A Proxy Outcome Approach for Causal Effect in Observational Studies: A Simulation Study
Table 2
Data example of a replicate/scenario, estimated effects (coefficients from logistic models) of exposure (), and known “causal”/confounding factors of on and proxy outcome .
Effects on B
Effects on C
Indicators for real causal factors (1 = Yes, 0 = No)
Coefficient
value
Coefficient
value
Causal to B
Causal to C
0.12
0.001
0.16
0.000
0
0
*
*
1
1
*
*
1
0
0.39
0.000
0.62
0.000
0
0
*
*
0
1
*
*
0
1
0.24
0.000
0.43
0.000
0
0
*
*
1
1
*
*
0
1
*
*
0
0
*
*
0
0
1.22
0.000
0.88
0.000
1
1
1.15
0.000
0.17
0.000
1
0
0.23
0.000
0.27
0.000
0
0
0.16
0.000
1.04
0.000
0
1
0.31
0.000
1.56
0.000
0
1
0.13
0.000
0.19
0.000
0
0
*
*
1
1
*
*
0
1
0.28
0.000
0.43
0.000
0
0
*
*
0
0
0.17
0.000
0.24
0.000
0
0
*
*
0
0
*
*
0
0
*
*
0
0
*
*
0
0
*
*
0
0
0.23
0.000
0.26
0.000
0
0
0.31
0.000
0.58
0.000
0
0
*
*
0
0
*
*
0
0
*
*
0
0
*
*
0
0
*
*
0
0
*
*
0
0
*
*
0
0
*
*
0
0
*
*
0
0
*
*
0
0
*
*
0
0
indicates variable is not known as a “causal” factor for B, therefore is not included in the models.
