interpreting odds ratios

[noetsi]

Ten years and I still struggle with this

I have a continuous predictor. Years of experience

I am predicting a dv that is success or not success (I am maximizing success)

My odds ratio is 1.103 (it is statistically significant as is the model).

I interpret that as For every year they have been a counselor the odds of being successful are about 1.1 times higher.

Is this correct (my interpretation)

 

[noetsi]

This question, which I just got asked, always confuses me with odds ratios.

So, a counselor with one year experience has a 1.1 better chance of success than a counselor with noexperience?

Can you go from an odds ration to a percent chance of being in one state?

 

[hlsmith]

Your first description is fine. As for the latter, chance and odds arent the same, you can score your data using the model or write a contrast statemet to get it.

 

[noetsi]

Yeah I know they aren't the same, usually. I have looked a long time for a way to quickly convert them, but if it exists I have not found it.

 

[hlsmith]

I guess I don't know what you mean by percent chance, probability?

 

[noetsi]

I mean what they often call relative risk I think. The percent chance of being in one level of the DV for a one unit change in the predictor.

 

[fed2]

im thinking you may want to fit the log( risk ) regression rather than logit, that will give estimates in terms of fold increase in risk. This works best if things aren't too close to 1 or 0. If they are, then there are certain conditions (rare disease assumptions) under which the rel risk and OR are about the same. Im not sure how to interpret that condition in this context, but something needs to be rare, as the name suggests.

 

[noetsi]

I don't know how to do that fed2. Do you know what this form of regression is called formally?

 

[obh]

This question, which I just got asked, always confuses me with odds ratios.



Can you go from an odds ration to a percent chance of being in one state?

One year increase in the counselor experience, will increase the odds of 1 in comparison to 0 by 10% (a.k.a. the odds will be multiplied by 1.1)

 

[fed2]

Relative risk regression according to this https://www.publichealth.columbia.edu/research/population-health-methods/relative-risk-regression

Well actually it would be implemented in 'glm' in r, generalized linear model, taking 'log' link and binomial family. Honestly I sometimes just answer this question as 'yes' when asked if it means same as rel-risk if it seems no harm would come from it. The other option is just to convert the odds ( p = odds / (odds + 1) ) and divide using logistic results i think is what hlsmith said above. This works for categories. The computer should be able to compute the predicted probability in each category for you automatically.

 

[hlsmith]

Ashley Naimi (sp?) just published a paper on how to do this in SAS in the American Journal of Epidemiology.

 

[noetsi]

I will see if I can get it. Probably have to wait a year

You know you are smart when you read American Journal of Epidemiology

 

[hlsmith]

It (the paper) also likely has R code. There are SAS SUG papers on it as well. It just comes down to using the link function instead of logit - I believe. There is a package in R, I haven't used called brm. Not the Bayesian package but one by James Robins that does this as well. @fed2 was just getting at generating the RR instead of OR, which also means you can generate risk differences, which are intuitive.