I don't know how you'd really do a study on this. It's far too subjective. One reader might say that he found the death of a certain character very emotional and he was crying so hard he couldn't continue reading, while another might read the same book, shrug and say, "Glad they got rid of that character. He just slowed down the story."
Yes, in general a writer should be careful not to spring dramatic moments too early, as the reader has not yet had a chance to get invested in the characters. I recall a book I read years ago, "The Ship Who Sang", which I think was generally an excellent book but I considered it flawed because the writer kept introducing characters, and then within a few pages that character would have some tragedy and the reader was clearly supposed to feel for him or her, but I didn't, because I'd only "known" this character for a couple of pages.
I'd worry less about killing a character (or introducing some other dramatic event) too late. Other than in the sense that any development in a story might come too early or too late: it doesn't fit the flow of the plot. If something happens too quickly, it can be abrupt, happening without adequate build-up to justify it. But if something takes too long, then the reader can be bored. Like, "Oh come on, obviously John is going to try to steal the money and disappear, get to it already."
But if someone could actually "study" this and come up with a formula, like "the ideal time to kill a main character is one-third of the way down page 183", well, at that point we wouldn't need human authors, we'd just program computers to write novels.
