• P Royston.
• Department of Medical Physics, Royal Postgraduate Medical School, London, U.K.
• Stat Med. 1991 Feb 1; 10 (2): 221-40.

AbstractThe identification of the human fertile phase as the time during which a woman or a couple may conceive is elusive. The fertile time depends on many factors in each individual menstrual cycle and may be said to be more of a statistical than a physiological entity. This paper reviews the application of statistical methods to three areas related to conception and the fertile phase. The first is the prediction and detection of ovulation from serial measurements, such as hormones, basal body temperature and cervical mucus, throughout the menstrual cycle. Typically, such variables increase from some baseline level to a peak around ovulation (the most fertile time), then subside to low levels in the postovulatory phase. The statistical challenge is to detect the rise (signalling the onset of potential fertility) and subsequent fall. Analytic methods considered include thresholds, Bayesian change-point models and particularly the cumulative sum (cusum) technique which is both simple to apply and understand, and effective. The second area comprises appropriate methods of analysing and interpreting data from clinical studies of the fertile phase, especially in so-called natural family planning (NFP) where it is usual for women to observe several indices of potential fertility. Such studies usually try to establish the temporal relationships between markers of the fertile phase and examine the success of different combinations of markers in delineating the fertile time in comparison with a standard 'defined' phase, for example, the interval from three days before to two days after the peak of luteinizing hormone. The third area is the assessment of the probability of conception on certain days of the cycle, which is vital to the understanding of the fertile phase and its application to NFP. Direct estimation of such probabilities is impractical; instead, resort must be made to estimation by maximum likelihood of the parameters of specially constructed models. Suitable models are described. Finally, the need for a new prospective study of the probability of conception in relation to the markers of the fertile phase used in the symptothermal method of NFP is discussed.

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