Active patients when slicing by date

You likely want a measure pattern similar to this one. This assumes that you have a Date table and there is no relationship to from it to the table with your patient data. If you do have a relationship, you can add REMOVEFILTERS(PatientTable) into the CALCULATE.

Active employees =
VAR mindate =
MIN ( Date[Date] )
VAR maxdate =
MAX ( Date[Date] )
RETURN
CALCULATE (
COUNT ( Table[Employee] ),
AND (
Table[StartDate] <= maxdate,
OR ( Table[TerminationDate] >= mindate, ISBLANK ( Table[TerminationDate] ) )
)
)

Pat

For Count refer to this: 

Active employees = 
VAR mindate =
MIN ( DateTable[Date] )
VAR maxdate =
MAX ( DateTable[Date])
RETURN
CALCULATE (
COUNT ( Admissions[PatientID] ),
AND (
Admissions[AdmitDate] <= maxdate,
OR ( Admissions[DischargDateFixed] >= mindate, ISBLANK ( Admissions[DischargDateFixed]  ) )
)
)

However, this is the same thing but rewritten which mahoneypat proposed earlier. That works, so kudos to this man.