I wouldn't quite call this a scientific study in a strict sense but for my graduate course in signal processing, statistics, and data mining, I wrote a paper on the subject of slowing down over time. I looked at distances from the mile up to the marathon and tried to find races with large sample sizes with freely available data where I could try to eliminate as much bias as possible (such as from weather). For instance, I collected nearly 800,000 entries from the NYC Marathon, which was probably the worst weather entry but had the most data. It's been suggested I publish it but it's not really my field of study and I there's more to do that I haven't quite done. I do heavy statistics in astronomy, so like I said, it's not really a strict scientific study, but I'd like to think I did a good scientific analysis for the class (I've been a graduate student for a few years, if that gives me any more credibility).
I took large sample sizes because I argued you couldn't follow individuals because of things like injuries and training variations, and I didn't use age records because those follow only the elite runners. Without giving away too much of the beef of it (in case I ever do publish it), my results were as follows:
-It is very clear that you see a broken power law form of the slow down. That is, you slow down by some relatively stable rate until a certain threshold age and then you slow down worse after that point. There wasn't enough data at the oldest ages (>70) to see if there was another break (my other limit was