Joint recovery of pulsatile and basal hormone secretion by stochastic nonlinear random-effects analysis

We present a nonlinear random-effects stochastic differential equation (SDE) model of combined basal and pulsatile hormone secretion with a series-specific hormone half-life and conditional pulse times. The construct uses a three-parameter pulse shape (generalized gamma function) to allow variably skewed secretory bursts superimposed on a finite basal hormone secretion rate. The analysis imbeds stochastic elements at three levels: a variable mass of hormone accumulation (of which the random effect is a part) during interpulse intervals, nonuniform secretion with hormone admixture into the circulation, and technical (sampling and assay) experimental uncertainty. We implement maximum likelihood estimates of secretory parameters (basal and pulsatile secretion and half-life) with asymptotic standard errors. The model applied to illustrative human luteinizing hormone (LH) time series suggests contrasts in basal LH secretion rates (e.g., greater in postmenopausal women than men) and LH secretory burst mass (e.g., higher in older women), but not LH burst frequency or distributional LH half-lives (7-40 min). For validation, in two infused (human recombinant) LH profiles, we implement partially constrained mono- and biexponential versions of the model with fixed (a priori assumed) versus variable LH basal secretion rates. We conclude that a statistically supported, nonlinear, random effects, SDE-based construct can evaluate jointly basal and pulsatile LH secretory rates and LH half-life in 24 h, episodically varying serum LH concentration profiles. This new reduced-parameter analytic strategy should be useful to explore further the pathophysiological mechanisms of altered neurohormone secretion.