Thanks everyone. I had seen "Accelerated life test" as a DOE option, and the "life" term got me to suspect that this could indeed be the platform I desire. I will read the article Mark suggested. It's strange because, for toxicologists simply looking to kill off organisms in a study, responses such as "time to death" or essentially half-life are easily modeled in the reliability and survival analyses of JMP, it's just that when the study KEEPS GOING that things get tricky (e.g., some organisms survive the treatment and others do not). To be fair, I have never once had a reviewer call me out for this because they are dealing with the same issues, though it would be nice if there was a formalized way to handle these types of situations (as much as you could expect to given what you might know ahead of time about your organisms and their physiologies).
Anderson B. Mayfield