Deconvolution of episodic hormone data: an analysis of the role of season on the onset of puberty in cows.

A new approach to the analysis of episodic hormone data is described. The method involves a stochastic model in which measured blood hormone concentration is represented as a convolution of individual pulses, each of which is thought of as the response to a burst of neural activity. Individual pulses are not constrained to occur in a fixed regular pattern in time. The methodology takes a series of blood hormone measurements and produces a spike train of pulse peak times together with a set of pulse shape parameters. This decomposition motivates some fresh approaches to the analysis of hormone data. For a given number of pulses the model is fit by minimizing a residual sum of squares criterion. This is a difficult combinatorial optimization problem. A randomized local adjustment algorithm is developed. Generalized cross-validation is used to select the number of pulses. The technique seems to produce reliable results on simulated data sets. The methodology is used to study some data concerned with the role of season of birth on the onset of puberty in bovine females. The analysis raises some interesting questions related to the maturation of the pituitary and hypothalamus.