I know you're trying to let the reader know that this guy is a doctor, but they should pick that up from the dialogue. I'd suggest using the name of the doctor thinks of himself as instead of "Dr. Killian". Probably his first name, but that's up to you. There are two reasons for this... first of all, you want to establish a consistent tag for the character that you'll use to refer to him throughout the narrative. Secondly, it pulls the reader out of the point of view when the character thinks of himself as something as formal as this. It's like you're watching him from the outside, not inside his head. One other problem with this bit is the "thanks everybody" at the end. It immediately makes me lose sympathy for the doctor, because it strikes me as being a rather casual thing to say right after his patient has died. Maybe you intended it that way, but the following paragraphs don't seem to suggest that at all, so I have to treat this as an honest mistake. Maybe you could just cut that part out and end the line with "time of death is 1530."

He went to the nurse’s station to write his note, anything to put off the scene that would take place when he went to talk to the family.
It was an impossible task. They would know the outcome as soon as he started with the “I’m sorry…” and then the crying and wailing would start, then the questions. Why did my father, mother, son, daughter die? What else could have been done? Why didn’t you do more? Why didn’t you do it sooner? Did you make a mistake?
And why didn’t you do it better, faster, more successfully? They’ll only be asking questions that you ask yourself. And you never have a good answer either. Except that you and your medicines are impotent against the ravages of time and disease. And did you make a mistake? Not in the code, that’s all protocol, automatic. But what if you had made the diagnosis sooner, started with different antibiotics, operated sooner? What then?

Okay, this isn't bad, but I do have some quibbles. For one thing, the reader is certainly wondering who died. He'll expect that this event is important to the story, because you open with it and devote the first paragraphs to it, yet he doesn't know anything about it. Who was the person that passed away? Why was the death significant? Or if it wasn't significant, then why are you beginning the story with it?

As it is, it's just a vague death in a hospital. Certainly we understand what the doctor is feeling after having lost a patient, but it's a cold understanding, because to us it's just another scene where somebody dies on the operating table(?). We need details, something to give us an emotional anchor about the character who died, or why it's so significant to lose a single patient to this doctor.

The way it reads now, the doctor is just wallowing in self pity about something we don't yet care about. We understand how bad he must feel and we don't necessarily blame him for that, but at the same time, we don't really care, either.

Anyway, that's my 2 cents.

Maybe the "Thanks everybody." line is realistic, and maybe it could be modified to something that communicated that Dr. Killian appreciated their efforts, that they had given it their best, or some such. I don't know what goes on in operating rooms, having always been under whenever I've been in one myself.

As I see it, you're currently setting Killian up to have a story critical confrontation with the family. The story is going to be about what happens when a doctor walks into the waiting room and says "I'm sorry...." With that purpose in mind, I'll make a couple of comments.

The first is that the story title is a bit...unsuited for the structure of this work. Traditionally, a title that directly addresses the audience this way dispenses with the fourth wall inside the text as well (whether because the author is directly addressing the actual audience or having them play the role of a fictional audience). For example: a fictional "It is with the most profound regrets" or "Dear John" letter might be titled this way.

For this work, you might want to consider rephrasing the title as a noun of some kind, like "Regret" or something like that.

Also, this story clearly starts in the operating room, with the death of a patient. But you haven't described either at all. I can see that you hid details about the patient on purpose, possibly to make it more of an "everyman" situation (though we'll run out of patience real quick if when he talks to the family you keep trying to hide the relationships in order to avoid giving away information about the patient). But neglecting to establish the setting in which the story begins is probably just a mistake. Even if you hide all the details about the patient (not too hard since the patient is a covered body at this point), we want to see the place where the story begins.

This is one reason that I usually don't like stories to begin with a line of dialogue. Before the scene is set, anything said is being spoken into a vacuum (in space, nobody can understand your opening lines, or something like that).

There is also the fact that, because Dr. Killian currently goes right from pronouncing death to dreading his task of informing the family, he seems to be wallowing in self-pity rather than any sorrow that he couldn't save the patient's life. By giving him a moment of reflection in the operating room before he goes to collect the personal information and tell the family, you can forestall some of that by showing that he would feel bad about letting someone die even if nobody was waiting for answers as to why.

>"Thanks everybody," Dr. Killian said. He
Maybe "Thanks, people," would ease the problem others referred to. I didn't have a problem with it.

>It was an impossible task. They would know
Well, no, merely an _unpleasant_ task.

>Why did my father, mother, son, daughter
In this case, the question will be "Why did my father die?" (or whichever it is) since there's only one corpse.

>And you never have a good answer either. >Except that you and your medicines are >impotent against the ravages of time and >disease.
Hey, that's a good answer.

I agree with Aero that the patient’s identity is important, even if it will have no other bearing on the story. If a person dies, they deserve to be recognized in other character's minds. It would not be unusual for a doctor to think briefly about the patient’s history and name. He may even think of something like – “He was glad Mrs. Cleaver’s suffering was over. She had been quite a fighter, but in the end the cancer won the war. Now, he wondered how her son would react to her death. He had the feeling he would not take the news quietly. Most of all, he worried about the grandchildren. They seemed to love their Mawmaw, so much.”