A new method for characterizing hormone pulses in a time series.

Abstract

There is general recognition that some glands secrete hormones, such as luteinizing hormone and growth hormone, primarily as pulses. When serial concentrations of hormones secreted episodically are plotted over time, the resultant time series exhibits visually distinct regions in which relatively large and rapid increases are followed by longer periods of relatively steady decline. The goal of the statistical analysis is to characterize the pattern of pulsatility in terms of pulse frequency, amplitude, baseline level and decay rate. Two processes determine hormone concentration: input and elimination. Input is the release of hormone by a gland either through basal or pulsatile secretion; we distinguish between these two modes of secretion in our model. Elimination is modeled by exponential decay. The convolution integral provides a mathematical framework to relate the combined contributions of these processes to hormone concentration. The noise in the observed time series is modeled as a combination of biological variability and experimental error. We model the net hormone input between samples as a series of observations from a mixture of two distributions representing basal and pulsatile input. We assume a distribution for the total net input during a pulse, but make no assumptions about the shape of the input function. For a given value of the clearance rate, we develop a method to identify individual pulses in the observed time series. This is accomplished by first subtracting an estimate of the basal input (based on a robust smoother), and then searching for significant pulses in the residual series. Conditional on the set of pulses found by the search algorithm, the model is fitted to the original time series using weighted least squares. The minimum Bayesian information criterion estimate of prediction error over a grid of values for the clearance rate is used to determine the final model. We compare the new method with several previously proposed methods using simulated data and find that the new method compares very favorably. A major difference is that existing methods tend to overidentify pulses at high sampling rates while the new method is more robust against this type of error.