[17] Assessing Temporal Coupling between Two or among Three or More Neuroendocrine Pulse Trains

We have reviewed classical cross-correlation analysis as modified with autoregressive modeling to correct for intrinsic autocorrelation in neuroendocrine time series as a robust and useful complementary tool for assessing the coupling between two neuroendocrine pulse trains. However, cross-correlation analysis cannot be applied to three series evaluated simultaneously, but rather must be applied pairwise. Moreover, cross-correlation analysis does not account for the occurrence of discrete and delimited events in the data or address the question of how often such individual events occur together compared to expected coincidence based on chance associations alone. Such discrete coincidence testing can be approached using computer simulations, as reviewed here and elsewhere. In addition, we show that explicit conditional probability analysis can be applied assuming binary, hypergeometric, or higher-order combinatorial algebra (reviewed above). All calculations can be carried out in a few seconds on a personal computer. We emphasize that probability analysis that assumes a random uniform distribution of peak locations over time would be inappropriate when there are strong systematic variations in pulse frequency throughout the sampling session. In those circumstances, we recommend the use of computer-stimulation methods. Finally, specific concordance values (27) can be calculated on microprocessors, so as to estimate the extent of concordance observed beyond that expected on the basis of chance assortment of the pulses. Of considerable practical importance to the experimental neuroscientist, we show that power analysis can be carried out to make preliminary estimates of the group sizes required for detecting a given degree of nonrandom concordance between two neurohormone series. Finally, we emphasize that no concordance testing is more accurate or valid than the sampling paradigm and the pulse-detection methodology applied to enumerate the number and location of discrete neurohormonal release episodes in the data (1, 21, 24, 27, 29-32).