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Logistic regression

Thaelina

I have to do logistic regression, but I have some trouble with my explanatory variable, it's kind of a continous variable with one group outside the continoum.

So:

age at exposure:

not exposed

I would like to see if there is a link between age of exposure and disease state, but because of the "not exposed" I have a categorical variable. The only way around this seems to be to remove the unexposed group, but that doesn't seem right. I've considered asigning a number for the "not exposed", but that doesn't seem right either, because they never were exposed.

What is the best way to proceed?

Accepted answers

All comments

Peter_Bartell

One thought for you is set up the predictor variable as Data type = Numeric and Modeling Type = Ordinal. And you can set the "No exposure" level as a zero level with some intuitive interpretation as the 1, 2, 3 etc. levels as you have articulated them.

An alternative approach could be model the exposed as a numeric predictor variable, leaving the unexposed completely out of the analysis...this answers the "If an individual IS exposed, here's the relationship?" Which would allow for interpolation (if it makes sense) for individuals exposed at say 1.5 years?

A third approach is lump all the exposed individuals into one group and call them "Exposed" and now include the unexposed in the data set.

There are probably other solutions as well...but these come to mind of the top of my head.

KarenC

To add to Peter's suggestions.
1. Analysis by graph builder. Plot the data to get an underlying understanding before moving on.
2. If the question is how does age impact outcomes within the exposed group then that is one analysis.
3. If the question is how does exposure/not exposed impact outcome that is another.
4. You could do a multiple comparison type analysis to compare each group either to a control (i.e., the unexposed) or to one another (pairwise comparisons), etc.

Lots of way to look at the data, but I would start with graph builder and go from there.

Thaelina

Thank you for your answer. I've already done solution 2 and 3.

The thing with number 2: Don't you run in to an immortality bias with that solution? I mean, we see an increased risk as the animals get exposed at a more advanced age, but the risk of this disease goes up as they age, so I don't really know how much information about the exposure we get from that?

The 3rd works well, I even tried lumping it into 3 groups (early/late/unexposed) and I completely get how to interpret that. It's mostly because I want a continous x, but including that stupid unexposed group, but I think solution 1 might fix that!

dale_lehman

This sounds like a survival problem - and your "not exposed" would be a censoring variable. In other words, the animal has not been exposed but might still become exposed. But if that approach would be valid here, I have a related question: survival models are continous models for the time to event but with a censoring variable. Another approach to such a problem (suggested above as well as used frequently in modeling things like insurance problems) is to use a two-step modeling procedure. First model the discrete event/no event frequency using a classification model (such as logistic regression) and then model the "severity" using only the data where the event has happened (this would be a continuous dependent variable). Can anybody shed light on the relative merits of using these two alternative ways to model such a problem?

Peter_Bartell

Dale Lehman's idea of a censored approach was one I was thinking of as well. This precisely why I was somewhat uncomfortable suggesting the kitchen sink ordinal only approach. The unexposed group is clearly different than the other exposed group from this censoring perspective and censoring/suvival models are ideally suited for just this scenario.

KarenC

This is a great discussion. The mix of methods plus the questions to be answered. The discrete y/n vs. the severity and how to treat the n category that has no severity. I don't have a good answer, would love to hear some other thoughts. However, I do think one has to be careful of the context of the questions to be answered. For example, are you trying to diagnosis? That is separate the y from the n. Or are you trying to manage? That would be in the y group can you separte the severity levels? And if that is the case should the n's be included? Have they just not entered the y group yet or are they really a control group and would never be in the y group? Then the questions such as are you in discovery mode (i.e., R&D) or some other mode? Risk/Cost of decisions made on the analysis.

I had not thought about censoring in these types of problems, will have to give that some more thought. However, as Dale mentioned, the survival type models are used for time to event, so you would have to think about how to treat severity as a time to event?