Bayesian Order-Restricted Inference for Hormonal Dynamics

• Activity Number: 422
• Type: Contributed
• Date/Time: Tuesday, August 2, 2011 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistics in Epidemiology
• Author(s): Michelle Renee Danaher*+ and Anindya Roy and Sunni L. Mumford and Enrique F. Schisterman and Paul S. Albert and Zhen Chen
• Companies: Eunice Kennedy Shriver National Institute of Child Health and Human Development and University of Maryland at Baltimore County and Eunice Kennedy Shriver National Institute of Child Health and Human Development and Eunice Kennedy Shriver National Institute of Child Health and Human Development and Eunice Kennedy Shriver National Institute of Child Health and Human Development and Eunice Kennedy Shriver National Institute of Child Health and Human Development
• Keywords: Bayesian procedures ; Hormone measurements ; Menstrual cycle ; Order-restricted inference ; Shape constraints

Abstract

Biomedical data often arise from well-understood biological processes. For example, hormone levels during the menstrual cycle are driven by well-established biological feedback mechanisms between luteinizing hormone, follicle-stimulating hormone, progesterone, and estrogen. Incorporating the known restrictions imposed by the underlying biological processes into the statistical model can greatly improve statistical efficiency and provide estimates of factors affecting menstrual cycle function that are interpretable within the context of known biological relationships. To address these constraints we propose a Bayesian procedure by specifying priors on the constraint space using a reparameterization via Minkowski decomposition. We perform simulations to investigate properties of the proposed methods and for comparison use an existing procedure that is similar to a Bayesian procedure, in which draws from an unconstrained posterior distribution are projected to a constraint space via optimization methods. Lastly, we demonstrate application of these methods to hormone data from the BioCycle study.