables:

  • dist: names of the districts of Uttar Pradesh

  • ID.area: numeric identifiers of districts

  • O: number of dowry deaths in each district in 2001

  • E: number of expected cases of each district in 2001

  • X1: standardized sex ratio covariate (number of females per 1000 males)

• carto: SpatialPolygonDataFrame object with the cartography of the 70 districts (year 2001) of Uttar Pradesh

• Q.xi: spatial adjacency matrix

Stomach cancer incidence data in Slovenia during the period 1995-2001 (Zadnik and Reich, 2006)

The Slovenia_stomach_cancer file contains the following objects:

• Data: contains the data set used. It is a data.frame object with the following variables:

  • ID.area: numeric district identifiers

  • O: number of stomach cancer cases in each area during 1995-2001

  • E: number of expected cases in each area during 1995-2001

  • X: standardized socioeconomic indicator

• coord: a matrix that contains the coordinates of the 192 areas of Slovenia

• Q.xi: spatial adjacency matrix

Slovenia data set is available from the package RASCO of R https://github.com/DouglasMesquita/RASCO. This dataset is also available from the web page of James Hogdes.

Lip cancer incidence data in Scotland during 1975-1980 (Breslow and Clayton, 1993)

The Scotland_lip_cancer.Rdata file contains the following objects:

• Data: contains the data set used. It is a dataframe with the following variables:

  • ID.area: numeric district identifiers

  • O: number of lip cancer cases in each area during 1975-1980

  • E: number of expected cases in each area during 1975-1980

  • AFF: standardized covariate indicating the proportion of the population engaged in agriculture, fishing, or forestry

• carto: SpatialPolygonDataFrame object with the cartography of the 56 districts of Scotland

• Q.xi: spatial adjacency matrix

Simulated data

Simulated_data folder contains a total of 18 .Rdata files (one file for each scenario and subscenario) used in Simulation Study 1 and Simulation Study 2. Each .Rdata file contains the same objects as Dowry_death_2001.Rdata (Data, carto, Q.xi) but a simulated covariate X2 is added to Data. Moreover, each .Rdata contains the following objects as well:

• log.risk: a vector that contains the simulated log risks
• simu.O: a list with 100 simulated counts data sets

The R code to simulate the data is available in SimuStudy1_simulate_data.R and SimuStudy2_simulate_data.R.

R code

R code to implement the procedures to alleviate spatial confounding described in the paper and to reproduce the tables and figures of the paper has been included.

• R/Real_data_analysis folder contains the R code used in the real data analysis.

  The main file to fit the null, spatial, RSR and spatial+ models is Null_Spatial_RSR_SpatPlus_models.R. Before running the models, the dataset argument (one of either "Dowry", "Slovenia" or "Scotland") must be defined at the top of the code.

  • Figure1.R: R script to reproduce Figure 1 of the paper.
  • Covariate_model_eigenvectors.R: R script to fit the covariate model based on the eigenvectors of the spatial precision matrix to remove the spatial dependence from the covariate before fitting the spatial+ model.
  • Covariate_model_Psplines.R: R script to fit the covariate model based on P-splines to remove the spatial dependence from the covariate before fitting the spatial+ model.
  • Covariate_model_TPsplines.R: R script to fit the covariate model based on thin plate splines to remove the spatial dependence from the covariate before fitting the spatial+ model.

• R/Simulation_Study_1 folder contains the R code used in Simulation Study 1.

  Before running the models, the arguments Scenario(1, 2 or 3) and Subscenario (cor=80, 50 or 20) must be defined at the top of the code.

  • SimuStudy1_simulate_data.R: R code to simulate the data for Simulation study 1.
  • Figure2.R: R code to reproduce Figure 2 of the paper.
  • SimuStudy1_Null.R: R script to fit the null model to the 100 simulated datasets.
  • SimuStudy1_Spatial.R: R script to fit the spatial model to the 100 simulated datasets.
  • SimuStudy1_RSR.R: R script to fit the RSR model to the 100 simulated datasets.
  • SimuStudy1_SpatialPlus_eigenvectors.R: R script to fit SpatPlus5, SpatPlus10, SpatPlus15 and SpatPlus20 models to the 100 simulated datasets.
  • SimuStudy1_SpatPlusP1.R: R script to fit SpatPlusP1 model to the 100 simulated datasets.
  • SimuStudy1_SpatPlusTP1.R: R script to fit SpatPlusTP1 model to the 100 simulated datasets.
  • SimuStudy1_SpatPlusP2.R: R script to fit SpatPlusP2 model to the 100 simulated datasets.
  • SimuStudy1_SpatPlusTP2.R: R script to fit SpatPlusTP2 model to the 100 simulated datasets.
  • Tables_6_7_8.R: R code to reproduce Table 6, 7 and 8 of the paper for each scenario and subscenario.
  • Tables_supplementary_A1_A2_A3_A4.R: R code to reproduce Tables A1, A2 and A3 of the supplementary material for each scenario and subscenario.

• R/Simulation_Study_2 folder contains the R code used in Simulation Study 2.

  Before running the models, the arguments Scenario(1, 2 or 3) and Subscenario (cor=80, 50 or 20) must be defined at the top of the code.

  • SimuStudy2_simulate_data.R: R code to simulate the data for Simulation study 2.
  • SimuStudy2_Null.R: R script to fit the null model to the 100 simulated datasets.
  • SimuStudy2_Spatial.R: R script to fit the spatial model to the 100 simulated datasets.
  • SimuStudy2_RSR.R: R script to fit the RSR model to the 100 simulated datasets.
  • SimuStudy2_SpatialPlus_eigenvectors.R: R script to fit SpatPlus5, SpatPlus10, SpatPlus15 and SpatPlus20 models to the 100 simulated datasets.
  • SimuStudy2_SpatPlusP1.R: R script to fit SpatPlusP1 model to the 100 simulated datasets.
  • SimuStudy2_SpatPlusTP1.R: R script to fit SpatPlusTP1 model to the 100 simulated datasets.
  • SimuStudy2_SpatPlusP2.R: R script to fit SpatPlusP2 model to the 100 simulated datasets.
  • SimuStudy2_SpatPlusTP2.R: R script to fit SpatPlusTP2 model to the 100 simulated datasets.
  • Table_9.R: R code to reproduce Table 9 of the paper for each scenario and subscenario.
  • Figures_supplementary_A3_A4_A5.R: R code to reproduce Figures A3, A4 and A4 of the supplementary material for each scenario and subscenario.

Computations were run using R-4.0.4, INLA version 21.02.23, mgcv version 1.8-40.

Acknowledgements

This work has been supported by Project PID2020-113125RB-I00/ MCIN/ AEI/ 10.13039/501100011033.

References

Urdangarin, A., Goicoa, T. and Ugarte, M.D. (2023). Evaluating recent methods to overcome spatial confounding. Revista Matemática Complutense 36, 333-360. DOI: 10.1007/s13163-022-00449-8.