A population-based approach to analyzing pulses in time series of hormone data

Abstract

Studies of reproductive physiology involve rapid sampling protocols that result in time series of hormone concentrations. The signature pattern in these times series is pulses of hormone release. Various statistical models for quantifying the pulsatile release features exist. Currently these models are fitted separately to each individual and the resulting estimates averaged to arrive at post hoc population-level estimates. When the signal-to-noise ratio is small or the time of observation is short (e.g., 6 h), this two-stage estimation approach can fail. This work extends the single-subject modelling framework to a population framework similar to what exists for complex pharamacokinetics data. The goal is to leverage information across subjects to more clearly identify pulse locations and improve estimation of other model parameters. This modelling extension has proven difficult because the pulse number and locations are unknown. Here, we show that simultaneously modelling a group of subjects is computationally feasible in a Bayesian framework using a birth-death Markov chain Monte Carlo estimation algorithm. Via simulation, we show that this population-based approach reduces the false positive and negative pulse detection rates and results in less biased estimates of population-level parameters of frequency, pulse size, and hormone elimination. We then apply the approach to a reproductive study in healthy women where approximately one-third of the 21 subjects in the study did not have appropriate fits using the single-subject fitting approach. Using the population model produced more precise, biologically plausible estimates of all model parameters. Copyright © 2017 John Wiley & Sons, Ltd.

Keywords: Bayesian; birth-and-death MCMC; hierarchical models; luteinizing hormone; reproductive hormones.

Figure 1

Observed hormone concentration profiles and posterior predictive fits of four of the ten healthy normal weight women pre-treatment. The observed hormone concentrations are in grey circles and the black lines represent posterior predictive fits (solid - population model, dashed - single subject). The top histogram under each hormone profile is the posterior distribution of pulse locations from the population model and the bottom histogram from the single-subject model.

Figure 2

Observed hormone concentration profiles and posterior predictive fits of 2 simulated series of 6 hour length. Grey circles represent observed hormone concentrations, and black lines represent posterior predictive fits (solid - population model, dashed - single subject). In each series, the upper histogram shows the posterior distribution of pulse locations from the population model and the bottom histogram from the single-subject model.