They would be classified as you would any other epidemiologic study, depending on the study design: observational, case-control, cohort, retrospective, prospective, etc.  The molecular element is only a tool to investigate something, such as genes or biomarkers.  Commonly these studies are case-control or observational or (often small)  followup cohort studies because they look at the molecular (or genetic) makeup of people and follow their outcomes or look (usually retrospectively) at their risk or odds of having a disease. 

Usually genetic epidemiological studies are case control or case only but  cohort designs could be used. Genetic epidemiological studies  would usually be observational.

Rothman and Greenland has a good chapter.

They would be classified as you would any other epidemiologic study, depending on the study design: observational, case-control, cohort, retrospective, prospective, etc.  The molecular element is only a tool to investigate something, such as genes or biomarkers.  Commonly these studies are case-control or observational or (often small)  followup cohort studies because they look at the molecular (or genetic) makeup of people and follow their outcomes or look (usually retrospectively) at their risk or odds of having a disease. 

Like any other epidemiological study, if you are not studying the effect of an intervention (like before and after studies), then it is an observational study. Classification depends on your objective. If you are comparing a group with a particular outcome to controls without that outcome and looking back to find possible cause/ risk factor/ gene then it is a case-control study. If you start with an exposure/ gene and comparing to a control group without that exposure and looking forward to see how many outcomes in each group then it is cohort study. If you are not sure if the exposure actually preceded the outcome in your data set then it is a cross sectional study. Most genetic studies are cross sectional or case control. A cohort just means a group with some common trait. For example all those with gene A and then within that group compare those with gene B vs those without gene B.

The appropriate choice in study design is essential for the successful execution of biomedical and public health research. There are many study designs to choose from within two broad categories of observational and intervention studies. Each design has its own strengths and weaknesses, and the need to understand these limitations is necessary to arrive at correct study conclusions.

Observational study designs, also called epidemiological study designs, are often retrospective and are used to assess potential causation in exposure-outcome relationships and therefore influence preventive methods. Observational study designs include ecological designs, cross sectional, case-control, case-crossover, retrospective and prospective cohorts. An important subset of observational studies is diagnostic study designs, which evaluate the accuracy of diagnostic procedures and tests as compared to other diagnostic measures. These include diagnostic accuracy designs, diagnostic cohort designs, and diagnostic randomized controlled trials.

Intervention studies are often prospective and are specifically tailored to evaluate direct impacts of treatment or preventive measures on disease. Each study design has specific outcome measures that rely on the type and quality of data utilized. Additionally, each study design has potential limitations that are more severe and need to be addressed in the design phase of the study. This manuscript is meant to provide an overview of study design types, strengths and weaknesses of common observational and intervention study designs.

I pray that this answered some part of your question.

Chaplain: Perry McClinton

I agree with Alice . He explained all designs for the author . Now author is to decide his objectives and design accordingly.

Depends on hwat you are assessing and how. There's a great page in the Hennekans book on classifying study design. If there's no intervention then it's an observational study, the design may be case control or cohort, .depends on how you structure your project.