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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