The use of beta-binomial distributions to describe hormone profiles in the normal menstrual cycle

Introduction Even in normally cycling women, the shapes of hormone levels may widely vary between cycles and between women. Over the last decades, finding ways to characterize and compare the cycle hormone waves has shown to be a very difficult task and most answers, in particular polynomials or splines, do not refer to physiologically meaningful parameters. Methods We present here an original concept able to characterize most hormone waves with only two parameters. The modeling attempt considered pregnanediol-3-alpha-glucuronide (PDG) and luteinising hormone (LH) levels in 326 cycles (with ultrasound-identified ovulation day) in 107 normally fertile women aged 18 to 45. The study searched for a convenient wave description process and carried out an extended search for the best fitting density distribution. The highly flexible beta-binomial distribution was shown to offer the best fit of most hormone waves and require only two readily available and understandable wave parameters: location and scale. Results In bell-shaped waves, the case of PDG curves, early peaks (respectively late peaks) may be fitted with a small (respectively great) location parameter and a small scale parameter; plateau shapes are obtained with higher scale parameters. I-shaped, J-shaped, and U-shaped waves (which are sometimes the shapes of LH curves) may be fitted with high scale parameter and, respectively, small, high, and medium location parameter. These location and scale parameters will be later correlated with feminine physiological events. Conclusion Our results demonstrate that complex methods may be avoided and that pauci-parameter analyses might be more advantageous regarding the use, application, and, especially, result interpretation within the context of feminine physiological events. The concept and method may be used in other physiological contexts whenever biomarker waves have to be correlated with specific subject characteristics.