A signal extraction approach to modeling hormone time series with pulses and a changing baseline

Hormones serve as regulating signals for many biological processes. In recent years, it was determined that many hormones are secreted in a pulsatile manner and that the pulsatile secretion pattern, in addition to the absolute concentration level, is important in regulating biological processes. Consequently, it is necessary to characterize the latent secretion patterns from measurements of concentration levels. The characterization is complicated by the presence of a biological circadian rhythm. When hormone concentrations are plotted over time, the resultant time series usually exhibits occasional short rises superimposed on a slowly changing baseline. This is a result of a mixture of pulsatile secretions and a circadian rhythm. In this article we present a signal extraction approach to model simultaneously a slowly changing component and a pulsatile component of a time series. A smoothing spline is used to model the baseline, and a multiprocess dynamic linear model is used to model the pulsatile component. An additive structure is assumed, and both components are estimated simultaneously using a multiprocess Kalman filter. The unknown parameters are estimated by approximate maximum likelihood. The locations and amplitudes of the pulses are also estimated as posterior means via the multiprocess Kalman filter. Bayesian confidence intervals can be constructed For the baseline. This approach is found to be robust in simulated data and effective in modeling hormone time series.