What theme is shared between Shakespeare's Macbeth and Robert Frost's "Out, Out"?

The poem and the Macbeth soliloquy from which Frost took its title, both explore the fleeting nature of human life. When Macbeth makes this speech at the end of the tragedy, he has lost all of his friends and knows he will soon be defeated and destroyed. He has also just found out that his wife has died. "Out, out brief candle," he says, before going on to describe life as meaningless: "a tale/ told by an idiot, full of sound and fury,/ signifying nothing."
Frost's use of these two words is interesting because unlike Macbeth's response to learning of his wife's death, which is a nihilistic rant in which he seems to have given up all hope and meaning, the other workers in Frost's poem seem to shrug off the death of the young man and continue working as if it doesn't matter to them. Both express a sense of the meaninglessness of life but for opposite reasons. Macbeth has lost the one person he had left, while the workers in the sawmill don't see the death of their young coworker as a loss. To Macbeth, the loss of his wife indicates that life in general is meaningless, while to the workers, the life of one individual isn't important enough to warrant an emotional response.

One theme shared between Shakespeare's play and Frost's poem is the idea that life goes on, even after someone we love dies. At the end of the poem, the little boy who cuts his hand off has died as a result of his tragic accident with the saw, and his family, "since they / Were not the one dead, turned to their affairs." Despite the fact that "No one believed" that he could possibly be dead—he is so young and the accident so swift and so deadly—his family, apparently, returns to their lives with a promptness that might seem insensitive or even unfeeling. However, we see the same quick return to life in Macbeth, too. After Macbeth learns of his wife's death, his response is, perhaps, not quite what we would imagine. He first says that, "She should have died hereafter." In other words, he says that she would have died at some point. The scene ends with Macbeth's words:

Blow wind, come wrack,At least we'll die with harness on our back.

The needs of life are pressing, and life cannot be put on hold just because we have lost someone dear to us. Macbeth prepares for battle immediately following his wife's death just as the boy's family must return to their own affairs. The lives to which the survivors return are certainly different; however, the message is the same: the living must go on after the dead are gone.