There are a LOT of evidence to connect cardiovascular disease (CVD) and saturated fat. Most of the reviews and and meta-analysis concluding something DIFFERENT, along the lines of “Saturated fats are NOT associated with all cause mortality”, (Chowdhury 2014, de Souza 2015, etc), are very recent and being considered as MISLEADING by most of the scientific community:

“(In response to the Chowdhury review) Walter Willett, chair of the Department of Nutrition at Harvard School of Public Health, warns that the conclusions are seriously misleading, as the analysis contains major errors and omissions and should be retracted.”

You know who is pushing for those misleading studies (Chowdhury et al.)?, yes, you guessed right: The Industry groups (Dairy Farmers, etc)