Setting a standard for low reading proficiency: A comparison of the bookmark procedure and constrained mixture Rasch model

In order to draw pertinent conclusions about persons with low reading skills, it is essential to use validated standard-setting procedures by which they can be assigned to their appropriate level of proficiency. Since there is no standard-setting procedure without weaknesses, external validity studies are essential. Traditionally, studies have assessed validity by comparing different judgement-based standard-setting procedures. Only a few studies have used model-based approaches for validating judgement-based procedures. The present study addressed this shortcoming and compared agreement of the cut score placement between a judgement-based approach (i.e., Bookmark procedure) and a model-based one (i.e., constrained mixture Rasch model). This was performed by differentiating between individuals with low reading proficiency and those with a functional level of reading proficiency in three independent samples of the German National Educational Panel Study that included students from the ninth grade (N = 13,897) as well as adults (Ns = 5,335 and 3,145). The analyses showed quite similar mean cut scores for the two standard-setting procedures in two of the samples, whereas the third sample showed more pronounced differences. Importantly, these findings demonstrate that model-based approaches provide a valid and resource-efficient alternative for external validation, although they can be sensitive to the ability distribution within a sample.

Global Sensitivity Analysis of a Homogenized Constrained Mixture Model of Arterial Growth and Remodeling

Growth and remodeling in arterial tissue have attracted considerable attention over the last decade. Mathematical models have been proposed, and computational studies with these have helped to understand the role of the different model parameters. So far it remains, however, poorly understood how much of the model output variability can be attributed to the individual input parameters and their interactions. To clarify this, we propose herein a global sensitivity analysis, based on Sobol indices, for a homogenized constrained mixture model of aortic growth and remodeling. In two representative examples, we found that 54–80% of the long term output variability resulted from only three model parameters. In our study, the two most influential parameters were the one characterizing the ability of the tissue to increase collagen production under increased stress and the one characterizing the collagen half-life time. The third most influential parameter was the one characterizing the strain-stiffening of collagen under large deformation. Our results suggest that in future computational studies it may - at least in scenarios similar to the ones studied herein - suffice to use population average values for the other parameters. Moreover, our results suggest that developing methods to measure the said three most influential parameters may be an important step towards reliable patient-specific predictions of the enlargement of abdominal aortic aneurysms in clinical practice.

Mixture Designs Generated by Orthogonal Arrays Developed Using Difference Schemes

This paper presents an algorithm for constructing mixture designs based on orthogonal arrays developed using difference schemes. The algorithm can also be applied to constrained mixture experiments. The algorithm allows the generation of efficient mixture designs for Scheffé canonical polynomials.

A Constrained Mixture Theory Model to Study Autoregulation in the Coronary Circulation

Coronary autoregulation is a short-term response manifested by a relatively constant flow over a wide range of perfusion pressures for a given metabolic state. This phenomenon is thought to be facilitated through a combination of mechanisms, including myogenic, shear dependent, and metabolic controls. The study of coronary autoregulation is challenging due to the coupled nature of the mechanisms and their differential effects through the coronary tree. In this paper, we developed a novel framework to study coronary autoregulation based on the constrained mixture theory. This structurally-motivated autoregulation model required calibration of anatomical and structural parameters of coronary trees via a homeostatic optimization approach using extensive literature data. Autoregulation was then simulated for two different coronary trees: subepicardial and subendocardial. The structurally calibrated model reproduced available baseline hemodynamics and autoregulation data for each coronary tree. The autoregulation analysis showed that the diameter of the intermediate and small arterioles varies the most in response to changes in perfusion pressure. Finally, we demonstrated the utility of the model in two application examples: 1) response to drops in epicardial pressure, and 2) response to drug infusion in the coronary arteries. The proposed structurally-motivated model could be extended to study long-term growth and remodeling in the coronary circulation in response to hypertension, atherosclerosis, etc.Key pointsCoronary autoregulation is defined as the capability of the coronary circulation to maintain the blood supply to the heart over a range of perfusion pressures. This phenomenon is facilitated through intrinsic mechanisms that control the vascular resistance by regulating the mechanical function of smooth muscle cells. Understanding the mechanisms involved in coronary autoregulation is one of the most fundamental questions in coronary physiology.This paper presents a structurally-motivated coronary autoregulation model that uses a nonlinear continuum mechanics approach to account for the morphometry and vessel wall composition in two coronary trees in the subepicardial and subendocardial layers.The model is calibrated against diverse experimental data from literature and is used to study heterogeneous autoregulatory response in the coronary trees. This model drastically differs from previous models, which relied on lumped parameter model formulations, and is suited to the study of long-term pathophysiological growth and remodeling phenomena in coronary vessels.