Thank you Lynn, that was exactly what I needed!

Since DATE was not recognized (Type DATE is not a defined system type.), I changed it to DATETIME and used CONVERT.

CONVERT(VARCHAR(12),CAST(MIN([Rxo].[DATE_WRITTEN]) OVER ( PARTITION BY [Rxo].[PATIENT_ID] ) AS DATETIME),110) AS MinStart, CONVERT(VARCHAR(12),CAST(MAX([Rxo].[EXPIRES]) OVER ( PARTITION BY [Rxo].[PATIENT_ID] ) AS DATETIME),110) AS MaxStart