The APA Style Blog offers some suggestions for how to cite a data set in APA format. 

Reference Example w/ DOI:

U.S. Department of Health and Human Services, Substance Abuse and Mental Health Services Administration, Office of Applied Studies. (2013). Treatment episode data set -- discharges (TEDS-D) -- concatenated, 2006 to 2009 [Data set]. doi:10.3886/ICPSR30122.v2

In-text Citation Options:

1.  "U.S. Department of Health and Human Services, Substance Abuse and Mental Health Services Administration, Office of Applied Studies (2013)"
2.  "(U.S. Department of Health and Human Services, Substance Abuse and Mental Health Services Administration, Office of Applied Studies, 2013)." 

If you use the in-text citation repeatedly, you’ll probably want to abbreviate the author name.