A transformation approach for incorporating monotone or unimodal constraints.

Journal Article (Journal Article)

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.

Full Text

Duke Authors

Cited Authors

  • Gunn, LH; Dunson, DB

Published Date

  • July 2005

Published In

Volume / Issue

  • 6 / 3

Start / End Page

  • 434 - 449

PubMed ID

  • 15831579

Electronic International Standard Serial Number (EISSN)

  • 1468-4357

International Standard Serial Number (ISSN)

  • 1465-4644

Digital Object Identifier (DOI)

  • 10.1093/biostatistics/kxi020


  • eng