Final answer:
A nurse working to evaluate patient outcomes after ECT is involved in analytical epidemiology, using observational studies to assess the treatment's efficacy.
Step-by-step explanation:
The branch of epidemiology that a nurse is involved in when seeking outcomes for patients whose depression was treated with electroconvulsive therapy (ECT) is known as analytical epidemiology.
Specifically, this type of epidemiology focuses on the study of disease outbreaks to establish associations between an agent—in this case, ECT—and a disease state, which is depression.
Through observational studies comparing groups of individuals, including those who have undergone ECT and those who have not, the nurse and other researchers can draw conclusions about the efficacy of this treatment method for depression.