Time Relationships and HQMF

Anyone who has developed a project schedule using one of the common project management tools has run across the number of different ways you can describe the relationship of  two activities with each other.  For example:

• Activity X starts after the start of Activity Y
• Activity X and Y start at the same time.
• Activity X starts after the end of Activity Y
• Activity X ends after the start of Activity Y

Et cetera (and note that the above is not a complete list).

One of the challenges in Query Health is being able to describe the relationship of two events with respect to each other:  For example, in the case where you want to find all cases where the patient was diagnosed with some particular disease within the measurement period.

There are a number of different ways to look at this.  The simplest is to understand that you have two events, X and Y, with a start and end time.  Thus, you can compare X.start or X.end to Y.start or Y.end.  You also have three atomic comparative operations, less than <, greater than > and equals (which you can combine to product less than or equal to, greater than or equal to, or not equals).

You can combine these into a relationship in the form X.time operator Y.time.  You have 2 choices for time on X and Y (start or end), and three choices for the operator (<, > or =).  That gives 2 x 2 x 3 or 12 different possible comparisons.  We've already eliminated some duplication by saying that X is first, and Y is second.  That way X.start > Y.start and Y.start < X.start are eliminated as duplicates.

The table below pretty much describes all possible atomic relationships, along with a short code to describe it.

X	starts	before	start of	Y	(SBS)
X	starts	concurrent with	start of	Y	(SCS)
X	starts	after	start of	Y	(SAS)
X	starts	before	end of	Y	(SBE)
X	starts	concurrent with	end of	Y	(SCE)
X	starts	after	end of	Y	(SAE)
X	ends	before	start of	Y	(EBS)
X	ends	concurrent with	start of	Y	(ECS)
X	ends	after	start of	Y	(EAS)
X	ends	before	end of	Y	(EBE)
X	ends	concurrent with	end of	Y	(ECE)
X	ends	after	end of	Y	(EAE)

We can combine some of these to form other interesting cases.  For example, event X occurs during event Y if X starts after or concurrently with Y starting, and ends before on concurrently with Y ending.  Event X and Y are concurrent if they start and end at the same time, et cetera.

SBS and SAS, SBE and EAS, SAE and EBS, EBE and EAE, SCE and ECS are inverses.  If X SBS Y, then Y SAS X, and so on.  We could remove the inverse and still be able to express any relationship just by swapping the position of X and Y.  I've marked the ones I suggest we keep and throw away in the table above.

(Just for fun, you might note that SCS and ECS are self inverses: X SCS Y implies Y SCS X, and so on).

Here is the HL7 Vocabulary for time relationships:

Code	Display Name	Definition
CONCURRENT	concurrent with	A relationship in which the source act's effective time is the same as the target act's effective time.
DURING	occurs during	A relationship in which the source act's effective time is wholly within the target act's effective time.
EAE	ends after end of
EAS	ends after start of
EBS	ends before start of
ECW	ends concurrent with	A relationship in which the source act's effective time ends with the end of the target act's effective time.
EDU	ends during
OVERLAP	overlaps with	A relationship in which the source act's effective time overlaps the target act's effective time in any way.
SAE	starts after end of
SAS	starts after start of	The source Act starts after the start of the target Act (i.e. if we say "ActOne SAS ActTwo", it means that ActOne starts after the start of ActTwo, therefore ActOne is the source and ActTwo is the target).
SBS	starts before start of
SCW	starts concurrent with	A relationship in which the source act's effective time starts with the start of the target act's effective time.
SDU	starts during

The non-atomic codes are underlined in the above (they are combinations of two relationships)
To simplify things, I've mapped the HL7 atomic codes to my atomic codes in the table below:

X	starts	before	start of	Y	(SBS)	SBS	starts before start of
X	starts	concurrent with	start of	Y	(SCS)	SCW	starts concurrent with
X	starts	after	start of	Y	(SAS)	SAS	starts after start of
X	starts	before	end of	Y	(SBE)
X	starts	concurrent with	end of	Y	(SCE)		Missing
X	starts	after	end of	Y	(SAE)	SAE	starts after end of
X	ends	before	start of	Y	(EBS)	EBS	ends before start of
X	ends	concurrent with	start of	Y	(ECS)		Missing
X	ends	after	start of	Y	(EAS)	EAS	ends after start of
X	ends	before	end of	Y	(EBE)
X	ends	concurrent with	end of	Y	(ECE)	ECW	ends concurrent with
X	ends	after	end of	Y	(EAE)	EAE	ends after end of

Looking at the table, you can see lines where my code is in italic and HL7 has a code, and other places where my code is in bold, and HL7 doesn't have a code.  These are discrepancies in the HL7 Vocabulary for comparing the time sequence of two events.  Missing codes represent conditions that cannot be expressed simply using an atomic relationship.  Added codes indicate cases which can be represented in more than one way.

For Query Health, we probably don't need the missing codes, but HL7 might consider adding them to address other use cases where the time relationship value set is used.   With respect to the extra code (SAS), I believe that we'll advise the use of SBS with the inversion indicator rather than SAS just for consistency.  Ideally, I'd like to avoid the inversion indicator all-together, and would propose that all twelve of these conditions be allowed to express time relationships in a natural way.

As for the non-atomic relatioships that HL7 has provided, I believe that they are fine for Query Health, and don't care to get into a deep analysis.  The number of meaningful ways that you could combine two or more of these atomic comparisons is more than I want to deal with right now.  When HQMF goes forward, I suspect that several harmonization proposals will be made, and deeply argued.  Might as well get it out of the way now.