I remember the occurrence of this type of construction from many moons ago, but not its particular reference :

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> Absent the doctor, the paramedic pronounced the victim deceased.
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I'm not clear as to what is going on in the phrase 'absent the doctor'.

There could be an ellipsis here :

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> Absent [being] the doctor ...
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The verb 'absent' can be used :

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> transitively : Her mother absented her from school.
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> or intransitively : The workers absented from work.
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[(examples from OED)](http://www.oed.com/view/Entry/648?rskey=36q49K&result=2&isAdvanced=false#eid)

But I am not clear whether 'absent' is a verb here.

The same kind of thing happens in :

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> The patient dead, there was no more to be done but sign the certificate.
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I am also interested in what role the definite article is playing.

For one could also say :

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> Dead the patient, the room became hushed.
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Is there such a thing as a 'hanging' adjective ?