1. As far as I am aware, there is no valid survey data on how MD's in general feel about DO's as a group. (If anyone knows of good-quality published data, I would be very interested to see the reference.) In my personal experience (years in medical clinics, medical schools/research centers, individual research laboratories) I haven't heard MD's deride individual DO's in public or in private. My impression is that it just isn't an issue for most MD's, it' s not something that they bother thinking about very much, if at all. Since DO's and MD's work side-by-side in many clinics and hospitals, it seems to me unlikely that there is a great deal of significant MD prejudice against DO's as a group. Back in the 1960's the AMA approved a merger in California where several hundred DO's were given MD degrees, which suggests that even the AMA, when pressed, views the two degrees as essentially equivalent by the time physicians finish their post-graduate training. So I don't believe that there's 'hatred' of DO's by MD's in general or in any significant numbers.
2. It's true that, compared to MD's, DO's rarely do research. Again, I haven't seen any survey data published, but based on my reading of biomedical scientific journals (Science, Nature, Cell, Blood, Annals of Internal Medicine, NEJM, JAMA, etc.) over the years, as well as recently, I'd estimate that I will see about 100 MD's listed as co-authors on articles before I find an article where a DO is listed as co-author. I almost never see an article from DO's at an osteopathic medical school.
You CAN find DO's publishing articles in some journals sponsored by the osteopathic organizations, such as the Journal of the American Osteopathic Association (JAOA). Evidently there are many academic and other DO's who feel that there should be research journals that are specifically published for DO's. Unfortunately the quality of the research articles in these journals is often low, and they are rarely if ever found in libraries outside of osteopathic medical schools, so they have negligible impact on the general biomedical literature that the vast majority of physician-scientists read.
If you go to my school (KCOM), there are a handful of basic science labs who have NIH grants and viable but small-scale research efforts, and you might be able to do enough work to get a publication (one of my classmates, who previously had a pharmacy doctorate, got a paper out from a lab in the Pharmacology Department durng his first 2 years). These are basic science-oriented lab studies and not human clinical research projects, however. I am not aware of any clinical faculty (i.e., DO's) here w/ NIH or NSF research grants, or who publish in anything other than the osteopathic-sponsored journals.
Some of the OMM (Osteopathic Manipulation & Medicine) Department faculty have "research projects" going on, but the one's I've heard about from students here at KCOM are generally not studies that I would recommend anyone spending their time and effort for-- small sample size, outmoded/nonspecific techniques and measures, lack of proper statistical design & analysis, etc. As far as I know, none of them has ended up with results, or published in a non-osteopathy-sponsored journal. Based on my search of the NIH grants database, none of our OMM department faculty have NIH grants. Generally, if you are looking for a place to do research, make sure they have NIH and/or NSF grants-- lots of $$$ is required.
3. Sure, apply to any school you want-- nobody's really checking to make sure that you apply only to their school or their field.
4. Apply to the best medical schools you can, where scores and grades may possibly get you in. Period. If you want to do research, have a record as a productive lab researcher before you apply, whether it's in college or between college and medical school. You need to know that you ACTUALLY LIKE doing research, and you need to be able to convince the admissions committee that you like it, otherwise you won't get in (at least at any place that's very good).
Very important-- apply to a federally funded, combined degree (MD-PhD) program [I could possibly be wrong, but I don't believe any of the DO-PhD programs are federally funded, so you have to pay the full tuition $$$.] Funding is key because they pay your tuition for the full 6-7 years to get both degrees, and they give you a stipend to live on (the other side of the coin is that you have a service provision-- one year of research work for every year of funding). You can still do research w/o the PhD, with only an MD or DO, but if you can swing it, it's a lot better to have the PhD experience and training.
Try to be optimistic: If you are a good physician and/or a good scientist, most people will respect you regardless of whether you have an MD or a DO behind your name, and if you're really good, you will love what you do and not care if someone else doesn't like you for one silly reason or another.
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