I have to design a hypothetical study in critical care medicine. The aim of the study is to examine wether the outcome of patients (survivor vs. non-survivor) is associated with certain ventilator settings during mechanical ventilation. Since all patients enrolled in this study are treated with mechanical ventilation, would it be reasonable to call this a retrospective case-control study, where the cases (death) and control (survivor) are exposed either to ventilator settings below a certain threshold or above?
If you are just starting with a whole bunch of patients that are on mechanical ventilation, then you have identified a cohort and you aren't doing case-control.
However, this sounds like it could be case-control approach if you approach and analyze it as such. In a case-control approach, you identify cases by some outcome measure, and take controls from a similar population without the outcome. So, if you started with a group of patients who died after mechanical ventilation, and then take some controls who did not die but were also on mechanical ventilation, you could call that case-control. The figure on Wikipedia shows how a case-control and retrospective cohort study are nearly the same, except for what the investigator takes as "known" going in.
In a non-experimental paradigm, there is little distinction between "independent" and "dependent" variables, since neither is manipulated by the investigator; everything is just an observation, and the estimated relationships are all correlative. In a cohort study, you fit a model of the form:
Outcome ~ Exposures + error
whereas in a case-control study you fit a model:
Exposures ~ Outcome + error
In the classic "lung cancer vs cigarettes" example, this is the difference between asking "Are people who smoke (exposure) more likely to get lung cancer (outcome)?" and asking "Are people who get lung cancer (outcome) more likely to be smokers (exposure) than people who are cancer-free?"
Often you use a case-control approach because cases are rare. It's more efficient in that circumstance to instead start with a bunch of cases and then identify controls that go with them to have a (at least roughly) balanced sample; otherwise, you might need 1000s of subjects in a study to find just a couple cases, and yet not have enough statistical power to say anything about them.
As with other correlative studies, whichever approach you take you need to be wary of drawing causative conclusions from correlation. If different ventilator settings are used for sicker patients, then you're likely to find correlations between settings and mortality that are not causative.