A self-excited threshold autoregressive state-space model for menstrual cycles: forecasting menstruation and identifying ovarian phases based on basal body temperature

Abstract: The menstrual cycle is composed of the follicular phase and subsequent luteal phase based on events occurring in the ovary. Basal body temperature (BBT) reflects this biphasic aspect of menstrual cycle and tends to be relatively low during the follicular phase. In the present study, we proposed a state-space model that explicitly incorporates the biphasic nature of the menstrual cycle, in which the probability density distributions for the advancement of the menstrual phase and that for BBT switch depend on a latent state variable. Our model derives the predictive distribution of the day of the next menstruation onset that is adaptively adjusted by accommodating new observations of BBT sequentially. It also enables us to obtain conditional probabilities of the woman being in the early or late stages of the cycle, which can be used to identify the duration of follicular and luteal phases, as well as to estimate the day of ovulation. By applying the model to real BBT and menstruation data, we show that the proposed model can properly capture the biphasic characteristics of menstrual cycles, providing a good prediction of the menstruation onset in a wide range of age groups. An application to a large data set containing 25,622 cycles provided by 3,533 woman subjects further highlighted the between-age differences in the population characteristics of menstrual cycles, suggesting wide applicability of the proposed model.