How can I prove or disprove the idea that social stress and social networks affect an individual's health?

Your first need is to define "stress" more precisely, and in a manner that is medically necessary. How are you measuring it? I have some ideas which are not mutually exclusive. We know that certain stress hormones can be chronically raised in those under long-term stress. Can you measure that or are you relying on others who do? Also, identify the "stress-related diagnoses" and the psychiatric diagnoses related to stress/anxiety. I would recommend finding an ICD-9 site in which you can run a search on them. What medications are prescribed for stress/anxiety? What medications are useful in the short-term and which in the long-term.