The Center for Disease Control and Prevention (CDC) has a clear definition of the general role of an epidemiologist, i.e., what an epidemiologist does. An epidemiologist uses a scientific, data-driven methodology to find the extent and causes of "health outcomes and diseases in populations." They identify the distribution of outcomes (where and how often people are affected) and the causes and risk factors for health outcomes in a defined population.
CDC: Epidemiology is the method used to find the causes of health outcomes and diseases in populations. In epidemiology, the patient is the community and individuals are viewed collectively. By definition, epidemiology is the study (scientific, systematic, and data-driven) of the distribution (frequency, pattern) and determinants (causes, risk factors) of health-related states and events (not just diseases) in specified populations (neighborhood, school, city, state, country, global). It is also the application of this study to the control of health problems (Source: Principles of Epidemiology, 3rd Edition).
In the Ecuadorean Amazon rain forest situation related to the dumping of crude oil production waste and to oil spills from production, an epidemiologist would use the scientific collection of data in the jungle and along Amazon rivers and streams--such as the Aguarico River and its streams--to identify the origin, causes and risk factors for health outcomes (e.g., cancers, skin rashes, sudden deaths) in the population affected, then suggest courses of action to prevent the continuation and spread of the outcomes.
The epidemiologist's task related to environmental health issues as seen in the film is to use the epidemiological method, defined above, to identify what the population is sick with (e.g., what type of skin rash) and to trace where the exposure came from and, importantly for the Ecuadorian lawsuit, when the exposure occurred. An epidemiologist's investigative analysis would address the defendant's counter-argument that the health issues originated as a result of oil spills occurring after PetroEcuador took over operations. For instance, the epidemiologist would take core samples and water samples--just as the court appointed independent expert did--to identify the contaminants present and when they first came to be present. The epidemiologist would trace connections between contaminants and health issues.
Like investigators at the scene of a crime, disease detectives begin by looking for clues. They systematically gather information, asking questions such as:
Who is sick?
What are their symptoms?
When did they get sick?
Where could they have been exposed?
Using statistical analysis, epidemiologists study answers to these questions to find out how a particular health problem was introduced. (CDC)