Modeling associations between latent event processes governing time series of pulsing hormones

This work is motivated by a desire to quantify relationships between two time series of pulsing hormone concentrations. The locations of pulses are not directly observed and may be considered latent event processes. The latent event processes of pulsing hormones are often associated. It is this joint relationship we model. Current approaches to jointly modeling pulsing hormone data generally assume that a pulse in one hormone is coupled with a pulse in another hormone (one-to-one association). However, pulse coupling is often imperfect. Existing joint models are not flexible enough for imperfect systems. In this article, we develop a more flexible class of pulse association models that incorporate parameters quantifying imperfect pulse associations. We propose a novel use of the Cox process model as a model of how pulse events co-occur in time. We embed the Cox process model into a hormone concentration model. Hormone concentration is the observed data. Spatial birth and death Markov chain Monte Carlo is used for estimation. Simulations show the joint model works well for quantifying both perfect and imperfect associations and offers estimation improvements over single hormone analyses. We apply this model to luteinizing hormone (LH) and follicle stimulating hormone (FSH), two reproductive hormones. Use of our joint model results in an ability to investigate novel hypotheses regarding associations between LH and FSH secretion in obese and non-obese women.