Basal body temperature curves and fitting with periodic smoothing splines

Fertility tracking phone apps are widely used by women today, in order to both achieve or prevent conception. Due to the health risks of hormone based contraceptions, many women opt for non-invasive methods, such as fertility tracking. Most of the algorithms for tracking fertility use parameters such as the basal body temperature (BBT), cycle length and days of menstruation. The widely used "coverline" method is based on daily charting of the BBT in order to identify a sudden temperature increase following ovulation. This method can only find ovulation after it has occurred and has been used as a contraception method for centuries. Our goal is to use curve fitting of the basal body temperature in order to model fertility during the whole cycle, and hence predict future ovulation. The method uses cubic periodic smoothing splines on a data set consisting of daily temperatures from 1151 women. The data is anonymized and was provided by the fertility tracking company Natural Cycles. We optimize the parameters of the smoothing spline algorithm through cross validation and statistical analysis with the given data. We then correlate the periodicity of the fitted curve with the day of ovulation, through the use of data containing results from ovulation tests. We finally use the splines to model future cycles and predict ovulation. We conclude that this method could be used for increasing accuracy in existing fertility tracking algorithms