A Proxy Outcome Approach for Causal Effect in Observational Studies: A Simulation Study
Table 1
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 A
Effects on C
Indicators for real causal factors (1 = Yes, 0 = No)
Coefficient
value
Coefficient
value
Causal to A
Causal to C
0.79
0.000
0.09
0.011
1
0
0.19
0.000
0.92
0.000
0
1
0.69
0.000
0.03
0.360
1
0
0.46
0.000
0.50
0.000
0
0
*
*
1
1
*
*
1
1
0.87
0.000
0.29
0.000
1
0
0.20
0.000
0.84
0.000
0
1
0.04
0.293
0.80
0.000
0
1
0.77
0.000
0.13
0.000
1
0
*
*
1
0
0.15
0.000
0.79
0.000
0
1
*
*
1
0
*
*
0
0
0.85
0.000
0.91
0.000
1
1
*
*
1
1
0.73
0.000
0.10
0.009
1
0
0.15
0.000
0.89
0.000
0
1
*
*
0
1
0.95
0.000
0.35
0.000
1
0
*
*
0
0
0.27
0.000
0.16
0.000
0
0
0.25
0.000
0.19
0.000
0
0
0.20
0.000
0.18
0.000
0
0
*
*
0
0
*
*
0
0
*
*
0
0
*
*
0
0
0.50
0.000
0.47
0.000
0
0
*
*
0
0
*
*
0
0
*
*
0
0
*
*
0
0
*
*
0
0
*
*
0
0
*
*
0
0
*
*
0
0
0.13
0.001
0.17
0.000
0
0
*
*
0
0
0.16
0.000
0.17
0.000
0
0
indicates variable is not known as a “causal” factor for A, therefore is not included in the models.
