A self-excited threshold autoregressive state-space model for menstrual cycles: Forecasting menstruation and identifying within-cycle stages based on basal body temperature.

The menstrual cycle is divided into hypothermic and hyperthermic phases based on the periodic shift in the basal body temperature (BBT), reflecting events occurring in the ovary. 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 the BBT switch depending 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 the 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 hypothermic and hyperthermic phases, possibly as well as 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. The application of the proposed model to a large data set containing 25 622 cycles provided by 3533 women further highlighted the between-age differences in the population characteristics of menstrual cycles, suggesting its wide applicability.