Hi,
This topic is old (I see that), however I am somewhat a kindred spirit, so I would like to answer this question as well as I currently can. Regarding SAS applicability in this field this book could be a reasonable choice to begin with https://www.sas.com/store/books/categories/examples/analysis-of-clinical-trials-using-sas-a-practica.... SAS is the industry standard for lots of aspects of clinical trials (except population kinetics).
Pharmaceutical companies (if they need a programmer) can pay for courses, but it would be reasonable to do some homework https://support.sas.com/edu/elearning.html?ctry=us&productType=library completing introductory courses (free) courses would be a good start to show that You are interested in programming and analytics.
Statistical background is also reasonable, but the very least would be reading these guidelines:
http://www.ich.org/fileadmin/Public_Web_Site/ICH_Products/Guidelines/Efficacy/E9/Step4/E9_Guideline....
https://www.fda.gov/downloads/drugs/guidancecomplianceregulatoryinformation/guidances/ucm073137.pdf
After this you can check if these are "the shoes you are willing to wear" :).
One more thing that could be useful is snooping around and finding more about the company you want to work for (different companies specialize in different things and may need different skills)
Regarding programming esp. to grasp some main principles, it is reasonable to try to learn to program with python (because there are lots of great tutorials and it is very fun to work with python, esp. by Charles Severance (yes, this is slightly off-topic, but this is where I want to pay homage for him, for being a great teacher).
Potential drawbacks - not being of mathematical background could pose problems, because it is actually far less complicated to train a non-medic statistician a thing or two about medicine, just enough for him to successfully analyze data, than it is to train a medic to be a programmer (or a statistician).