Table 1 Bias in the estimation of treatment effect (β1 = 1), for different values of the confounder effect (β2) and of sample size, for 3 logistic regression models: unadjusted for confounder, adjusted in sample-based model, and adjusted in true model
Sample size | Unadjusted analysis | Adjusted, sample-based model | Adjusted, true model | Unadjusted analysis | Adjusted, sample-based model | Adjusted, true model |
|---|---|---|---|---|---|---|
Continuous confounder effect β2 = 0 | Binary confounder effect β2 = 0 | |||||
2 × 50 | 0.021 | 0.033 | 0.021 | 0.023 | 0.034 | 0.023 |
2 × 100 | 0.011 | 0.017 | 0.011 | 0.012 | 0.017 | 0.012 |
2 × 200 | 0.006 | 0.009 | 0.006 | 0.005 | 0.008 | 0.005 |
2 × 500 | 0.003 | 0.004 | 0.003 | 0.001 | 0.003 | 0.001 |
2 × 1000 | 0.000 | 0.001 | 0.000 | 0.000 | 0.001 | 0.000 |
Continuous confounder effect β2 = − 0.5 | Binary confounder effect β2 = − 0.5 | |||||
2 × 50 | 0.014 | 0.038 | 0.025 | 0.015 | 0.040 | 0.026 |
2 × 100 | 0.001 | 0.017 | 0.011 | 0.002 | 0.020 | 0.013 |
2 × 200 | − 0.005 | 0.009 | 0.006 | − 0.006 | 0.008 | 0.005 |
2 × 500 | − 0.009 | 0.003 | 0.002 | − 0.010 | 0.003 | 0.002 |
2 × 1000 | − 0.009 | 0.002 | 0.001 | − 0.010 | 0.002 | 0.001 |
Continuous confounder effect β2 = − 1 | Binary confounder effect β2 = − 1 | |||||
2 × 50 | − 0.018 | 0.038 | 0.022 | − 0.021 | 0.038 | 0.023 |
2 × 100 | − 0.031 | 0.017 | 0.010 | − 0.034 | 0.019 | 0.011 |
2 × 200 | − 0.037 | 0.008 | 0.005 | − 0.040 | 0.008 | 0.004 |
2 × 500 | − 0.039 | 0.004 | 0.003 | − 0.043 | 0.003 | 0.002 |
2 × 1000 | − 0.040 | 0.002 | 0.001 | − 0.044 | 0.002 | 0.001 |