It is almost always easier to borrow ideas and techniques from other fields than to reinvent them. A PhD student, another academic and I, are studying two competing processes. These are crystallisation into two different crystals, called alpha and gamma, of a small molecule called glycine. The formation of alpha and gamma appear to be mutually exclusive, one or the other forms, not both. Crystallisation is statistical, it is at least partly random, and they are irreversible, once a crystal forms it persists.
So we need statistical tools to deal with these competing random processes. I would much prefer to borrow these than to invent them, I am no statistician. Helpfully, there is an important and well-studied problem where there are competing processes, and which is irreversible: death. Death is irreversible, and sadly there are a number of different processes that compete to hasten our end: different types of cancer, heart disease, cirrhosis, bungy jumping accidents, etc. This is a bit depressing but has resulted in a sub-field of medical statistics dedicated to studying quantitatively the statistics of mortality when we need to consider more than one cause.
To see how competing processes make life difficult consider what happens if I were to: A) take up jogging and get fit, or B) start playing Russian Roulette with a six-shooter once every weekend. Both would reduce my chances of dying of heart failure, in fact playing Russian Roulette would reduce the chances much more than getting fit as I’d likely be dead in about a month, and therefore would be very unlikely to die to heart failure before that happened.
That was kind of a stupid example but it illustrates a real and important problem, which is that in the presence of competing risks, you can’t simply optimise things by minimising one risk, here that of heart failure, without looking at what happens to other risks. You have to look at the total risk of course, but also if you want to focus on a particular risk, say that of a relapse after heart surgery, in patients also subject to dying of other causes, you have tease apart these risks.
This is a genuinely tricky problem, mathematicians since Daniel Bernoulli (1700-1982) have been wrestling with it, but the method I have my eye to the model data on crystallisation only dates from the late 1990s. To paraphrase Newton, I intend to go farther here by standing on the shoulders of giants, as I don’t think I’d be able get far without their broad shoulders.