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

摘要

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