Using Cox cluster processes to model latent pulse location patterns in hormone concentration data

Abstract

Many hormones, including stress hormones, are intermittently secreted as pulses. The pulsatile location process, describing times when pulses occur, is a regulator of the entire stress system. Characterizing the pulse location process is particularly difficult because the pulse locations are latent; only hormone concentration at sampled times is observed. In addition, for stress hormones the process may change both over the day and relative to common external stimuli. This potentially results in clustering in pulse locations across subjects. Current approaches to characterizing the pulse location process do not capture subject-to-subject clustering in locations. Here we show how a Bayesian Cox cluster process may be adapted as a model of the pulse location process. We show that this novel model of pulse locations is capable of detecting circadian rhythms in pulse locations, clustering of pulse locations between subjects, and identifying exogenous controllers of pulse events. We integrate our pulse location process into a model of hormone concentration, the observed data. A spatial birth-and-death Markov chain Monte Carlo algorithm is used for estimation. We exhibit the strengths of this model on simulated data and adrenocorticotropic and cortisol data collected to study the stress axis in depressed and non-depressed women.

Keywords: Bayesian analysis; Deconvolution; Mixture models; Point processes; Pulsatile hormones.

Fig. 1.

Observed ACTH and cortisol hormone concentration data for one pair of control and depressed subjects (top panel). Fitted intensity functions for ACTH and cortisol (second panel) with random effects for cluster size and width and the strict repulsion prior on the cluster locations. The gray lines are the 10% and 90% pointwise credible intervals. The bottom two panels are the joint posterior distributions of the cluster centers for the controls (top histogram) and depressed subjects (bottom histogram).

Fig. 2.

Simulated and fitted intensity function for a randomly selected simulation for each model: (a) Strong clustering, (b) Weaker clustering, and (c) No clustering. Each simulated dataset had 26 subjects. The top panel represents the true intensity function (solid line) and the estimated intensity function (dashed line). The gray lines are the 10% and 90% pointwise credible intervals. The height of the peaks is . The width of the peaks is The peak center locations make up . The second panel shows the posterior distributions of the estimated cluster centers.