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

Correspondence to:

Saman Abdullah
Service de Biostatistique-Bioinformatique,
Hospices Civils de Lyon
162, avenue Lacassagne
FR-69003
Lyon
France
Phone: (+33) 6 11 01 66 96   

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.


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Conflict of Interest

The authors declare they have no conflicts of interest in relation to the present methodological work.

  • References

  • 1 Alliende ME. Mean versus individual hormonal profiles in the menstrual cycle. Fertil Steril 2002; 78 (01) 90-96.
  • 2 Besse P, Ramsay JO. Principal components analysis of sampled functions. Psychometrika 1986; 51 (02) 285-311.
  • 3 Guo W. Functional data analysis in longitudinal settings using smoothing splines. Stat Methods Med Res 2004; 13 (01) 49-62.
  • 4 Grimm KJ, Ram N. A Second-Order Growth Mixture Model for Developmental Research. Res Human Dev 2009; 06 (2–3): 121-143.
  • 5 Ecochard R, Guillerm A, Leiva R, Bouchard T, Direito A, Boehringer H. Characterization of follicle stimulating hormone profiles in normal ovulating women. Fertil Steril 2014; 102 (01) 237-243.
  • 6 Hall JE, Schoenfeld DA, Martin KA, Crowley Jr WF. Hypothalamic gonadotropin-releasing hormone secretion and follicle-stimulating hormone dynamics during the luteal-follicular transition. J Clin Endocrinol Metab 1992; 74 (03) 600-607.
  • 7 Park SJ, Goldsmith LT, Skurnick JH, Wojtczuk A, Weiss G. Characteristics of the urinary luteinizing hormone surge in young ovulatory women. Fertil Steril 2007; 88 (03) 684-690.
  • 8 Direito A, Bailly S, Mariani A, Ecochard R. Relationships between the luteinizing hormone surge and other characteristics of the menstrual cycle in normally ovulating women. Fertil Steril 2013; 99 (01) 279-285.
  • 9 Blackwell LF, Vigil P, Alliende ME, Brown S, Festin M, Cooke DG. Monitoring of ovarian activity by measurement of urinary excretion rates using the Ovarian Monitor, Part IV: the relationship of the pregnanediol glucuronide threshold to basal body temperature and cervical mucus as markers for the beginning of the post-ovulatory infertile period. Hum Reprod 2016; 31 (02) 445-453.
  • 10 Blackwell LF, Vigil P, Cooke DG, d’Arcangues C, Brown JB. Monitoring of ovarian activity by daily measurement of urinary excretion rates of oestrone glucuronide and pregnanediol glucuronide using the Ovarian Monitor, Part III: variability of normal menstrual cycle profiles. Hum Reprod 2013; 28 (12) 3306-3315.
  • 11 Genolini C, Falissard B. kml:k-means for longitudinal data. Comput Stat 2010; 25 (02) 317-328.
  • 12 Nagin DS, Odgers CL. Group-based trajectory modeling in clinical research. Ann Rev Clin Psychol 2010; 06: 109-138.
  • 13 Muthén B. Latent variable analysis: growth mixture modeling and related techniques for longitudinal data. In: Handbook of Quantitative Methodology for the Social Sciences. ed. Kaplan D. Newbury Park, CA: Sage; 2004: 345-368.
  • 14 Nylund KI, Asparouhov T, Muthén BO. Deciding on the number of classes in latent class analysis and growth mixture modeling: a Monte Carlo simulation study. Struct Equ Model 2007; 14 (04) 535-569.
  • 15 Niu F, Zhou J, Le TH, Ma JZ. Testing the trajectory difference in a semi-parametric longitudinal model. Stat Methods Med Res 2017; 26 (03) 1519-1531.
  • 16 Nierop AF, Niklasson A, Holmgren A, Gelander L, Rosberg S, Albertsson-Wikland K. Modelling individual longitudinal human growth from fetal to adult life – QEPS I. J Theor Biol 2016; 406: 143-165.
  • 17 Collins WP, Collins PO, Kilpatrick MJ, Manning PA, Pike JM, Tyler JP. The concentrations of urinary oestrone-3-glucuronide, LH and pregnanediol-3alpha-glucuronide as indices of ovarian function. Acta Endocrinol (Copenh) 1979; 90 (02) 336-348.
  • 18 Hennig C, Kutlukaya M. Some thoughts about the design of loss functions. Revstat Stat J 2007; 05 (01) 19-39.
  • 19 Rigby RA, Stasinopoulos DM. Generalized Additive Models for Location, Scale and Shape. Appl Stat 2005; 54 (03) 507-554.
  • 20 Stasinopoulos DM, Rigby RA. Generalized additive models for location scale and shape (GAMLSS) in R. J Stat Softw 2007; 23 (07) 1-46.

Correspondence to:

Saman Abdullah
Service de Biostatistique-Bioinformatique,
Hospices Civils de Lyon
162, avenue Lacassagne
FR-69003
Lyon
France
Phone: (+33) 6 11 01 66 96   

  • References

  • 1 Alliende ME. Mean versus individual hormonal profiles in the menstrual cycle. Fertil Steril 2002; 78 (01) 90-96.
  • 2 Besse P, Ramsay JO. Principal components analysis of sampled functions. Psychometrika 1986; 51 (02) 285-311.
  • 3 Guo W. Functional data analysis in longitudinal settings using smoothing splines. Stat Methods Med Res 2004; 13 (01) 49-62.
  • 4 Grimm KJ, Ram N. A Second-Order Growth Mixture Model for Developmental Research. Res Human Dev 2009; 06 (2–3): 121-143.
  • 5 Ecochard R, Guillerm A, Leiva R, Bouchard T, Direito A, Boehringer H. Characterization of follicle stimulating hormone profiles in normal ovulating women. Fertil Steril 2014; 102 (01) 237-243.
  • 6 Hall JE, Schoenfeld DA, Martin KA, Crowley Jr WF. Hypothalamic gonadotropin-releasing hormone secretion and follicle-stimulating hormone dynamics during the luteal-follicular transition. J Clin Endocrinol Metab 1992; 74 (03) 600-607.
  • 7 Park SJ, Goldsmith LT, Skurnick JH, Wojtczuk A, Weiss G. Characteristics of the urinary luteinizing hormone surge in young ovulatory women. Fertil Steril 2007; 88 (03) 684-690.
  • 8 Direito A, Bailly S, Mariani A, Ecochard R. Relationships between the luteinizing hormone surge and other characteristics of the menstrual cycle in normally ovulating women. Fertil Steril 2013; 99 (01) 279-285.
  • 9 Blackwell LF, Vigil P, Alliende ME, Brown S, Festin M, Cooke DG. Monitoring of ovarian activity by measurement of urinary excretion rates using the Ovarian Monitor, Part IV: the relationship of the pregnanediol glucuronide threshold to basal body temperature and cervical mucus as markers for the beginning of the post-ovulatory infertile period. Hum Reprod 2016; 31 (02) 445-453.
  • 10 Blackwell LF, Vigil P, Cooke DG, d’Arcangues C, Brown JB. Monitoring of ovarian activity by daily measurement of urinary excretion rates of oestrone glucuronide and pregnanediol glucuronide using the Ovarian Monitor, Part III: variability of normal menstrual cycle profiles. Hum Reprod 2013; 28 (12) 3306-3315.
  • 11 Genolini C, Falissard B. kml:k-means for longitudinal data. Comput Stat 2010; 25 (02) 317-328.
  • 12 Nagin DS, Odgers CL. Group-based trajectory modeling in clinical research. Ann Rev Clin Psychol 2010; 06: 109-138.
  • 13 Muthén B. Latent variable analysis: growth mixture modeling and related techniques for longitudinal data. In: Handbook of Quantitative Methodology for the Social Sciences. ed. Kaplan D. Newbury Park, CA: Sage; 2004: 345-368.
  • 14 Nylund KI, Asparouhov T, Muthén BO. Deciding on the number of classes in latent class analysis and growth mixture modeling: a Monte Carlo simulation study. Struct Equ Model 2007; 14 (04) 535-569.
  • 15 Niu F, Zhou J, Le TH, Ma JZ. Testing the trajectory difference in a semi-parametric longitudinal model. Stat Methods Med Res 2017; 26 (03) 1519-1531.
  • 16 Nierop AF, Niklasson A, Holmgren A, Gelander L, Rosberg S, Albertsson-Wikland K. Modelling individual longitudinal human growth from fetal to adult life – QEPS I. J Theor Biol 2016; 406: 143-165.
  • 17 Collins WP, Collins PO, Kilpatrick MJ, Manning PA, Pike JM, Tyler JP. The concentrations of urinary oestrone-3-glucuronide, LH and pregnanediol-3alpha-glucuronide as indices of ovarian function. Acta Endocrinol (Copenh) 1979; 90 (02) 336-348.
  • 18 Hennig C, Kutlukaya M. Some thoughts about the design of loss functions. Revstat Stat J 2007; 05 (01) 19-39.
  • 19 Rigby RA, Stasinopoulos DM. Generalized Additive Models for Location, Scale and Shape. Appl Stat 2005; 54 (03) 507-554.
  • 20 Stasinopoulos DM, Rigby RA. Generalized additive models for location scale and shape (GAMLSS) in R. J Stat Softw 2007; 23 (07) 1-46.