Producing an odds ratio for a continous variable - i know many people disagree... but...

[Tara Boyle]

Hi I've got the following regression

reg continousvar treatmentvar ptcomordbitiy

It produced co efficients however I would like to describe the odds ratio in my text
I know some people disagree, however as described here in pg 4, I do agree that odds ratios are best to use in the written discussion to describe findings.

https://spia.uga.edu/faculty_pages/r...MLENotes6a.pdf

If I had to exp(coefficients) produced from the above, will this be an accurate odds ratio? or perhaps 'ODDS of occurring'?

[Clyde Schechter]

If I had to exp(coefficients) produced from the above, will this be an accurate odds ratio? or perhaps 'ODDS of occurring'?

No, it will give you neither of those. In fact, as far as I know, there is no name for the exponentiated coefficients of an ordinary linear regression. Nor, as far as I know, is there anything useful to be said about them.

If your continuous outcome variable is restricted the 0 to 1 interval, you might look into -fracreg logit-, which would interpret the continuous variable as a probability estimate and would fit a logistic model. The resulting coefficients, when exponentiated, would be odds ratios. Perhaps this is what you have in mind?

Added: I do not understand the relevance of the paper you linked to. All of the material there uses discrete ordinal outcome variables.

[Tara Boyle]

Hmm thanks for replying so quickly.
Ok, I get confused so specialist statisticians on here say we can not generate odds ratios for continuous variables, yet papers like here present ODDS for every age increase. How is this possible?

https://www.thelancet.com/action/sho...2819%2930550-X

The material presented in post 1 was really to quote:

'As was the case for binary logits, odds ratios are a nice, intuitive way of discussing the substantive impact of your covariates. They’re probably best used “textually” – that is, as part of the written discussion of your research findings, rather than reported in a table or the like' - when referring to continuous variables

[Clyde Schechter]

At the link in #3, the title of the table says that they are modeling "predictors of advanced schistosomiasis," the latter clearly being a dichotomous variable, not continuous.

[Denise Vella]

Sharp ! Point taken…. So how would you present a regression modelling a continuous variable eg age on a categorical variable eg. Lung cancer.

would it just be with co efficients ?

[Clyde Schechter]

I'm not sure what you're asking here. When we say we model variable 1 ON variable 2 we usually mean that variable1 is the dependent variable and variable 2 is the independent one. (In fact, there is a statistical package, MPlus, in which the word ON is a keyword used to distinguish dependent and independent variables in exactly this way.) So, in that sense, if we model age on lung cancer, this would be -regress age i.lung_cancer-, or your standard analysis of variance or t-test contrasting the mean age in lung cancer patients with the mean age in non-lung-cancer patients. This is not a situation where odds ratios would be appropriate. The results could be presented as a regression coefficient for lung_cancer and its confidence interval, with the comment that this coefficient estimates the mean age difference between lung-cancer patients and non-lung-cancer patients. Or it could be presented as a table with two rows, each showing the estimated mean age and confidence interval in one of the two types of patients. (The -margins- command, after -regress-, can produce this table.) Often both ways of showing the results are used.

However, if we model lung-cancer ON age, that is a different story. There are a number of ways of doing that. We can do a linear probability model: -regress lung_cancer c.age-. This would enable us to assess the lung cancer risk differences at different ages. Or we can do a logistic regression model: -logit lung_cancer c.age-. In this situation we get regression coefficients which, when exponentiated, estimate the odds ratio per unit of age (the unit of age is usually years, at least in adults). If you don't want to do the exponentiation yourself (and I don't recommend you do that), Stata offers the convenience command -logistic- which presents the results directly as odds ratios rather than coefficients.

There are also other ways to model a dichotomous outcome on a continuous regressor, but if you want your results presented as odds ratios, then -logit-/-logistic- is your method of choice.