A bivariate model of two pulsatile hormones: A Bayesian approach.

Abstract

Many hormones are secreted in rapid bursts, called pulses, that regulate endocrine systems. Since pulsatility is important in regulation, changes in pulsatile secretion and in the associations between hormones may be related to important physiological changes, such as puberty, along with endocrine disorders. Therefore, to understand how endocrine systems are regulated, we are interested in characterizing associations between hormones. In particular, when pulsatile associations are of interest, the goals are to estimate the temporal relationship between the pulses and to test whether the pulsatile association is significant. Unfortunately, there are few statistical methods developed to address these goals. In the first part of this dissertation, we address estimation of the association. We develop a bivariate deconvolution model of pulsatile hormone data using a Bayesian approach. In particular, we concentrate on incorporating (1) temporal association components that model driver-response associations, where a pulsatile release of one hormone (the driver) is associated with a pulsatile release of another hormone (the response) and (2) components that model associations between other pulsatile characteristics. We describe, in detail, the model for the one-to-one, driver-response case and show how birth-death Markov chain Monte Carlo can be used to estimate the relevant posterior distributions. In the second part of the dissertation, we address testing the association. We assume that the time between the driver and response pulses are beta distributed random variates scaled between the two surrounding driver pulses. Under this model, a test of the association is to test whether the parameters defining the beta distribution are consistent with a uniform distribution. We propose a test based on the marginal highest posterior density intervals. We found that performing the test at the individual level results in higher than expected false positive rates. Thus, testing using a population model seems more appropriate. In the last part of the dissertation, we assess the applicability of Approximate Entropy (ApEn) as a measure of pulsatile regularity. We conclude that it is difficult to distinguish whether changes in ApEn are related to differences in pulsatile regularity or some other more deterministic quantities not related to regularity.