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. Author manuscript; available in PMC: 2015 Oct 1.
Published in final edited form as: Ann Epidemiol. 2014 Aug 12;24(10):747–753. doi: 10.1016/j.annepidem.2014.07.014

Table 3.

Misspecified parameters for adjustment of collider-stratification bias in a cohort (N=100,000) defined by the DAG in Figure 41

Trial Misspecified
parameter2,3 		Degree of
misspecification		 True
ORYX|z 		Biased
ORYX|z,S=1 		Bias adjusted
ORYX|z,S-adj 		Bias RMSE
D1 None None 1.97 (1.90, 2.05) 1.34 (1.27, 1.41) 1.98 (1.90, 2.05) 0.0031 0.0190
D2 βS −20% 1.97 (1.90, 2.05) 1.34 (1.27, 1.41) 1.97 (1.89, 2.05) −0.0042 0.0203
D3 βS −10% 1.97 (1.90, 2.05) 1.34 (1.27, 1.41) 1.98 (1.90, 2.05) 0.0036 0.0197
D4 βS +10% 1.97 (1.90, 2.05) 1.34 (1.27, 1.41) 1.97 (1.90, 2.04) −0.0067 0.0194
D5 βS +20% 1.97 (1.90, 2.05) 1.34 (1.27, 1.41) 1.95 (1.88, 2.02) −0.0263 0.0317
D6 eβSX −20% 1.97 (1.90, 2.05) 1.34 (1.27, 1.41) 1.75 (1.69, 1.82) −0.2186 0.2194
D7 eβSX −10% 1.97 (1.90, 2.05) 1.34 (1.27, 1.41) 1.87 (1.80, 1.94) −0.1065 0.1081
D8 eβSX +10% 1.97 (1.90, 2.05) 1.34 (1.27, 1.41) 2.08 (2.01, 2.16) 0.1089 0.1106
D9 eβSX +20% 1.97 (1.90, 2.05) 1.34 (1.27, 1.41) 2.18 (2.10, 2.27) 0.2101 0.2110
D10 eβSY −20% 1.97 (1.90, 2.05) 1.34 (1.27, 1.41) 1.75 (1.69, 1.82) −0.2230 0.2238
D11 eβSY −10% 1.97 (1.90, 2.05) 1.34 (1.27, 1.41) 1.86 (1.80, 1.93) −0.1088 0.1104
D12 eβSY +10% 1.97 (1.90, 2.05) 1.34 (1.27, 1.41) 2.08 (2.01, 2.16) 0.1115 0.1131
D13 eβSY +20% 1.97 (1.90, 2.05) 1.34 (1.27, 1.41) 2.19 (2.11, 2.27) 0.2155 0.2163
D14 eβSZ1 −20% 1.97 (1.90, 2.05) 1.34 (1.27, 1.41) 2.00 (1.93, 2.07) 0.0250 0.0312
D15 eβSZ1 −10% 1.97 (1.90, 2.05) 1.34 (1.27, 1.41) 1.99 (1.92, 2.06) 0.0137 0.0232
D16 eβSZ1 +10% 1.97 (1.90, 2.05) 1.34 (1.27, 1.41) 1.97 (1.89, 2.04) −0.0067 0.0200
D17 eβSZ1 +20% 1.97 (1.90, 2.05) 1.34 (1.27, 1.41) 1.96 (1.89, 2.03) −0.0156 0.0245
D18 eβSYX −20% 1.97 (1.90, 2.05) 1.34 (1.27, 1.41) 2.00 (1.93, 2.07) 0.0269 0.0328
D19 eβSYX −10% 1.97 (1.90, 2.05) 1.34 (1.27, 1.41) 1.99 (1.91, 2.06) 0.0138 0.0233
D20 eβSYX +10% 1.97 (1.90, 2.05) 1.34 (1.27, 1.41) 1.97 (1.90, 2.04) −0.0057 0.0197
D21 eβSYX +20% 1.97 (1.90, 2.05) 1.34 (1.27, 1.41) 1.96 (1.89, 2.03) −0.0130 0.0228
E1 None None 1.97 (1.90, 2.05) 1.62 (1.52, 1.73) 1.98 (1.91, 2.05) 0.0049 0.0194
E2 βS −20% 1.97 (1.90, 2.05) 1.62 (1.52, 1.73) 1.96 (1.89, 2.04) −0.0104 0.0230
E3 βS −10% 1.97 (1.90, 2.05) 1.62 (1.52, 1.73) 1.97 (1.90, 2.05) −0.0021 0.0197
E4 βS +10% 1.97 (1.90, 2.05) 1.62 (1.52, 1.73) 1.98 (1.91, 2.05) 0.0105 0.0208
E5 βS +20% 1.97 (1.90, 2.05) 1.62 (1.52, 1.73) 1.99 (1.92, 2.06) 0.0149 0.0227
E6 eβSX −20% 1.97 (1.90, 2.05) 1.62 (1.52, 1.73) 1.95 (1.88, 2.02) −0.0269 0.0325
E7 eβSX −10% 1.97 (1.90, 2.05) 1.62 (1.52, 1.73) 1.96 (1.89, 2.03) −0.0112 0.0217
E8 eβSX +10% 1.97 (1.90, 2.05) 1.62 (1.52, 1.73) 1.99 (1.92, 2.07) 0.0212 0.0285
E9 eβSX +20% 1.97 (1.90, 2.05) 1.62 (1.52, 1.73) 2.01 (1.94, 2.09) 0.0378 0.0424
E10 eβSY −20% 1.97 (1.90, 2.05) 1.62 (1.52, 1.73) 1.95 (1.88, 2.02) −0.0252 0.0313
E11 eβSY −10% 1.97 (1.90, 2.05) 1.62 (1.52, 1.73) 1.96 (1.89, 2.04) −0.0103 0.0214
E12 eβSY +10% 1.97 (1.90, 2.05) 1.62 (1.52, 1.73) 1.99 (1.92, 2.07) 0.0203 0.0277
E13 eβSY +20% 1.97 (1.90, 2.05) 1.62 (1.52, 1.73) 2.01 (1.94, 2.08) 0.0360 0.0407
E14 eβSZ1 −20% 1.97 (1.90, 2.05) 1.62 (1.52, 1.73) 1.98 (1.91, 2.06) 0.0089 0.0207
E15 eβSZ1 −10% 1.97 (1.90, 2.05) 1.62 (1.52, 1.73) 1.98 (1.91, 2.05) 0.0068 0.0199
E16 eβSZ1 +10% 1.97 (1.90, 2.05) 1.62 (1.52, 1.73) 1.98 (1.90, 2.05) 0.0029 0.0191
E17 eβSZ1 +20% 1.97 (1.90, 2.05) 1.62 (1.52, 1.73) 1.97 (1.90, 2.05) 0.0011 0.0189
E18 eβSZ1 −20% 1.97 (1.90, 2.05) 1.62 (1.52, 1.73) 1.92 (1.85, 1.99) −0.0522 0.0555
E19 eβSYX −10% 1.97 (1.90, 2.05) 1.62 (1.52, 1.73) 1.95 (1.88, 2.02) −0.0241 0.0306
E20 eβSYX +10% 1.97 (1.90, 2.05) 1.62 (1.52, 1.73) 2.01 (1.94, 2.08) 0.0346 0.0394
E21 eβSYX +20% 1.97 (1.90, 2.05) 1.62 (1.52, 1.73) 2.04 (1.96, 2.11) 0.0652 0.0679
1

Simulated prevalences in the hypothetical population were held constant as follows: P(S=1|Y=0,X=0,Z=0)= 0.2, P(X=1|Z=0) = 0.3 and P(Y=1|X=0, Z=0) = 0.5. The true ORYX|Z was simulated as 2.

2

For trials D1-D21, each hypothetical population, the true bias parameters were specified as follows: βS = 0.2, eβSX = 5.0, eβSY = 5.0, eβSZ1 = 5.0, and eβSYX = 5.0.

3

For trials E1-E21 each hypothetical population, the true bias parameters were specified as follows: βS = 0.2, eβSX = 2.0, eβSY = 2.0, eβSZ1 = 2.0, and eβSYX = 0.8.