State plane analysis of short hormonal time series in man

Periodic (24-hour) time series consisting of half-hourly hormonal (aldosterone, renin activity, corticosterone, cortisol) concentration values in human plasma can be plotted on a two-dimensional plane. The resulting closed polygon (named here as vectoradrenalgram (VAG) because of its analogy to the vectorcardiogram) generates an area which is linearly related to the derivative of the cross correlation function at zero lag. In addition and independently of the above property, the VAG's area is a measure of bivariate correlation; this measure appears suitable to the analysis of short time series because it is dependent on the variable time and free from parametric constraints. Time series from 18 normal subjects, under different experimental conditions, and 9 patients with primary aldosteronism have been used in the evaluation of this method. Analysis by VAG's area can also be applied to portions of the 24-hour cycle and to multivariate systems: in the latter case, one or both coordinates represent a set of two or more correlated variates. This analysis can also provide features for a pattern ciassification scheme. A priori available knowledge of the biological systems has aided here the VAG's interpretation. Additional evaluation of this type of analysis may be necessary when applied to other less defined systems.