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A transformation approach for incorporating monotone or unimodal constraints.

Publication ,  Journal Article
Gunn, LH; Dunson, DB
Published in: Biostatistics (Oxford, England)
July 2005

Samples of curves are collected in many applications, including studies of reproductive hormone levels in the menstrual cycle. Many approaches have been proposed for correlated functional data of this type, including smoothing spline methods and other flexible parametric modeling strategies. In many cases, the underlying biological processes involved restrict the curve to follow a particular shape. For example, progesterone levels in healthy women increase during the menstrual cycle to a peak achieved at random location with decreases thereafter. Reproductive epidemiologists are interested in studying the distribution of the peak and the trajectory for women in different groups. Motivated by this application, we propose a simple approach for restricting each woman's mean trajectory to follow an umbrella shape. An unconstrained hierarchical Bayesian model is used to characterize the data, and draws from the posterior distribution obtained using a Gibbs sampler are then mapped to the constrained space. Inferences are based on the resulting quasi-posterior distribution for the peak and individual woman trajectories. The methods are applied to a study comparing progesterone trajectories for conception and nonconception cycles.

Duke Scholars

Published In

Biostatistics (Oxford, England)

DOI

EISSN

1468-4357

ISSN

1465-4644

Publication Date

July 2005

Volume

6

Issue

3

Start / End Page

434 / 449

Related Subject Headings

  • Statistics & Probability
  • Progesterone
  • Pregnancy
  • Models, Statistical
  • Models, Biological
  • Menstrual Cycle
  • Humans
  • Fertilization
  • Female
  • Biometry
 

Citation

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Gunn, L. H., & Dunson, D. B. (2005). A transformation approach for incorporating monotone or unimodal constraints. Biostatistics (Oxford, England), 6(3), 434–449. https://doi.org/10.1093/biostatistics/kxi020
Gunn, Laura H., and David B. Dunson. “A transformation approach for incorporating monotone or unimodal constraints.Biostatistics (Oxford, England) 6, no. 3 (July 2005): 434–49. https://doi.org/10.1093/biostatistics/kxi020.
Gunn LH, Dunson DB. A transformation approach for incorporating monotone or unimodal constraints. Biostatistics (Oxford, England). 2005 Jul;6(3):434–49.
Gunn, Laura H., and David B. Dunson. “A transformation approach for incorporating monotone or unimodal constraints.Biostatistics (Oxford, England), vol. 6, no. 3, July 2005, pp. 434–49. Epmc, doi:10.1093/biostatistics/kxi020.
Gunn LH, Dunson DB. A transformation approach for incorporating monotone or unimodal constraints. Biostatistics (Oxford, England). 2005 Jul;6(3):434–449.
Journal cover image

Published In

Biostatistics (Oxford, England)

DOI

EISSN

1468-4357

ISSN

1465-4644

Publication Date

July 2005

Volume

6

Issue

3

Start / End Page

434 / 449

Related Subject Headings

  • Statistics & Probability
  • Progesterone
  • Pregnancy
  • Models, Statistical
  • Models, Biological
  • Menstrual Cycle
  • Humans
  • Fertilization
  • Female
  • Biometry