Physiological and other medical studies often use hormone measurements over a period of time from multiple subjects to investigate hormone dynamics, secretion-generating mechanisms and interactions. Hormone dynamics are characterized by basal and episodic secretions. Both secretions may be governed by circadian rhythms and may be signals that provide a means of physiological communications. Very few data analytic tools exist for exploring such data in a meaningful yet flexible way. Conventional statistical assessments based on strong and often unrealistic assumptions may lead to ambiguous or even incorrect conclusions. The broad, long-term objective of this proposal is to fully develop statistical techniques to model and understand such physiological data. These techniques will make less restrictive assumptions; explicitly take into account and exploit the inherent biological process; and when appropriate, relate it to covariate information. The specific aims are to build (1) nonparametric mixed-effects models for circadian rhythms; (2) partial spline models for hormone pulse detection with a nonconstant baseline; (3) stochastic models for basal and pulsatile hormone secretion-generating mechanisms; (4) partial spline and stochastic models for bivariate responses with applications to the investigation of possible hormone associations. Spline smoothing methods will be used to achieve flexibility. Methods for estimation, model selection and testing of relevant hypotheses will be developed. Computer codes will also be developed and posted to the public domain. Much of this work is motivated by and will be carried out in collaboration with biomedical researchers. The health-related implications of this investigation are a better quantitative understanding of the physiological processes, which may be used to define more accurately disease states, to compare therapies for disorders associated with the human circadian pacemaker, and to investigate the possible effects of demographic, environmental and psychological variables on circadian rhythms and hormone secretions.