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Table 3 Empirical bias (×10−4) for birthweight and 95% confidence interval for sample size 150

From: Binomial outcomes in dataset with some clusters of size two: can the dependence of twins be accounted for? A simulation study comparing the reliability of statistical methods based on a dataset of preterm infants

  

Logistic regression

GLMM PQL

GLMM GH

GEE

Percent.

Random Int.

Empirical

95% Conf

Empirical

95% Conf

Empirical

95% Conf

Empirical

95% Conf

Twins

variance

bias

Interv.

bias

Interv.

bias

Interv.

bias

Interv.

Outcome Death 4 variables

 

0.02

2.00

9.60

[9.30 ;10.00]

-4.30

[-7.30 ; -1.30]

7.10

[6.60 ; 7.60]

0.00

[-0.60 ; 0.60]

0.05

2.00

9.90

[9.60 ; 10.30]

-45.90

[ -50.10 ; -41.70]

4.60

[4.00 ; 5.20]

0.30

[-0.20 ; 0.80]

0.10

2.00

9.90

[9.60 ; 10.30]

-44.30

[ -48.40 ; -40.20]

0.90

[ 0.20 ; 1.70]

0.50

[0.20 ; 0.90]

0.20

2.00

9.80

[9.50 ; 10.20]

-33.20

[-36.90 ; -29.50]

-1.20

[-1.90 ; -0.40]

0.40

[0.10 ; 0.80]

0.02

1.00

5.60

[5.30 ; 6.00]

-11.90

[-15.30 ; -8.50]

2.20

[1.60 ; 2.70]

0.10

[-0.20 ; 0.50]

0.05

1.00

5.60

[5.20 ; 6.00]

-60.80

[-65.90 ; -55.80]

-0.70

[-1.40 ; -0.00]

0.10

[-0.30 ; 0.50]

0.10

1.00

5.40

[5.00 ; 5.70]

-61.40

[ -66.40 ; -56.30]

-4.10

[-4.80 ; -3.30]

-0.20

[-0.50 ; 0.20]

0.20

1.00

5.60

[5.20 ; 6.00]

-47.20

[ -51.90 ; -42.40]

-5.30

[-6.10 ; -4.50]

-0.00

[-0.40 ; 0.30]

0.02

0.50

2.80

[2.50 ; 3.20]

-14.30

[-17.90 ; -10.70]

-1.80

[-2.40 ; -1.10]

0.00

[-0.50 ; 0.50]

0.05

0.50

2.70

[2.30 ; 3.10]

-65.50

[-71.00 ; -60.10]

-4.80

[-5.60 ; -4.10]

-0.20

[-0.60 ; 0.10]

0.10

0.50

2.60

[2.20 ; 2.90]

-64.00

[-69.30 ; -58.80]

-6.90

[-7.80 ; -6.10]

-0.50

[-0.90 ; -0.10]

0.20

0.50

2.60

[2.20 ; 2.90]

-48.90

[-53.80 ; -43.90]

-7.60

[-8.50 ; -6.80]

-0.50

[-0.90 ; -0.20]

Outcome Death 2 variables

 

0.02

2.00

9.60

[9.30 ; 10.00]

-4.30

[-7.30 ; -1.30]

7.10

[6.60 ; 7.60]

0.00

[-0.60 ; 0.60]

0.05

2.00

9.90

[9.60 ; 10.30]

-45.90

[-50.10 ; -41.70]

4.60

[4.00 ; 5.20]

0.30

[-0.20 ; 0.80]

0.10

2.00

9.90

[9.60 ; 10.30]

-44.30

[-48.40 ; -40.20]

0.90

[0.20 ; 1.70]

0.50

[0.20 ; 0.90]

0.20

2.00

9.80

[9.50 ; 10.20]

-33.20

[-36.90 ; -29.50]

-1.20

[-1.90 ; -0.40]

0.40

[0.10 ; 0.80]

0.02

1.00

5.60

[5.30 ; 6.00]

-11.90

[-15.30 ; -8.50]

2.20

[1.60 ; 2.70]

0.10

[-0.20 ; 0.50]

0.05

1.00

5.60

[5.20 ; 6.00]

-60.80

[-65.90 ; -55.80]

-0.70

[-1.40 ; -0.00]

0.10

[-0.30 ; 0.50]

0.10

1.00

5.40

[5.00 ; 5.70]

-61.40

[-66.40 ; -56.30]

-4.10

[-4.80 ; -3.30]

-0.20

[-0.50 ; 0.20]

0.20

1.00

5.60

[5.20 ; 6.00]

-47.20

[-51.90 ; -42.40]

-5.30

[-6.10 ; -4.50]

-0.00

[-0.40 ; 0.30]

0.02

0.50

2.80

[2.50 ; 3.20]

-14.30

[-17.90 ; -10.70]

-1.80

[-2.40 ; -1.10]

0.00

[-0.50 ; 0.50]

0.05

0.50

2.70

[2.30 ; 3.10]

-65.50

[-71.00 ; -60.10]

-4.80

[-5.60 ; -4.10]

-0.20

[-0.60 ; 0.10]

0.10

0.50

2.60

[2.20 ; 2.90]

-64.00

[-69.30 ; -58.80]

-6.90

[-7.80 ; -6.10]

-0.50

[-0.90 ; -0.10]

0.20

0.50

2.60

[2.20 ; 2.90]

-48.90

[-53.80 ; -43.90]

-7.60

[-8.50 ; -6.80]

-0.50

[-0.90 ; -0.20]

Outcome O2 Dep. 4 variables

 

0.02

2.00

9.60

[9.30 ; 10.00]

-4.30

[-7.30 ; -1.30]

7.10

[6.60 ; 7.60]

0.00

[-0.60 ; 0.60]

0.05

2.00

9.90

[9.60 ; 10.30]

-45.90

[-50.10 ; -41.70]

4.60

[4.00 ; 5.20]

0.30

[-0.20 ; 0.80]

0.10

2.00

9.90

[9.60 ; 10.30]

-44.30

[-48.40 ; -40.20]

0.90

[0.20 ; 1.70]

0.50

[0.20 ; 0.90]

0.20

2.00

9.80

[9.50 ; 10.20]

-33.20

[-36.90 ; -29.50]

-1.20

[-1.90 ; -0.40]

0.40

[0.10 ; 0.80]

0.02

1.00

5.60

[5.30 ; 6.00]

-11.90

[-15.30 ; -8.50]

2.20

[1.60 ; 2.70]

0.10

[-0.20 ; 0.50]

0.05

1.00

5.60

[5.20 ; 6.00]

-60.80

[-65.90 ; -55.80]

-0.70

[-1.40 ; -0.00]

0.10

[-0.30 ; 0.50]

0.10

1.00

5.40

[5.00 ; 5.70]

-61.40

[-66.40 ; -56.30]

-4.10

[-4.80 ; -3.30]

-0.20

[-0.50 ; 0.20]

0.20

1.00

5.60

[5.20 ; 6.00]

-47.20

[-51.90 ; -42.40]

-5.30

[-6.10 ; -4.50]

-0.00

[-0.40 ; 0.30]

0.02

0.50

2.80

[2.50 ; 3.20]

-14.30

[-17.90 ; -10.70]

-1.80

[-2.40 ; -1.10]

0.00

[-0.50 ; 0.50]

0.05

0.50

2.70

[2.30 ; 3.10]

-65.50

[-71.00 ; -60.10]

-4.80

[-5.60 ; -4.10]

-0.20

[-0.60 ; 0.10]

0.10

0.50

2.60

[2.20 ; 2.90]

-64.00

[-69.30 ; -58.80]

-6.90

[-7.80 ; -6.10]

-0.50

[-0.90 ; -0.10]

0.20

0.50

2.60

[2.20 ; 2.90]

-48.90

[-53.80 ; -43.90]

-7.60

[-8.50 ; -6.80]

-0.50

[-0.90 ; -0.20]

Outcome O2 Dep. 2 variables

 

0.02

2.00

9.60

[9.30 ;10.00]

-4.30

[-7.30 ; -1.30]

7.10

[6.60 ; 7.60]

0.00

[-0.60 ; 0.60]

0.05

2.00

9.90

[9.60 ; 10.30]

-45.90

[-50.10 ; -41.70]

4.60

[4.00 ; 5.20]

0.30

[-0.20 ; 0.80]

0.10

2.00

9.90

[9.60 ; 10.30]

-44.30

[-48.40 ; -40.20]

0.90

[0.20 ; 1.70]

0.50

[0.20 ; 0.90]

0.20

2.00

9.80

[9.50 ; 10.20]

-33.20

[-36.90 ; -29.50]

-1.20

[-1.90 ; -0.40]

0.40

[0.10 ; 0.80]

0.02

1.00

5.60

[5.30 ; 6.00]

-11.90

[-15.30 ; -8.50]

2.20

[1.60 ; 2.70]

0.10

[-0.20 ; 0.50]

0.05

1.00

5.60

[5.20 ; 6.00]

-60.80

[-65.90 ; -55.80]

-0.70

[-1.40 ; -0.00]

0.10

[-0.30 ; 0.50]

0.10

1.00

5.40

[5.00 ; 5.70]

-61.40

[-66.40 ; -56.30]

-4.10

[-4.80 ; -3.30]

-0.20

[-0.50 ; 0.20]

0.20

1.00

5.60

[5.20 ; 6.00]

-47.20

[-51.90 ; -42.40]

-5.30

[-6.10 ; -4.50]

-0.00

[-0.40 ; 0.30]

0.02

0.50

2.80

[2.50 ; 3.20]

-14.30

[-17.90 ; -10.70]

-1.80

[-2.40 ; -1.10]

0.00

[-0.50 ; 0.50]

0.05

0.50

2.70

[2.30 ; 3.10]

-65.50

[-71.00 ; -60.10]

-4.80

[-5.60 ; -4.10]

-0.20

[-0.60 ; 0.10]

0.10

0.50

2.60

[2.20 ; 2.90]

-64.00

[-69.30 ; -58.80]

-6.90

[-7.80 ; -6.10]

-0.50

[-0.90 ; -0.10]

0.20

0.50

2.60

[2.20 ; 2.90]

-48.90

[-53.80 ; -43.90]

-7.60

[-8.50 ; -6.80]

-0.50

[-0.90 ; -0.20]