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  • Title: A Bayesian change-point problem with an application to the prediction and detection of ovulation in women.
    Author: Carter RL, Blight BJ.
    Journal: Biometrics; 1981 Dec; 37(4):743-51. PubMed ID: 7337793.
    Abstract:
    Under the assumptions of independent normally distributed and sequentially observed responses, a Bayesian rule for detecting a change from a constant mean response is derived. It is known that both basal body temperature (BBT) and preovulatory estrogen values undergo such a change in mean value at some random time during the menstrual cycle. The Bayesian rule is applied to estrogen to predict ovulation and to BBT to detect ovulation. Data from an aggregate of women are used to obtain prior information about the change-points and the parameters that define the changes in estrogen and BBT. A method is proposed by which the accumulation of information for a specific women can be incorporated into the aggregate prior information. For most normally menstruating women, the sequence of hormonal events leading up to and following occurrence of ovulation is the same. Rise in estrogen induces a midcycle surge of luteinizing hormone (LH) to a peak, followed by ovulation and then a sharp rise in plasma progesterone which in turn increases basal body temperature (BBT) to a higher level. Therefore, detection of change-points in estrogen and BBT can help predict and detect ovulation. This paper presents sequential Bayesian solutions to the problems of detecting changes in both estrogen and BBT under assumptions of independent normally distributed and sequentially observed responses. The Bayesian solutions are applied to an aggregate of women who were observed throughout their menstrual cycles. In 33 women, ovulation was predicted in advance of the LH peak, and thus in advance of the actual ovulation. Ovulation was predicted an average of 3.55 days prior to the LH peak with a standard deviation of 1.46 days. In another 41 women, BBT observations were taken during 1 menstrual cycle; in 38 of these women, BBT shift was detected after it had occurred, the detection occurring at an average of 2.58 days after the change point with a standard deviation of 1.31 days where the change point is the day prior to the rise in BBT. In 24 women for whom change points in both estrogen and BBT were detected, a midcycle 'fertile period' can be marked off; average length of the 'fertile period' was 7.38 days with a standard deviation of 1.81 days. All women had length or= to 11 days. A method is proposed by which the accumulation of information for a specific woman can be incorporated into the aggregate prior information.
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