It's long been known that epidemiology and economics are related to each other. Richer countries can afford good sanitation, vaccination, comprehensive and high quality health care and so on. This all comes together in the well known phenomenon of epidemiological transition: where the risk of infectious diseases and infant mortality declines with better public health and other services, while the risk of non-communicable and diseases of old age tends to increase with greater sedentary lifestyles and increasing lifespans. But so far this has just been an historical observation. What we really need is some way of quantitatively developing a robust method to FORECAST what will happen, and not just for the very ill-defined cluster of infectious diseases or diseases of old age, but for specific conditions. So, that's the problem. What's the solution? Well the obvious place to start is to amass a wealth of epidemiological data for a particular disease and the corresponding economic data that measures development status of the susceptible population. So, data on the risk of dementia in Nigeria in 1990, coupled with the Nigerian GDP per capita in the same year, for example. Do this for enough countries and we have a dataset that's meta-analyzable. Sure there's bound to be outliers, but get enough variance of the right kind into mix and we should get a correlation between GDP per capita and disease risk.
Here's the rub: there is no single study that reports the epidemiological component of such a dataset. There are global systematic reviews of course, but these tend to be bedeviled by problems in multiple disease definitions, variable case detection methods, and different selected age groups. And this is assuming they're all of the same methodological quality and community-based of course (studies concerning the metabolic health of Thai monks would not be welcome). But there are a few, albeit very select and overlapping (in terms of risk factors), diseases where such data may be available. The WHO for example recently published results from the 2010 Global Burden of Disease survey. Unfortunately, results are grouped by WHO region, which reduces statistical power substantially (not to mention making it cumbersome to calculate the aggregated GDP per capita), but the data from previous versions are also available, and in some cases may also be published out in a systematic review containing country-specific information.
The WHO also maintains a global mortality database, which reports disease-specific mortality for some diseases across multiple countries. True mortality is not the same as incidence or prevalence, but for a few diseases where the mortality:incidence ratio is pretty stable between different levels of economic development and the cause of death is not open to interpretation (stroke may be a good example here), it could be a suitable proxy.
There's also the Diabetes Atlas published by the IDF, which gives diabetes prevalence country-by-country with downloadable data. But be warned: the IDF fills in countries with missing data using geospatial extrapolation (using the prevalence reported in neighbouring countries). This may be okay for some purposes but artificially inflates the sample size for the purposes of correlating global GDP per capita with disease risk (or in this case, prevalence).
Possibly the most exciting and comprehensive source of global, standardized and reliable data on disease risk if afforded by the various Cancer Incidence in 5 Continents series of data aggregations published by IARC. Using downloaded data it's possible to perform a GDP-incidence correlation on pretty much any tumour even the rare ones. This is what we've been doing over the last 12 months or so. The results, They're surprising and appear to be also robust. Does cancer risk always increase with GDP. Pretty much yes, but not always. The most surprising correlations we get are in those cases where there are few or no strong or well-established risk factors for a disease (I'm ignoring age as a risk factor here of course the IARC data is age-standardized). Take leukemia. Sure there are things like radiation exposure that are well-established risk factors. But the frequency of excessive exposure to radiation (the stuff that occurs naturally; exposure associated with healthcare would be accounted for in any GDP correlation most likely) is almost certainly highly concentrated geographically within small areas, and in any case would not be strongly associated with GDP. Below is a chart showing the correlation with leukemia (note the correlation works with the log of GDP per capita otherwise it's difficult to visually detect).