Modeling of hormone secretion-generating mechanisms with splines: a pseudo-likelihood approach

A flexible and robust approach is proposed for the investigation of underlying hormone secretion-generating mechanisms. Characterizing hormone time series is a difficult task as most hormones are secreted in a pulsatile manner and pulses are often masked by slow decay. We model hormone concentration as a filtered counting process where the intensity function of the counting process is modeled nonparametrically using periodic splines. The intensity function and parameters are estimated using a combination of weighted least squares and pseudo-likelihood based on the first two moments. Our method uses concentration measurements directly, which avoids the difficult task of estimating pulse numbers and locations. Both simulations and applications suggest that our method performs well for estimating the intensity function of the pulse-generating counting processes.