the odd in logistic regression is expressed per increase of one unit of the independent continues variable
If I want to express it per increase of sd do I multiply de odds per unit with the value of the sd?
Use the z-transformed values (z = (x-mean(x))/sd(x) ) of the predictor to fit the logistic model. The coefficients will then be log odds ratios for one SD change of the predictor.
I am a bit concerned about using standardized predictors. If getting the predictor values on different scales in different experiments is a problem (in this case your approach would make the coefficients from different experiments numerically comparable) then my first question was what the (practical, scientific) value of the predictor is? There seems to be a relevant problem with the measurement of this predictor... can this be useful anyway? It may be that everything is fine, but for me all the alarm bells start ringing...
To calculate the odds per increase of standard deviation (SD) with logistic regression using one continuous predictor, you can follow these steps:
1. Estimate the coefficient: Run the logistic regression model with your continuous predictor variable. Obtain the coefficient estimate (β) for the continuous predictor in the logistic regression equation.
2. Calculate the standard deviation (SD): Calculate the standard deviation of your continuous predictor variable.
3. Calculate the odds ratio: Compute the odds ratio (OR) using the formula: OR = exp(β × SD), where exp() denotes the exponential function.
4. Interpret the odds ratio: The resulting odds ratio represents the change in odds for a one-unit increase in the continuous predictor variable's SD. For example, an odds ratio of 2 means that for every one SD increase in the predictor variable, the odds of the outcome occurring are expected to double.
Note that this calculation assumes a linear relationship between the continuous predictor and the log-odds of the outcome in logistic regression. Also, keep in mind that interpreting odds ratios should consider the context of your specific study and the characteristics of the predictor variable.
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