I found an article that notes that "data on the immigrant population, as recorded in the CPS, NHIS, census, and vital statistics, do not distinguish between naturalized immigrants, permanent residents, nonimmigrants (e.g., temporary workers, students, and visitors), and illegal immigrants" (Siahpush, M., & Singh, G. K. (2002). Ethnic-immigrant differentials in health behaviors, morbidity, and cause-specific mortality in the United States: an analysis of two national data bases. Human Biology, 74(1), 83-109). In other words, given the nature of the population, it won't be possible to get comprehensive statistics.
However, it might be possible to get a sense of trends for specific populations of undocumented immigrants. For example, this document mentions the prevalence of diabetes amongst Latinos:
"The CCPP conducts pharmaceutical policy training courses in the US and abroad; trains fellows in pharmaceutical policy research; works with WHO and other international partners on joint research initiatives to improve use of medicines; develops interventions for medicines-related policy and behavior change and methods to evaluate their impact; and provides a global forum for exchanging research results and identifying new issues in the field. One important initiative of the Center is the development and regional implementation of a training courses on use of prescribing and dispensing data for medicines policy research to strengthen urgently needed skills of managers and analysts of the rapidly expanding government and private insurance programs in many non-industrialized countries."
Effect Measure is "a forum for progressive public health discussion and argument as well as a source of public health information from around the web that interests the editor(s)." They have a primer on the WHO and the WHO's connection to big pharma.
*Okay, after posting my answer, I saw someone else had answered this, but as a "comment", so it was still listed as "unanswered"... sorry for the same results; I deleted the quotes from abstracts because of this, but I can still send you my search strategy on PubMed if you'd like!
By doing a search in PubMed, I found a review from the Netherlands specifically discussing cardiovascular disease and osteoporosis.
The citation is:
Gooren, L., Giltay, E., Bunck, M. (2008). Long-term treatment of transsexuals with cross-sex hormones: extensive personal experience. Journal of Endrocrinol Metabolism 93(1). Retrieved May 1, 2008, from PubMed database.
I also found a clinical trial, with the citation:
Mueller, A., Kiesewetter, F., Binder, H., Beckmann, M., Dittrich, R. (2007). Long-term administration of testosterone undecanoate every 3 months for testosterone supplementation in female-to-male transsexuals. Journal of Clinical Endocrinol Metabolism 92(9). Retrieved May 1, 2008, from PubMed Database.
I would be more than happy to send you my search strategy and subsequent results if you would like, and if you have access to PubMed. Just so far from glancing, there are probably at least 20 results that would be suited to what you're looking for.
I'm enrolled in a health class and I've asked my teacher questions about transitioning males and the affects of testosterone on their body, especially considering that estrogen seems to have a protective effect on female bodies. I haven't gotten a straight answer. Particularly, I'm wondering if testosterone makes someone who is transitioning more susceptible to osteoporous and heart disease. It would be great to get this information from a source that has trans people's interests at heart.