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Table 2 Selected simulation study results. C&J: Copas and Jackson bias bound approach

From: Application and investigation of a bound for outcome reporting bias

Odds ratio

Sample size variability parameter

Mean trial size

n

m

True bias: median1

Difference between unsuppressed pooled and C&J-adjusted: median (2.5th, 97.5th) centiles

Difference between unsuppressed pooled and maximum imputation-adjusted: median (2.5th, 97.5th) centiles

1

0.05

25

4

1

0.175

-0.059 (-0.170, 0.117)

-0.142 (-0.334, 0.016)

1

0.05

25

3

2

0.345

-0.087 (-0.293, 0.228)

-0.323 (-0.653, -0.053)

1

0.05

300

4

1

0.052

-0.014 (-0.048, 0.043)

 

1

0.05

300

3

2

0.101

-0.021 (-0.084, 0.071)

 

1

0.35

25

4

1

0.159

-0.055 (-0.161, 0.121)

-0.146 (-0.371, 0.030)

1

0.35

25

3

2

0.317

-0.079 (-0.277, 0.220)

-0.310 (-0.661, -0.051)

1

0.35

300

4

1

0.053

-0.015 (-0.049, 0.048)

 

1

0.35

300

3

2

0.103

-0.021 (-0.087, 0.077)

 

0.5

0.05

25

4

1

0.176

-0.043 (-0.159, 0.153)

-0.236 (-0.437, -0.060)

0.5

0.05

25

3

2

0.343

-0.064 (-0.280, 0.277)

-0.593 (-0.943, -0.300)

0.5

0.05

300

4

1

0.049

-0.013 (-0.047, 0.045)

 

0.5

0.05

300

3

2

0.096

-0.019 (-0.082, 0.071)

 

0.5

0.35

25

4

1

0.155

-0.066 (-0.199, 0.200)

-0.358 (-0.650, -0.150)

0.5

0.35

25

3

2

0.314

-0.091 (-0.311, 0.307)

-0.546 (-0.946, -0.245)

0.5

0.35

300

4

1

0.044

-0.020 (-0.060, 0.048)

 

0.5

0.35

300

3

2

0.085

-0.031 (-0.104, 0.075)

 

1

0.05

25

9

1

0.101

-0.030 (-0.080, 0.039)

-0.056 (-0.125, 0.013)

1

0.05

25

5

5

0.479

-0.063 (-0.270, 0.198)

 

1

0.05

300

9

1

0.031

-0.006 (-0.022, 0.019)

 

1

0.05

300

5

5

0.138

-0.014 (-0.075, 0.063)

 

1

0.35

25

9

1

0.101

-0.033 (-0.086, 0.059)

-0.077 (-0.182, 0.011)

1

0.35

25

5

5

0.481

-0.068 (-0.274, 0.221)

 

1

0.35

300

9

1

0.032

-0.007 (-0.025, 0.025)

 

1

0.35

300

5

5

0.144

-0.015 (-0.080, 0.076)

 

0.5

0.05

25

9

1

0.105

-0.019 (-0.072, 0.065)

-0.126 (-0.206, -0.045)

0.5

0.05

25

5

5

0.477

-0.042 (-0.250, 0.239)

 

0.5

0.05

300

9

1

0.030

-0.005 (-0.021, 0.019)

 

0.5

0.05

300

5

5

0.130

-0.013 (-0.072, 0.063)

 

0.5

0.35

25

9

1

0.102

-0.026 (-0.086, 0.083)

-0.027 (-0.096, 0.071)

0.5

0.35

25

5

5

0.467

-0.062 (-0.281, 0.261)

 

0.5

0.35

300

9

1

0.017

-0.017 (-0.036, 0.020)

 

0.5

0.35

300

5

5

0.094

-0.043 (-0.110, 0.046)

 
  1. 1 calculated as the median of the distribution of values across simulations for the difference between the pooled log(OR) from all n + m trials and the pooled log(OR) based on the selected trials