A comparison of methods for analyzing time series of pulsatile hormone data

Abstract

Many endocrine systems are regulated by pulsatile hormones - hormones that are secreted intermittently in boluses rather than continuously over time. To study pulsatile secretion, blood is drawn every few minutes for an extended period. The result is a time series of hormone concentrations for each individual. The goal is to estimate pulsatile hormone secretion features such as frequency, location, duration, and amount of pulsatile and non-pulsatile secretion and compare these features between groups. Various statistical approaches to analyzing these data have been proposed, but validation has generally focused on one hormone. Thus, we lack a broad understanding of each method's performance. By using simulated data with features seen in reproductive and stress hormones, we investigated the performance of three recently developed statistical approaches for analyzing pulsatile hormone data and compared them to a frequently used deconvolution approach. We found that methods incorporating a changing baseline modeled both constant and changing baseline shapes well; however, the added model flexibility resulted in a slight increase in bias in other model parameters. When pulses were well defined and baseline constant, Bayesian approaches performed similar to the existing deconvolution method. The increase in computation time of Bayesian approaches offered improved estimation and more accurate quantification of estimation variation in situations where pulse locations were not clearly identifiable. Within the class of deconvolution models for fitting pulsatile hormone data, the Bayesian approach with a changing baseline offered adequate results over the widest range of data.

Keywords: Bayesian; birth-and-death MCMC; deconvolution; model validation; simulation; spline.

Figure 1

Example experimental pulsatile hormone data. (A) Adrenocorticotropic hormone (ACTH) sampled every 10 min [10] for 24 h; (B) cortisol sampled every 10 min for 24 h [10]; (C) luteinizing hormone (LH) sampled every 10 min for 12 h during the luteal phase of the menstrual cycle [25]; and (D) LH sampled every 10 min for 12 h during the follicular phase of the menstrual cycle [25].

Figure 2

An example simulated series for 9 of the 10 models. Parameters defining these models can be found in Table II. Data were generated at 10-min intervals for a 24-h period. Each series has 144 simulated concentration values.

Figure 3

False positive and negative rates (top panel), average bias in average baseline (2nd panel), average bias in half-life (3rd panel) and average bias in average pulse mass (bottom panel). Column 1 shows the influence of changes in the signal-to-noise ratio and column 2 show the influence of circadian changes in the baseline and pulse mass. Standard error bars are not provided because they are visually negligible for most models. Each bar is the average from fits of 500 simulated series.

Figure 4

Average fitted baseline concentration curve versus the true baseline concentration curve. The range of the y-axis a smaller range than the range of the observed hormone concentration levels to emphasize differences in the baseline estimates. The range of the hormone concentration levels in the simulation are typically 0 to 15 concentration units.