Interpretation of logistic regression results

#1
Hello,

I am currently working on a project using quantitative analysis. I have 3 models for the logistic regression: unadjusted, minimally adjusted, and fully adjusted. The unadjusted models show evidence of an association for some of the exposure variables with the outcome. However, upon adjusting for confounders, the strength of the association attenuates but the size of the effect (odds ratio) increases. I am unclear about how to interpret this in the research paper I am writing.

Thank you for the help.

Regards
Kritika Jain
 

Karabiner

TS Contributor
#2
the strength of the association attenuates but the size of the effect (odds ratio) increases
I am not sure what you mean by this. Odds ratio indicates the strength of the association
between the focus variable and the outcome. So what you seem to say is "the strength of
the association decreases, but the strength of the association increases"?

With kind regards

Karabiner
 
#3
Sorry for the confusion. I meant to say that the OR is increasing, but the confidence interval is widening and includes a null value of 1 upon adjusting for confounders.
Crude OR = 3.47 (1.29–9.29)
Minimally adj. OR = 4.02 (0.56-28.90)
Fully adj. OR = 4.34 (0.45-42.27)
 

hlsmith

Less is more. Stay pure. Stay poor.
#4
If you have legitimate confounders - include them and that is your result. You could also address the confounders via using weights, so you would end up with a marginal instead of conditional estimate. Not sure if doing this may decrease your SEs since you would have fewer variables in the model.

The follow-up question would be, how big is your sample and what proportion of the outcome of interest?
 
#5
Thanks for the reply.
The sample consists of 518,050 observations and 0.002% is the prevalence for the outcome of the interest.
I believe that reporting marginal estimates would be beyond the scope of this dissertation. Since the OR consistently shows a positive association between exposure and outcome, would it worth mentioning that the widened CI and lack of evidence is due to a lack of power and small number of people with outcome of interest?
 

Karabiner

TS Contributor
#6
518,050 observations and 0.002% is the prevalence
So you want to predict k=10 cases. Fortunately, hlsmith asked the right question. But it is a bit surprising
that you did not consider this information relevant by yourself.

It is quite logical that using 2 or more variables for the prediction of just 10 events leads to overfitting,
i.e. the prediction within the sample improves, but generalizabilty beyond the sample data decreases,
hence the larger standard error.
 

hlsmith

Less is more. Stay pure. Stay poor.
#8
Follow-up, how many predictors are in the model and how are they formatted (e.g., categorical with blank groups or continuous, etc.)?