A Bayesian approach to modeling associations between pulsatile hormones

Abstract

Many hormones are secreted in pulses. The pulsatile relationship between hormones regulates many biological processes. To understand endocrine system regulation, time series of hormone concentrations are collected. The goal is to characterize pulsatile patterns and associations between hormones. Currently each hormone on each subject is fitted univariately. This leads to estimates of the number of pulses and estimates of the amount of hormone secreted; however, when the signal-to-noise ratio is small, pulse detection and parameter estimation remains difficult with existing approaches. In this article, we present a bivariate deconvolution model of pulsatile hormone data focusing on incorporating pulsatile associations. Through simulation, we exhibit that using the underlying pulsatile association between two hormones improves the estimation of the number of pulses and the other parameters defining each hormone. We develop the one-to-one, driver-response case and show how birth-death Markov chain Monte Carlo can be used for estimation. We exhibit these features through a simulation study and apply the method to luteinizing and follicle stimulating hormones.

Figure 1

Observed and expected LH and FSH concentrations for one subject. The top figure is LH, and the bottom is FSH. The solid grey lines are the observed hormone concentration profiles and the solid black line is the mean of the posterior predictive distribution for the bivariate fit and the dashed black line is the expected curve for the univariate fits. The histograms on the bottom axes represent the joint posteriors of the pulse locations for the univariate fit (top) bivariate fit (bottom). The data are from Pincus et al. (1998).

Figure 2

An example expected and simulated hormone concentrations. The top figure is the driver hormone, and the bottom the response hormone. The true pulse locations are the ticks just under the observed series. The grey lines with the “dots” are the observed data, the solid grey lines are the true hormone concentrations. The solid black lines are the expected bivariate fits and the dashed black lines the expected univariate fits. The histogram below each series is the joint posterior distribution of the pulse locations for the univariate fit (top) and the bivariate fit (bottom).