Synchronization of hormonal time series: analytical approaches

Comparison of the patterns of episodic secretion of two or more hormones measured simultaneously often suggests that peak levels tend to occur at around the same time. This visual impression can be misleading, however, as some peaks will occur simultaneously due to chance alone. Traditional cross-correlation methods are suitable for evaluating linkages among circadian and other smoothly varying rhythms, but are less well suited to correlating ultradian peaks. This paper proposes a method which entails identifying peaks of hormone secretion as discrete events in several different series, and counting the frequency of simultaneous and near-simultaneous peaks in temporal 'windows' of increasing width. The expected rates of random coincidences can be assessed by a variety of methods, including simulations and probability calculations. The method described utilizes simple techniques which make few assumptions about the character or stationarity of the series, comparing coincidence rates in the appropriately paired series with those in which a series in one subject is deliberately 'mismatched' with that of another subject. Using this approach, a significant excess of simultaneous peaks of luteinizing hormone (LH) and prolactin was found in normal subjects as compared with mismatched series (17% versus 6%; p less than 0.05). Hypogonadotrophic men treated with pulsatile gonadotrophin-releasing hormone (GnRH) have an even higher coincidence rate (26%). By contrast, the rate of coincidence between pulses of LH and cortisol is not significantly greater than that which would be expected due to chance.