topic re: ">999.999" odds ratio in logistic regression model in Statistical Procedures

re: ">999.999" odds ratio in logistic regression model

baseballyanks1 — Fri, 14 Aug 2020 03:09:36 GMT

Trying to figure out why I'm getting an absurd OR for a continuous variable log_X that does not have any missing values. Any ideas?

proc logistic data=WORK.DISEASE_MM;
	class Gender1 (ref="0") / param=glm;
	model Strata1 (event='1')= gender1 log_X log_Y age/ link=logit clparm=both clodds=both alpha=0.05 
		technique=fisher scale=none aggregate lackfit;
run;

Odds Ratio Estimates and Profile-Likelihood Confidence Interverals

Effect Estimate 95% CI

gender1 1 vs 0 7.321 3.514 16.152

log_Y 0.617 0.075 5.004

log_X >999.999 >999.999 >999.999

Age 0.926 0.894 0.955

Re: re: ">999.999" odds ratio in logistic regression model

Norman21 — Fri, 14 Aug 2020 05:51:06 GMT

Welcome to the Community!

This looks like it could be a problem with the data, such as an outlier. Can you provide more information?

Re: re: ">999.999" odds ratio in logistic regression model

baseballyanks1 — Fri, 14 Aug 2020 11:14:36 GMT

Thanks for the welcome message! 😄 Long time visitor, first time poster.

That's what I was thinking too, about an outlier, but the data range for log_X is 3.390 to 4.421 (compared to log_Y, 1.853 to 3.346).

Happy to provide any other information needed!

Re: re: ">999.999" odds ratio in logistic regression model

Norman21 — Fri, 14 Aug 2020 11:31:43 GMT

The estimate of the logistic regression coefficient is for a one unit change in log_X score, given the other variables in the model are held constant. In your case, a one unit change would go from 3.390 to 4.390, almost the entire range. What is the estimate for log_X? Is it a large number?

Can you provide some of the other output?

Re: re: ">999.999" odds ratio in logistic regression model

Ksharp — Fri, 14 Aug 2020 12:02:46 GMT

What is your logistic regression coefficient of log_X (beta)?
I guess it is very big due to odds ratio= e^beta .

Re: re: ">999.999" odds ratio in logistic regression model

Ksharp — Fri, 14 Aug 2020 12:13:23 GMT

Also try UNITS statement to adjust unit of odds ratio :

units log_X=0.1 ;
units log_X=2*SD ;

Re: re: ">999.999" odds ratio in logistic regression model

baseballyanks1 — Sat, 15 Aug 2020 14:41:31 GMT

Sorry for the late reply.

The estimate for log_X is 10.3647 with a 95% CI of 7.3216-13.4078

Included more output below

Re: re: ">999.999" odds ratio in logistic regression model

baseballyanks1 — Sat, 15 Aug 2020 14:45:59 GMT

Thanks for the suggestion, when I include a units statements I do get actual values for log_x OR: 79.685 with 95% CI 24.050-318.803

Re: re: ">999.999" odds ratio in logistic regression model

baseballyanks1 — Sat, 15 Aug 2020 14:48:53 GMT

I tried KSharp's suggestion of including a Units statement, which yields actual values (79.685, 95% CI 24.050-318.803). As you said, do you think it's so high due to the spread of the data for log_X (I.e. only encompassing a 1-unit change) as opposed to log_Y or could something else be going on to drive it?

Re: re: ">999.999" odds ratio in logistic regression model

Rick_SAS — Sat, 15 Aug 2020 15:19:13 GMT

Basically it is a combination of your data and the model. See the article "Formats for p-values and odds ratios in SAS." On that page, search for the phrase "let's try to understand why the odds ratio is so extreme," which will take you near the end of the article.

Re: re: ">999.999" odds ratio in logistic regression model

baseballyanks1 — Sat, 15 Aug 2020 15:27:07 GMT

Thanks for the heads up! In the case presented on that link, there were a severely limited number of data points (3 observations). But for the continuous variable log_X there are no missing data points (n=236) without any clear outliers. Despite having a similar profile, Log_Y doesn't yield such an extreme OR.

Re: re: ">999.999" odds ratio in logistic regression model

Norman21 — Sat, 15 Aug 2020 17:29:31 GMT

Interesting!

There is a paper that describes a problem similar to yours. They suggest the solution is to use Penalised Logistic Regression using the Firth option. Perhaps this is worth a try.

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4944325/

https://documentation.sas.com/?docsetId=statug&docsetTarget=statug_logistic_examples15.htm&docsetVersion=15.1&locale=en

Re: re: ">999.999" odds ratio in logistic regression model

baseballyanks1 — Sat, 15 Aug 2020 19:29:40 GMT

Yeah, it seemed odd to me, I've never seen this issue with a continuous variable like this with a sample size at a decent size of this dataset.

Thanks so much for that suggestion, I'll take a look now and will try to run it!

Re: re: ">999.999" odds ratio in logistic regression model

baseballyanks1 — Sat, 15 Aug 2020 20:36:23 GMT

Just ran

proc logistic data = WORK.disease;
model strata1(event='1') = log_X / firth;
run;

proc logistic data = WORK.disease;
model strata1(event='1') = log_X;
run;

Still getting the ">999.99" issue. I can include a unit statement, but the Firth model (unless my code is wrong) didn't seem to do much.

Re: re: ">999.999" odds ratio in logistic regression model

Norman21 — Sun, 16 Aug 2020 08:14:49 GMT

Thanks for trying. It looks like KSHARPs solution is best:

units log_X=0.1 ;
units log_X=2*SD ;

Re: re: ">999.999" odds ratio in logistic regression model

SteveDenham — Mon, 17 Aug 2020 12:09:23 GMT

Sometimes a picture is worth a thousand analyses. Try plotting your observed values versus logX. I suspect you will see a very apparent trend.

SteveDenham

Re: re: ">999.999" odds ratio in logistic regression model

baseballyanks1 — Mon, 17 Aug 2020 12:18:21 GMT

Fair suggestion. I've plotted log_X for the binary outcome (disease/no disease) as well as against age but nothing seems obviously out of the ordinary, unless I'm missing something.

Re: re: ">999.999" odds ratio in logistic regression model

SteveDenham — Mon, 17 Aug 2020 17:04:02 GMT

@baseballyanks1 :

I think if you exchange the X and Y axes on this, it should be a little more apparent. Disease (=1) is associated with large values of logX, no disease(=0) with small values. While there is some overlap, the disease group "stretches" out more in the positive logX direction from the group median than the no disease group. Those points will drive the fit of the regression line, so that you get a fairly large slope. By eyeball, I would estimate the slope at something like 9 (difference in logits / difference in logX) = 3.72/.4, which is really close to the ~10 value of the ML estimates.

SteveDenham