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Logistic Regression
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Adjusted log OR

Adjusted log OR

The slope $ \beta_1$ for the covariate $x_{1{j}}$ in a logistic regression

$\mathrm{logit}(p_j) = \beta_0 + \beta_1 x_{1j} + \beta_2 x_{2j} + \cdots + \beta_k x_{kj}$

is viewed as the adjusted log OR of primary interest.

In order to start over again, you need to clear the model formula.

From the data above, A pair of columns for "Yes" count and "No" count must be selected one by one.

Log OR corresponds exactly to the slope estimate $\hat{\beta}$ of the simple logistic regression $\mathrm{logit}(p_j) = \alpha + \beta x_{j}$ with covariate $x_{j}$ of primary interest.

The result of fitting the logistic regression is obtained in the table below. To test the null hypothesis $ H_0: \beta_i = 0$, the Wald test statistic Slope/SE is constructed, and the Pvalue is approximated by the standard normal distribution.

The slope coefficient $ \beta_1$ of the primary interest $x_{1{j}}$ is adjusted in a multiple logistic regression with covariates $x_{2{j}}$ up to $x_{k{j}}$, which can be added one by one.

When the last additional covariate $x_{k{j}}$ is categorical, say categorical value 'A' or 'B', the effect of adjustment can be visualized by interaction with the status, 'A' or 'B', of $x_{k{j}}$ as described in the legend box.

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