Fitting nonlinear and constrained generalized estimating equations with optimization software

Modelling and estimation of nonlinear quantile regression with clustered data

In regression applications, the presence of nonlinearity and correlation among observations offer computational challenges not only in traditional settings such as least squares regression, but also (and especially) when the objective function is nonsmooth as in the case of quantile regression. Methods are developed for the modelling and estimation of nonlinear conditional quantile functions when data are clustered within two-level nested designs. The proposed estimation algorithm is a blend of a smoothing algorithm for quantile regression and a second order Laplacian approximation for nonlinear mixed models. This optimization approach has the appealing advantage of reducing the original nonsmooth problem to an approximated L 2 problem. While the estimation algorithm is iterative, the objective function to be optimized has a simple analytic form. The proposed methods are assessed through a simulation study and two applications, one in pharmacokinetics and one related to growth curve modelling in agriculture.

A physiological model for autonomic heart rate regulation in human endotoxemia

The systemic inflammatory response syndrome often accompanies critical illnesses and can be an important cause of morbidity and mortality. Marked abnormalities in cardiovascular function accompany acute illnesses manifested as sustained tachyarrhythmias, which are but one component of systemic dysregulation. The realization that cardiac pacemaker activity is under control of the autonomic nervous system has promoted the analysis of heart rate (HR) variation for assessing autonomic activities. In acute illnesses, autonomic imbalance manifesting in part as parasympathetic attenuation is associated with increased morbidity in patients who manifest systemic inflammatory response syndrome phenotype. Driven by the premise that biological phenotypes emerge as the outcome of the coordinated action of network elements across the host, a multiscale model of human endotoxemia, as a prototype model of systemic inflammation in humans, is developed that quantifies critical aspects of the complex relationship between inflammation and autonomic HR regulation. In the present study, changes in HR response to acute injury, phenotypically expressed as tachycardia, are simulated as a result of autonomic imbalance that reflects sympathetic activity excess and parasympathetic attenuation. The proposed model assesses both the anti-inflammatory and cardiovascular effects of antecedent stresses upon the systemic inflammatory manifestations of human endotoxemia as well as a series of nonlinear inflammatory relevant scenarios. Such a modeling approach provides a comprehensive conceptual framework linking inflammation and physiological complexity via a multiscale model that may advance the translational potential of systems modeling in clinical research.

Multiscale model for the assessment of autonomic dysfunction in human endotoxemia

Severe injury and infection are associated with autonomic dysfunction. The realization that a dysregulation in autonomic function may predispose a host to excessive inflammatory processes has renewed interest in understanding the role of central nervous system (CNS) in modulating systemic inflammatory processes. Assessment of heart rate variability (HRV) has been used to evaluate systemic abnormalities and as a predictor of the severity of illness. Dissecting the relevance of neuroimmunomodulation in controlling inflammatory processes requires an understanding of the multiscale interplay between CNS and the immune response. A vital enabler in that respect is the development of a systems-based approach that integrates data across multiple scales, and models the emerging host response as the outcome of interactions of critical modules. Thus, a multiscale model of human endotoxemia, as a prototype model of systemic inflammation in humans, is proposed that integrates processes across the host from the cellular to the systemic host response level. At the cellular level interacting components are associated with elementary signaling pathways that propagate extracellular signals to the transcriptional response level. Further, essential modules associated with the neuroendocrine immune crosstalk are considered. Finally, at the systemic level, phenotypic expressions such as HRV are incorporated to assess systemic decomplexification indicative of the severity of the host response. Thus, the proposed work intends to associate acquired endocrine dysfunction with diminished HRV as a critical enabler for clarifying how cellular inflammatory processes and neural-based pathways mediate the links between patterns of autonomic control (HRV) and clinical outcomes.