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I am having a bit of a tough time with some logistic regression terminology. I have performed a multivariable logistic regression analysis where I have regressed a binary variable (death, where 1 = dead and 0 = alive) on some covariates, one of which is age (measured in years). I am then looking at what happens to the outcome when I increase age by 10 years, holding all else constant.

The resulting model gives me some parameter estimates. The one for age is $\hat{\beta}_{age}=-0.015$. So I multiply this parameter by 10 (years) and exponentiate the result getting $exp(10*-0.015)=0.86$. So, I'm a bit confused as to how to report this. Which of the following is correct?

  1. A 10 year increase in age is associated with a multiplicative $(1-0.86)*100% = 13.92$% decrease in the odds of death, holding all over variables constant; or
  2. The odds ratio is decreased a multiplicative $(1-0.86)*100% = 13.92$% for each 10 year increase in age, holding all other variables constant?

Essentially, I'm confused over whether the result is a 13.92% decrease in the odds or odds ratio? Can you help me clarify.

Thanks for your help!

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This can be reported as:

The odds of death are reduced by 14% with every 10 year increase in age, i.e. the odds ratio was 0.86, after controlling for other factors.

or:

After controlling for other factors, the odds ratio for 10 year increase in age was 0.86, i.e. the odds of death were reduced by 14% with every 10 year increase in age.

Hope that helps.

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  • $\begingroup$ This is very helpful, @rnso. I really appreciate it. I knew I was missing something subtle here, but just needed someone to clarify for me. Many thanks! $\endgroup$ – StatsStudent Jul 12 '15 at 21:42

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