Epidemiological studies cannot be used to show that meat causes cardiovascular disease (or that anything causes a disease), only whether that thing (such as meat consumption) is associated with a disease (such as CVD). However, an epidemiological study can show that a given factor doesn't cause a disease if the study shows no association. For example, if you did a study of European countries and found the more meat people consume in each country, the less cardiovascular disease that country's population has, you'd have proven that meat does not cause cardiovascular disease:
FOOD CONSUMPTION AND THE ACTUAL STATISTICS OF CARDIOVASCULAR DISEASES: AN EPIDEMIOLOGICAL COMPARISON OF 42 EUROPEAN COUNTRIES:
http://www.foodandnutritionresearch.net/index.php/fnr/article/view/31694
You have to look at the Discussion section where they say:
"The results of our study show that animal fat (and especially its combination with animal protein) is a very strong predictor of raised cholesterol levels."
BUT:
"Interestingly, the relationship between raised cholesterol and CVD indicators in the present study is always negative."
So, eating more animal derived protein and fat is associated with higher cholesterol, and higher cholesterol levels are associated with lower CVD rates.
And the Conclusion section:
"Irrespective of the possible limitations of the ecological study design, the undisputable finding of our paper is the fact that the highest CVD prevalence can be found in countries with the highest carbohydrate consumption, whereas the lowest CVD prevalence is typical of countries with the highest intake of fat and protein. The polarity between these geographical patterns is striking."
However, if you did a study of 96,469 7th Day Adventists you might find that "significant associations with vegetarian diets were detected for cardiovascular mortality, noncardiovascular noncancer mortality, renal mortality, and endocrine mortality".
Sounds great, however, if you look at the study, they excluded 11,956 of the 96,469 because they'd had a history of a specific prior cancer diagnosis (except nonmelanoma skin cancers) or of cardiovascular disease (CVD) (coronary bypass, angioplasty/stent, carotid artery surgery, myocardial infarction, or stroke; or angina pectoris or congestive heart failure treated in the past 12 months.
I'm guessing they'd have gotten a different result if they'd included these people. Why were they excluded? I don't know or understand why.
And of course they were comparing to "non-vegetarians". But how else did their diet and lifestyle differ from veg*ns? More junk food? More carbs? More stress? Less social cohesion? Less exercise? Who knows?
This is the study that is often used by veg*ns to make the claim that a veg*n diet is healthier than one with meat:
http://jamanetwork.com/journals/jamainternalmedicine/fullarticle/1710093?resultClick=24