Informative Models for the Joint Distribution of a Vector from Its Marginal Distributions

• Activity Number: 554 - Novel Methods in Longitudinal Data Analysis
• Type: Contributed
• Date/Time: Thursday, August 11, 2022 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Marepalli B Rao* and Rigwed B Tatu and Koffi B Wima and Karthikeyan B Meganathan and Tianyuan Guan
• Companies: University of Cincinnati and Cincinnati Children Hospital and University of Cincinnati and University of Cincinnati and Kent State University
• Keywords: Destructive Samples; Joint Distribution; Marginal Distribution; Spina Bifida; Patch; Biodegradable

Abstract

When a patch is implanted to cover the gap on the back of the fetus, diagnosed with Spina Bifida, one side of the patch will be facing amniotic fluid and the other side cerebrospinal fluid of the fetus. The cerebrospinal fluid is synthesized as phosphate buffer saline form for experimental purposes. If the patch is in place for a certain length of time, we want to measure how rough the patch is on either side at the end of the period. Ideally, we want to measure roughness at 0, 4, 8, 12, and 16 weeks. The roughness of a patch is symbolized by a random vector (X, Y, Z, U, V). There is one practical difficulty. For the measurement, the patch has to be removed from the gap, dried, stretched, and sent through a machine. The patch cannot be used again. The sample is virtually getting destructed for the measurement needed. In other words, the vector cannot be observed. However, in a laboratory experiment, each component of the vector can be observed individually. We propose models, which have information on the joint distribution of the vector from the marginal distributions. We outline methods extracting information on the joint distribution from the marginal distributions.