There is nothing wrong with getting a result with an extremely high odds ratio (OR). However, issues arise when there is a gigantic confidence interval which is the position you are finding yourself in (95% CI:2.04-27.24). The standard error for this variable is quite large (most likely) and is giving you such a large discrepancy in the actual estimate. With this being said, the specific fidning you have is worth reporting as the OR does not cross zero and therefore appears to be consistently significant but there are a couple of things to note:
1) you should mention that the actual strength of the relationship is questionable due to the large standard error;
2) You should look at the other variables in your model to see if there is an interaction going on with this particular variable and see if something is influencing the effect.
One another topic, the hosmer-lemeshow statistic suggests that your data does not fit the model very well which further suggests that you should see what potential variables are affecting this.
Unfortunately, I am needing to cut my answer short-ish, but feel free to contact if you would like further information.
There is nothing wrong with getting a result with an extremely high odds ratio (OR). However, issues arise when there is a gigantic confidence interval which is the position you are finding yourself in (95% CI:2.04-27.24). The standard error for this variable is quite large (most likely) and is giving you such a large discrepancy in the actual estimate. With this being said, the specific fidning you have is worth reporting as the OR does not cross zero and therefore appears to be consistently significant but there are a couple of things to note:
1) you should mention that the actual strength of the relationship is questionable due to the large standard error;
2) You should look at the other variables in your model to see if there is an interaction going on with this particular variable and see if something is influencing the effect.
One another topic, the hosmer-lemeshow statistic suggests that your data does not fit the model very well which further suggests that you should see what potential variables are affecting this.
Unfortunately, I am needing to cut my answer short-ish, but feel free to contact if you would like further information.
Crude odds ratio: the ratio of odds when there is just one odds ratio (OR) resulting from a single independent variable and the dependent variable. It is 'crude' because it provides as estimate of experiencing something (DV) given the levels of a single (IV) without correcting for the variances of the other variables.
Adjusted OR: the ratio of odds when one or more independent variables are added to a model in order to predict the dependent variable. In other words, the OR of one variable is adjusted for all of the other independent variables that you have included.
Clarification: Let's say you are wanting to predict death (DV: two levels (yes/no)) and one model you just have the number of hospitalizations. This would produce a 'crude OR' for hospitalization number in predicting death. Now let's say you keep this variable and add age, gender, marriage, and race into the model. This results in a slightly different OR for hospitalization number as it is now adjusted for the previously mentioned demographic variables (age, gender, etc.). Remember now that each variable has a referent category which; therefore the adjusted OR for death by the number of hospitalizations is the OR when the variance for all of the other independent variables are accounted for (typically all of them are placed as using the referent category).
The model you have provides the adjusted ORs (AOR) for each of the independent variables adjusting for the variance of said variables. So yea you have adjusted odds ratios. However, this this bit of information I must now again state that your model does a poor job at correctly predicting the dependent variable probablilities (A Hosmer & Lemeshow test of p
An odds ratio of 27 is not really all that high. It corresponds to a proportion of about 96%. So I don't think it's anything to worry about. A log odds ratio of 18 or 27, on the other hand, would be pretty unreasonably high (basically indistinguishable from 100%.)
It's also totally natural that CIs will be bigger when odds are high. This is because of the non-linear nature of the logit transform. If some response is happening around e.g. 50% of the time, then a small change in odds ratio corresponds to a very big change in proportion (for example, stepping from an odds ratio of 2 to an odds ratio of 3 corresponds to stepping from 66% to 75%), whereas when the response is happening close to 100% of the time, then a large change in odds ratio only corresponds to a small change in proportion (for example, stepping from an odds ratio of 15 to an odds ratio of 16 corresponds to stepping from 93.75% to 94.11%). It follows, then, that when some response is happening close to 100% of the time, there is a very wide range of odds ratios that corresponds to more or less the same percentage response; and, therefore, the CI expressed in terms of odds or log odds is going to be very wide.
Long story short, there does not seem to be anything strange going on in these results.
Regardless of what was previously said, it is still worthwhile to necessary to note the wide confidence interval. What the previous post is referring to is when the dependent and independent variables are measuring nearly or ARE the same thing OR when there are only a few occurrences of the particular IV. When this is the case the a person will obtain ORs 95% CI of 999.99 or something ridiculous like that. This is a HUGE problem because if your predicting a particular outcome how the hell can you interpret this?
However, the CI you presented was not unreasonable and did not cross below 1.00 which lead to it having a statistically significant result. At the same time the effect was estimated to range by a factor of 13.5 which is why you would include it in the model but mention that it was not a stable result. Now if the result you obtained was 4.50 (95% CI: 0.5 - 6.5) then this would be a result that you should NOT report. I hope that this makes sense.
Also if you leave this variable out, does the Hosmer Lemeshow Test become non-significant, If so than this may suggest leaving this variable out of the model. A large value for the Hosmer Lemeshow test suggests a clear indication of a substantial problem with the model that you are fitting (Hosmer and Lemeshow, 2000).
Wishing you all the best,
Logan Netzer
Hosmer DW, Lemeshow S. Applied Logistic Regression (2nd Edition).... Not cited the best but it lets you know the source.