Detection and characterization of peaks and estimation of instantaneous secretory rate for episodic pulsatile hormone secretion.

We have developed a new computer program for detection of "peaks" in sequential hormone measurements in longitudinal studies of episodic hormone secretion. The program provides: (a) several statistically based approaches to the estimation of the random measurement error as a function of hormone level; (b) peak detection based on analysis of first derivatives with logic that has been optimized for asymmetrical peaks with exponential decays; (c) several approaches to the estimation of tolerances for the first and second derivatives; (d) a sensitive curve-fitting approach, to distinguish between upstrokes, exponential decays, and flat baselines; (e) ability to detect multiple overlapping peaks; (f) analysis of "robustness" by systematically varying the threshold around the most-likely value; (g) superimposition of detected peaks, to evaluate "average peak shape"; (h) analysis of the "decay rate," to obtain an estimate of the disappearance rate constant and half-life; (i) use of a "discrete deconvolution" approach, to solve for the apparent instantaneous rate of secretion, and provision of an error analysis to obtain estimates of the precision of these derived values; and (j) correlation with other relevant series as a means of cross validating. The program has been tested extensively on real and synthetic data, and appears to perform well. The frequency of "false positive" peaks can be held at any desired low level, and can be prevented from increasing as sampling frequency increases. The number of arbitrary assumptions, approximations, or thresholds is held to an absolute minimum. These methods are natural, logical, and follow from first principles of statistics.