But what happens if we control for major depression?
As you can see, both social phobia and major depression are independently
associated with the likelihood of having nicotine dependence.
Given that both social phobia and major depression are positively associated with
a likelihood of being nicotine dependent.
In our predictor or splinter variables are both binary,
we can interpret the odds ratio in the following way.
Young adult daily smokers, the sample population with social phobia
are 2.3 times more likely to have nicotine dependence than young adult
daily smokers without social phobia after controlling for major depression.
Also, daily smokers with major depression are 3.7 times more
likely to have nicotine dependence than daily smokers without depression,
after controlling for the presence of social phobia.
Because the confidence intervals on our odds ratios overlap,
we can not say that major depression is more strongly associated with nicotine
dependence than the social phobia.
For the population of young adult daily smokers,
we can say that those with social phobia are anywhere between 1.2 to 4.6 times
more likely to have nicotine dependence than those without social phobia.
And those with major depression are between 2.7 and 5.0 times more likely to
have nicotine dependence than those without major depression.
Both of these estimates are calculated after accounting for
the alternate disorder.
As with multiple regression, when using logistic regression,
we can continue to add variables to our model in order to evaluate multiple
predictors of our binary categorical response variable.
Presence or absence of nicotine dependence symptoms.
Another example of confounding occurs when a logistic progression model is run to
test the association between panic disorder as the explanatory variable and
nicotine dependence, the response variable.
Panic disorder is an anxiety disorder characterized by recurring panic attacks.
Here we see a significant association, and note that young adult daily smokers with
panic disorder in our sample are 2.1 times more likely to have
nicotine dependence than young adult daily smokers without panic disorder.
However, when we add major depression to the model,
panic disorder is no longer significantly associated with nicotine dependence.
Here we have an example of confounding.
We would say that major depression confounds the relationship between panic
disorder and nicotine dependence because the P-Value for panic disorder
is no longer significant when major depression is included in the model.
Further, because panic disorder is no longer associated with nicotine
dependence, we would not interpret the corresponding odds ratio, but
would interpret the significant odds ratio between major depression and
nicotine dependence.
That is, young adult smokers with major depression are 3.6 times more likely
to have nicotine dependence than young adult smokers without major depression
after controlling for panic disorder.