On Modeling Ovarian Aging and Menopause Timing.

Mathematical modeling of ovarian aging and menopause timing has a long history, dating back a half-century to the models of Nobel Prize winner Robert G. Edwards. More recently, such models have been used to investigate clinical interventions for women, which underscores the importance of scientific rigor in model development and analysis. In this paper, we analyze a recent model published in the biophysics literature. We first correct an error which invalidates claims about menopause age in different populations. We then use stochastic analysis to show how this model is a reparameterization of a prior model and put it in the framework of several prior models, which enables the application of extreme value theory. We prove some general extreme value theory results and use them to obtain detailed estimates of menopause age in this model. In particular, we derive a new expected menopause age formula which is orders of magnitude more accurate than the previous heuristic estimate. We further obtain rigorous analytical estimates of the full menopause age distribution and all its moments. We conclude by using these mathematical results to elucidate the physiological sources of menopause age variability.