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Table 3 Mean Square Error (MSE) in log scale (n = 1500)

From: Comparison of robustness to outliers between robust poisson models and log-binomial models when estimating relative risks for common binary outcomes: a simulation study

RR

Prob (Y = 1)

Contamination rate

Association bet Z and Y: Linear

Association bet Z and Y: Linear

Association bet Z and Y: Non-Linear

Association bet Z and Y: Non-Linear

Level of association bet Z and X, Z and Y: Moderate

Level of association bet Z and X, Z and Y: Strong

Level of association bet Z and X, Z and Y: Moderate

Level of association bet Z and X, Z and Y: Strong

 

LB

RP

LB

RP

LB

RP

LB

RP

1.5

10%

0%

0.025

0.025

0.027

0.027

0.025

0.025

0.024

0.024

2%

0.026

0.025

0.025

0.024

0.036

0.026

0.033

0.026

5%

0.049

0.038

0.045

0.038

0.066

0.044

0.063

0.046

25%

0%

0.008

0.008

0.008

0.008

0.009

0.009

0.008

0.008

2%

0.010

0.010

0.009

0.010

0.011

0.010

0.013

0.012

5%

0.018

0.017

0.019

0.019

0.027

0.020

0.038

0.028

40%

0%

0.004

0.004

0.004

0.004

0.004

0.004

0.004

0.004

2%

0.005

0.005

0.006

0.006

0.006

0.006

0.008

0.007

5%

0.010

0.010

0.013

0.014

0.016

0.014

0.027

0.021

2.0

10%

0%

0.028

0.028

0.027

0.027

0.027

0.027

0.029

0.029

2%

0.040

0.038

0.035

0.035

0.057

0.039

0.053

0.038

5%

0.105

0.085

0.096

0.081

0.134

0.091

0.135

0.093

25%

0%

0.009

0.009

0.010

0.010

0.009

0.009

0.009

0.010

2%

0.012

0.013

0.014

0.014

0.016

0.014

0.018

0.016

5%

0.034

0.031

0.013

0.035

0.051

0.036

0.065

0.047

40%

0%

0.005

0.005

0.005

0.005

0.005

0.005

0.005

0.005

2%

0.007

0.007

0.007

0.008

0.008

0.008

0.011

0.010

  

5%

0.018

0.018

0.021

0.022

0.026

0.023

0.039

0.034

  1. Association between Z and X always linear.
  2. LB: Log-Binomial Model.
  3. RP: Robust Poisson.
  4. Mean square error was calculated by taking the sum of the squared bias in log scale and the variances.