In the spirit of the type of analyses presented in the Perfect Health Diet, I wanted to post some correlations that appear to imply causation. These two graphs plot Potassium and Sodium Excretion (which is assumed to be a good proxy for intake, assuming people in the study were at steady-state) versus the Odds Ratio of mortality. The odds ratio is a normalized measure of the probability of death.
The first graph illustrates that in this sample, the more potassium consumed (and hence excreted), the lower the odds ratio of mortality.
I think these types of analyses could be used to set standards for a whole range of vitamins, minerals, and perhaps other "Goldilocks" substances. Goldilocks substances are things which are healthy in moderation, but either too much or too little can be harmful or hazardous. Obviously, some substances such as toxins and radiation are inherently harmful, even down to the smallest dose (but see hormesis theory).
Source. Urinary Sodium and Potassium Excretion, Mortality, and Cardiovascular Events N Engl J Med 2014; 371:1267 September 25, 2014. This study looked at over 100,000 people from dozens of countries.