Objective assessment of concordance of secretory events in two endocrine time series

A new objective method is presented for investigating the presence of a temporal relationship between episodic release of two hormones. The two time series of hormone concentrations are first analysed by an objective method for peak detection. Both data series are then transformed into "quantized" or discretized series by recording the occurrence of a hormone pulse as an "event", characterized by the onset, the maximum, or another unique feature. The two quantized series are then matched, and the number of concordant events and discordant events are counted. Each point in series A is compared with a "time-window" of a selected number of points in series B, to accommodate small degree of mismatch between events in the two series. An index of concordance is computed, compensating for any spurious random coincidence: the "Specific Concordance", to evaluate the frequency of concordant events in excess of those expected on the basis of chance alone. This calculation is systematically repeated, interposing a range of time-lags between the two series. A graph of Specific Concordance versus time-lag indicates the time-lag corresponding to a maximal concordance. Simulations of random series of events are performed, and their degree of concordance is evaluated in a similar fashion, thus generating frequency distributions of Specific Concordance values under the null hypothesis of no temporal relationship. This permits the selection of criteria for statistical significance at any desired p-level, for one or many lag times, and for one or multiple subjects. Various degrees of concurdance can also be stimulated to evaluate the performance (sensitivity, statistical power) of this approach. These methods have been implemented as a collection of short microcomputer programmes, and applied to the study of the temporal relationship between beta-endorphin and cortisol in normal subjects sampled every 10 min for 24 h. This analysis demonstrated concordance between events in the two series, with synchronous occurrence of beta-endorphin and cortisol release events significantly more frequently than expected on the basis of random association (p less than 0.01).