There have been lots of reports that nuclear DNA variations can predispose human subjects to many diseases. But little information is available whether this is the case in mitochondrial DNA sequence variations.
It is an interesting question, since haplogroups help define genetic populations. Currently at UIS, in the esearh group of inborn errors of metabolism we are studying mitochondrial diseases (particularly now we are with MELAS), and in the literature review we have seen that the level of heteroplasmy is fundamental for the development of mitochondrial diseases. Then it is likely that the presence of specific Halogrupos could contribute equally to the development of certain types of diseases, and one way to prove this may be the mitochondrial DNA sequencing in several tissues of different populations to first determine the presence of these haplogroups, and then determine whether the existence of a haplogroup with a specific pathology.
There is a topic to keep in mind is that several genes encoding proteins involved in mitochondria are nuclear DNA level, another point to keep in mind if you wanto to know whether the existence of a haplogroup with a specific pathology.
For now is all, again interesting question, and very good research topic.
There is a very large literature on associations of mitochondrial haplogroups with a wide range of diseases. Most of these are single reports of an association with no independent vertification. As far as I know, only Multiple Sclerosis and Parkinsons associations with the European haplogroup J have been replicated, but there may be others that I do not know about. Most of the literature is about the European haplogroups, but there is some literature now investigating associations with the Asian haplogroups.
You specifically asked about how to prove associations with haplogroups. Basically, you find case and control groups for your disease, determine the haplogroup of each individual by genotyping (which can be done in very many ways). Then use statistical tests to see if the frequency of each haplogroup in your population is statistically significantly different between your cases and controls. There are many variations on this method, but that is the basic idea.