By definition, under-represented groups are often not known - therefore the first step is to try to get an overview of who these groups are. Once these groups begin to become active themselves, this is usually a first step towards visibility.
Further to this, I would recommend action research. Action research is research that is carried out by people who are directly involved in the subject matter, in this case working or representing specific groups. Action research is research that aims to collect information on a specific group or setting while at the same time effecting changes in that group or setting. There are pitfalls involved with action research but it is in some cases the only possible form of research. In the field of social inclusion, this is often research that has to be carried out with the help of social workers or social educators. Thus a first step would be to provide training to social workers and social educators on how to use their work also for research purposes thus helping us improve the knowledge base on under-represented groups.

I definitely agree with the importance of give visibility to unrepresented groups and to practice active research.

I would also point out that being under represented is a dynamic concept that goes beyond that of under represented minorities in a country.
Under representation is very context related. To make an example: in the Regione Lazio, participatory budgeting projects always were facing the issue of giving more voice to people from the capital (Roma) than those from rural/suburban areas to decide about the budget issues. To cope with this problem, a variety of methodologies were combined together, from engagement techniques during the participation day to simple surveys, to technological voting devices, with the double aim of engaging people in participation as possible, but also of getting voices from more marginalised areas.
To make another example: school students are generally underrepresented among the social actors (legislative and regulatory entities, teachers, tutors) in the possibility to give their voice in relevant matters, as the implementation of subject curricula, or as the processes of alternating training. Combining a variety of engagement techniques may help in overcoming similar kind of underrepresentation (eg: living lab approach in the DESCI Erasmus plus project; Panels and focus group, deliberative engagement ad testing facilities in the DIYPES Erasmus plus project) .
In synthesis, considering under representation as dynamic and context dependent may help in identifying and test new mix of approaches and methods both top down and bottom up in policy design.
 

This topic is in the scope of my study, I engage in partipatory action research as a part of the Black Emancipatory Action Research methodological orientation to complete my thesis. I agree that democratic community participation empowers the researched as well as reseachers through knowledge exchangem e.g. for policy development to address disproportionate under-representation of people of African descent in academia. Sorry I con't help with case studies on addiction but you may find a presentation I made at the Vitae Researcher Development International Conference 2015 in the documents in my site.