Suppose someone is both depressed and aggressive, with much of the aggression and anger directed toward himself/herself. Such a person is likely at higher risk of suicide (and I believe is more likely to have been born in winter). Further suppose that this person with depression is being treated for depression and lack of sleep without drugs and the person suddenly starts sleeping much better. Would you retest him/her for depression, even if he/she claims his moods are no better?
Treating a significant improvement in sleep as a marker and forerunner of well-being, I believe you would, based on simple logic:
(depressed->poor sleep)->(not poor sleep-> not depressed).
This is the famous (a->b) -> (-b->-a)
In words, if a person is depressed, he has poor quality sleep and/or poor quantity of sleep. If he does not have poor sleep, he is not depressed. Better test!