# How to calculate odds ratio per unit decrease of continuous variable

I have a logistic regression model obtained in R comparing association between two index diagnoses (0 or 1) with Age (continuous) + Sex (Factor) + Renal.Fn (continuous). My variable of interest is Renal.Fn.

 model <- glm(diagnosis ~ Age + Sex + Renal.Fn, data = data, family = "binomial")


Currently to obtain Odds Ratio:

exp(coef(model))       # Renal.Fn 0.9884664
exp(confint(model))[]  # Renal.Fn 0.9848022 0.9920815


My interpretation: Per unit increase in renal function the odds of diagnosis of interest reduces.

I wish to demonstrate the opposite. For example: Per unit decrease in renal function, the odds of diagnosis increases.

Question:

1. Is it correct to take 1 / exp(coef) to derive the odds per unit decrease?
2. Is it subsequently correct to take 1/exp(coef) ^10 to derive odds per ten unit decrease?
• So $\log{\frac{\pi}{1-\pi}}=\alpha+A+S+R.Fn$, right? What you usually do is to use $\frac{e^{...+R.Fn(x+1)}}{1+e^{...+R.Fn(x+1)}}=e^{R.Fn}\frac{e^{...+R.Fn(x)}}{1+e^{...+R.Fn(x)}}$. Now just put $x-1$ instead of $x+1$, which will indeed give you $e^{-R.Fn}$. – FisherDisinformation May 4 '16 at 19:56
• @ArtificialBreeze Thanks, thats right. So essentially I can take 1 / 0.9884664 to derive the odds ratio per unit reduction? Thanks for the detailed formula, this is the problem with R as its all hidden.. – chapdoc May 4 '16 at 20:19
• Yes, that's it. You can repeat the same for your bullet point #2 :) – FisherDisinformation May 4 '16 at 20:29
• @ArtificialBreeze thanks very much, appreciate the assistance – chapdoc May 4 '16 at 20:40