The group principally responsible for determining how effect a minimum price policy would be is the Sheffield Alcohol Research Group, and it is their work that appears the most authoritative.
This is from the Scottish Govt, who have (I think) already implemented the 50p/unit min.pricing policy
"The Chief Medical Officer believes that - like the smoking ban - minimum price would save lives within a year. Research by the University of Sheffield estimated that the proposed minimum price of 50p per unit would result in the following benefits:
Alcohol related deaths would fall by about 60 in the first year and 318 by year ten of the policy
A fall in hospital admission of 1,600 in year 1, and 6,500 per year by year ten of the policy
A fall in crime volumes by around 3,500 offences per year
A financial saving from harm reduction (health, employment, crime etc) of £942m over ten years
Some people may not feel that they are part of Scotland's alcohol problem, but through the introduction of minimum pricing, everyone will feel the economic and social benefits of the solution through healthier, happier, safer families and communities."
http://www.scotland.gov.uk/Topics/Health/Services/Alcohol/minimum-pricing
And I guess we will see what if any impact it has over time.
Its all about education and lifestyle; Live a life where you drink moderately, eat a balanced diet and exercise a bit and this will protect you against the most common harms, including liver disease.