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Table 1 Simulation results for estimated regression coefficients following indiCAR and Leroux et al. [7] where each area consists of a random number of subjects between 10 and 1000

From: Individual level covariate adjusted conditional autoregressive (indiCAR) model for disease mapping

True value

indiCAR

Leroux et al. [7] approach

\(\beta _0\) −0.20

\(\beta _1\) −2.50

\(\beta _2\) 0.70

\(\beta _{32}\) −2.00

\(\beta _{33}\) −1.50

\(\beta _{34}\) 0.20

\(\beta _{35}\) 0.50

\(\beta _{36}\) 0.80

\(\gamma\) 0.20

\(\sigma\) 0.40

\(\lambda\)

\(\gamma\) 0.20

\(\sigma\) 0.40

\(\lambda\)

\(\lambda\)

Estimated coefficient

 0.00

−0.178

−2.500

0.700

−1.997

−1.500

0.201

0.501

0.800

0.199

0.396

0.019

0.198

0.442

0.069

 0.25

−0.174

−2.499

0.699

−1.997

−1.498

0.200

0.501

0.801

0.198

0.395

0.251

0.198

0.421

0.304

 0.50

−0.162

−2.500

0.700

−2.001

−1.501

0.200

0.500

0.801

0.198

0.396

0.503

0.198

0.413

0.523

 0.75

−0.152

−2.501

0.701

−2.005

−1.499

0.201

0.500

0.800

0.198

0.394

0.736

0.198

0.407

0.722

 0.99

−0.144

−2.499

0.700

−2.000

−1.500

0.200

0.499

0.799

0.199

0.396

0.958

0.199

0.412

0.950

 

Empirical standard error

 0.00

0.033

0.016

0.012

0.059

0.039

0.025

0.026

0.026

0.021

0.030

0.028

0.022

0.035

0.056

 0.25

0.037

0.016

0.011

0.060

0.039

0.027

0.026

0.027

0.017

0.033

0.101

0.017

0.035

0.106

 0.50

0.042

0.016

0.012

0.058

0.040

0.027

0.027

0.026

0.016

0.029

0.130

0.016

0.028

0.120

 0.75

0.054

0.016

0.012

0.061

0.039

0.028

0.027

0.028

0.013

0.025

0.114

0.014

0.025

0.106

 0.99

0.209

0.017

0.012

0.064

0.038

0.027

0.027

0.027

0.012

0.020

0.037

0.013

0.020

0.043

 

Average of the simulated standard error

 0.00

0.034

0.016

0.012

0.061

0.039

0.027

0.027

0.027

0.021

0.016

0.026

0.022

0.018

0.031

 0.25

0.036

0.016

0.012

0.061

0.039

0.028

0.027

0.027

0.017

0.017

0.053

0.018

0.018

0.058

 0.50

0.041

0.016

0.012

0.062

0.039

0.028

0.027

0.027

0.015

0.018

0.079

0.015

0.018

0.080

 0.75

0.028

0.016

0.012

0.062

0.039

0.028

0.027

0.027

0.014

0.019

0.086

0.014

0.019

0.086

 0.99

0.130

0.016

0.012

0.062

0.040

0.028

0.027

0.028

0.013

0.019

0.034

0.013

0.020

0.038