Table 1 Difference between univariable- and multivariable exposure effects as combination of confounding bias and the noncollapsibility effect
From: Noncollapsibility and its role in quantifying confounding bias in logistic regression
| Difference between multivariable- and univariable effect estimate \(({{\varvec{\beta}}}_{1}^{\boldsymbol{^{\prime}}}-{{\varvec{\beta}}}_{1}\)) |
Confounding bias (\({{\varvec{\beta}}}_{1}-{{\varvec{\beta}}}_{1}^{\boldsymbol{*}}\)) |
Noncollapsibility effect (\({{\varvec{\beta}}}_{1}^{\boldsymbol{*}}-{{\varvec{\beta}}}_{1}^{\boldsymbol{^{\prime}}}\)) |
|---|---|---|
| Negative | Negative value | Negative value |
| Zero | Negative value | |
| Negative value | Zero | |
| Positive value | Greater negative value than the positive confounding bias value | |
| Greater negative value than the positive noncollapsibility effect value | Positive value | |
| Zero | Zero | Zero |
| Equal positive value as the negative noncollapsibility effect value | Equal negative value as the positive confounding bias value | |
| Equal negative value as the positive noncollapsibility effect value | Equal positive value as the negative confounding bias value | |
| Positive | Positive value | Positive value |
| Zero | Positive value | |
| Positive value | Zero | |
| Negative value | Greater positive value than the negative confounding bias value | |
| Greater positive value than the negative noncollapsibility effect value | Negative value |