Methods Inf Med 2018; 57(03): 101-110
DOI: 10.3414/ME17-01-0102
Original Article
Schattauer GmbH

A Quadriparametric Model to Describe the Diversity of Waves Applied to Hormonal Data

Saman Abdullah
1  Hospices Civils de Lyon, Service de Biostatistique-Bioinformatique, Lyon, France
2  Université de Lyon, Lyon, France
3  Université Lyon 1, Villeurbanne, France
4  CNRS, UMR 5558, Laboratoire de Biométrie et Biologie Évolutive, Équipe Biostatistique-Santé, Villeurbanne, France
,
Thomas Bouchard
5  Department of Family Medicine, University of Calgary, Calgary, Alberta, Canada
,
Amna Klich
1  Hospices Civils de Lyon, Service de Biostatistique-Bioinformatique, Lyon, France
2  Université de Lyon, Lyon, France
3  Université Lyon 1, Villeurbanne, France
4  CNRS, UMR 5558, Laboratoire de Biométrie et Biologie Évolutive, Équipe Biostatistique-Santé, Villeurbanne, France
,
Rene Leiva
6  Bruyère Research Institute, CT Lamont Primary Health Care Research Centre, Ottawa, Canada
7  Department of Family Medicine, University of Ottawa, Ontario, Canada
,
Cecilia Pyper
8  National Perinatal Epidemiology Unit, University of Oxford, Oxford, United Kingdom
,
Christophe Genolini
9  INSERM, UMR 1027, Université Toulouse III, Toulouse, France
,
Fabien Subtil
1  Hospices Civils de Lyon, Service de Biostatistique-Bioinformatique, Lyon, France
2  Université de Lyon, Lyon, France
3  Université Lyon 1, Villeurbanne, France
4  CNRS, UMR 5558, Laboratoire de Biométrie et Biologie Évolutive, Équipe Biostatistique-Santé, Villeurbanne, France
,
Jean Iwaz
1  Hospices Civils de Lyon, Service de Biostatistique-Bioinformatique, Lyon, France
2  Université de Lyon, Lyon, France
3  Université Lyon 1, Villeurbanne, France
4  CNRS, UMR 5558, Laboratoire de Biométrie et Biologie Évolutive, Équipe Biostatistique-Santé, Villeurbanne, France
,
René Ecochard
1  Hospices Civils de Lyon, Service de Biostatistique-Bioinformatique, Lyon, France
2  Université de Lyon, Lyon, France
3  Université Lyon 1, Villeurbanne, France
4  CNRS, UMR 5558, Laboratoire de Biométrie et Biologie Évolutive, Équipe Biostatistique-Santé, Villeurbanne, France
› Author Affiliations
Funding This study was partially funded by Quidel Corporation, San Diego, CA, USA.
Further Information

Publication History

received: 28 October 2017

accepted: 28 November 2017

Publication Date:
02 May 2018 (online)

Summary

Background: Even in normally cycling women, hormone level shapes may widely vary between cycles and between women. Over decades, finding ways to characterize and compare cycle hormone waves was difficult and most solutions, in particular polynomials or splines, do not correspond to physiologically meaningful parameters.

Objective: We present an original concept to characterize most hormone waves with only two parameters.

Methods: The modelling attempt considered pregnanediol-3-alpha-glucuronide (PDG) and luteinising hormone (LH) levels in 266 cycles (with ultrasound-identified ovulation day) in 99 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.

Results: The highly flexible beta-binomial distribution offered the best fit of most hormone waves and required only two readily available and understandable wave parameters: location and scale. In bell-shaped waves (e.g., PDG curves), early peaks may be fitted with a low location parameter and a low scale parameter; plateau shapes are obtained with higher scale parameters. I-shaped, J-shaped, and U-shaped waves (sometimes the shapes of LH curves) may be fitted with high scale parameter and, respectively, low, high, and medium location parameter. These location and scale parameters will be later correlated with feminine physiological events.

Conclusion: Our results demonstrate that, with unimodal waves, complex methods (e.g., functional mixed effects models using smoothing splines, second-order growth mixture models, or functional principal-component- based methods) may be avoided. The use, application, and, especially, result interpretation of four-parameter analyses might be advantageous within the context of feminine physiological events.