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Table 2 Simulation results for the low accuracy scenario

From: A double SIMEX approach for bivariate random-effects meta-analysis of diagnostic accuracy studies

Random-effects

ρ

\(\overline {\eta }\)

\(\overline {\xi }\)

\(\sigma ^{2}_{\eta }\)

\(\sigma ^{2}_{\xi }\)

ρ

Failure

distribution

 

bias (s.e.)

bias (s.e.)

bias (s.e.)

bias (s.e.)

bias (s.e.)

rate %

  

Normal-Normal

  

Normal

0.2

0.00 (0.32)

0.01 (0.22)

-0.16 (0.51)

-0.07 (0.22)

-0.02 (0.27)

0.5

 

0.6

0.00 (0.32)

0.01 (0.21)

-0.19 (0.49)

-0.09 (0.21)

-0.07 (0.20)

0.0

 

0.8

0.01 (0.33)

0.01 (0.21)

-0.15 (0.51)

-0.08 (0.21)

-0.08 (0.14)

0.3

  

Binomial-Normal

  
 

0.2

0.02 (0.33)

0.00 (0.22)

-0.09 (0.54)

-0.04 (0.23)

0.00 (0.30)

1.0

 

0.6

0.00 (0.33)

0.00 (0.22)

-0.11 (0.53)

-0.05 (0.23)

-0.01 (0.22)

1.4

 

0.8

0.01 (0.34)

0.00 (0.22)

-0.05 (0.56)

-0.04 (0.23)

-0.01 (0.14)

4.0

  

SIMEX

  
 

0.2

0.03 (0.34)

-0.01 (0.22)

0.00 (0.54)

0.02 (0.24)

-0.02 (0.28)

0.0

 

0.6

0.01 (0.33)

-0.01 (0.22)

-0.02 (0.53)

0.01 (0.23)

-0.06 (0.21)

0.0

 

0.8

0.02 (0.34)

-0.01 (0.22)

0.03 (0.55)

0.01 (0.23)

-0.07 (0.14)

0.0

  

Normal-Normal

  

t

0.2

-0.04 (0.40)

0.01 (0.27)

0.44 (0.83)

0.21 (0.37)

-0.02 (0.25)

0.5

 

0.6

-0.01 (0.39)

0.03 (0.27)

0.35 (0.78)

0.20 (0.36)

-0.09 (0.20)

0.2

 

0.8

-0.01 (0.39)

0.02 (0.27)

0.39 (0.80)

0.21 (0.36)

-0.08 (0.14)

0.2

  

Binomial-Normal

  
 

0.2

-0.01 (0.44)

-0.01 (0.28)

0.80 (1.01)

0.32 (0.42)

0.00 (0.28)

1.3

 

0.6

0.01 (0.42)

0.01 (0.28)

0.70 (0.95)

0.32 (0.42)

-0.03 (0.21)

1.2

 

0.8

-0.01 (0.43)

0.00 (0.29)

0.81 (1.01)

0.36 (0.43)

-0.01 (0.13)

2.7

  

SIMEX

  
 

0.2

-0.01 (0.44)

-0.03 (0.29)

0.92 (0.96)

0.43 (0.42)

-0.02 (0.26)

0.0

 

0.6

0.02 (0.43)

0.00 (0.29)

0.81 (0.91)

0.42 (0.42)

-0.08 (0.20)

0.0

 

0.8

0.00 (0.43)

-0.01 (0.29)

0.87 (0.94)

0.47 (0.44)

-0.07 (0.13)

0.0

  

Normal-Normal

  

Skew-normal

0.2

-0.55 (0.27)

0.13 (0.21)

-0.45 (0.37)

-0.09 (0.21)

0.09 (0.26)

1.0

(low skewness)

0.6

-0.44 (0.29)

-0.02 (0.21)

-0.38 (0.40)

-0.09 (0.21)

-0.05 (0.20)

0.4

 

0.8

-0.41 (0.29)

-0.11 (0.21)

-0.34 (0.42)

-0.10 (0.21)

-0.09 (0.14)

0.2

  

Binomial-Normal

  
 

0.2

-0.55 (0.28)

0.12 (0.21)

-0.41 (0.38)

-0.07 (0.22)

0.12 (0.28)

1.8

 

0.6

-0.45 (0.30)

-0.03 (0.22)

-0.32 (0.42)

-0.06 (0.23)

0.02 (0.21)

1.8

 

0.8

-0.42 (0.31)

-0.12 (0.22)

-0.27 (0.45)

-0.06 (0.23)

-0.01 (0.15)

5.9

  

SIMEX

  
 

0.2

-0.55 (0.28)

0.11 (0.22)

-0.35 (0.38)

-0.01 (0.22)

0.09 (0.26)

0.0

 

0.6

-0.45 (0.30)

-0.04 (0.22)

-0.26 (0.42)

0.01 (0.23)

-0.04 (0.20)

0.0

 

0.8

-0.42 (0.31)

-0.14 (0.22)

-0.21 (0.45)

0.01 (0.23)

-0.08 (0.14)

0.0

  

Normal-Normal

  

Skew-normal

0.2

-0.51 (0.28)

0.34 (0.19)

-0.41 (0.39)

-0.16 (0.17)

0.26 (0.22)

1.0

(high skewness)

0.6

-0.32 (0.31)

0.23 (0.20)

-0.27 (0.45)

-0.11 (0.20)

0.09 (0.15)

0.1

 

0.8

-0.20 (0.31)

0.15 (0.21)

-0.21 (0.48)

-0.09 (0.21)

-0.01 (0.11)

0.2

  

Binomial-Normal

  
 

0.2

-0.51 (0.29)

0.33 (0.19)

-0.36 (0.41)

-0.15 (0.18)

0.31 (0.20)

2.9

 

0.6

-0.32 (0.31)

0.23 (0.21)

-0.21 (0.48)

-0.08 (0.21)

0.17 (0.16)

4.1

 

0.8

-0.20 (0.33)

0.15 (0.22)

-0.11 (0.53)

-0.05 (0.23)

0.07 (0.10)

8.5

  

SIMEX

  
 

0.2

-0.51 (0.29)

0.32 (0.20)

-0.30 (0.40)

-0.10 (0.18)

0.27 (0.22)

0.0

 

0.6

-0.32 (0.32)

0.22 (0.21)

-0.13 (0.48)

-0.03 (0.21)

0.11 (0.15)

0.0

 

0.8

-0.20 (0.33)

0.14 (0.22)

-0.05 (0.52)

-0.01 (0.22)

0.00 (0.11)

0.0

  1. Bias and average of the estimated standard errors (s.e.) for the estimators of \(\overline {\eta }, \overline {\xi }, \sigma ^{2}_{\eta }, \sigma ^{2}_{\xi }, \rho \), on the basis of 1, 000 replicates with n=10. Failure rates larger than 5% in bold