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I am doing logistic regression to assess the influence of a novel parameter on the risk for a certain disease and I have 2 questions:

(1) Is it appropriate to logarithmize one or more independent variables in logistic regression analysis? I want to describe odds ratios per per 1-SD increase, and, as parameter I am investigating is not normally distributed, this would make a 1-SD increase more concrete. Also, the odds ratios look much better if I use the logarithmized parameter an independent variable and then calculate SD-scores, rather than calculating SD scores of the untransformed variable.

(2) How can I describe my reasons for log-transforming the marker in my METHODS section on my paper? Should I simply put that I want to make a one SD increase more concrete?

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    $\begingroup$ The log transformation is a very special case of nonlinearly modeling the effect of a predictor. It is unlikely to fit well enough in most situations, and zero and negative predictor values are disallowed. $\endgroup$
    – Frank Harrell
    Dec 2, 2014 at 13:34
  • $\begingroup$ Thanks for the answer. Negative and zero predictor values are not possible in this case. Logarithmizing the predictor does improve the model in terms of 2-Log-Likelihood, Cox&Snell R2 and Nagelkerke R2. $\endgroup$
    – martin.l.
    Dec 2, 2014 at 14:12
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    $\begingroup$ That does not address whether logarithmic shapes fit the data. $\endgroup$
    – Frank Harrell
    Dec 2, 2014 at 23:02
  • $\begingroup$ Then my question is, how can I determine how well a specific transformation fits the data? $\endgroup$
    – martin.l.
    Dec 3, 2014 at 8:55
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    $\begingroup$ Make estimation of the transformation an explicit part of the model. That way you get flexibility and statistical tests "know" how many degrees of freedom are actually in effect. Regression splines are perhaps the best approach. You can see detailed examples at biostat.mc.vanderbilt.edu/RmS#Materials under Handouts. $\endgroup$
    – Frank Harrell
    Dec 3, 2014 at 13:34

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