Parameter recovery for a skew-normal IRT model under a Bayesian approach: hierarchical framework, prior and kernel sensitivity and sample size

Item response theory (IRT) comprises a set of statistical models which are useful in many fields, especially when there is an interest in studying latent variables (or latent traits). Usually such latent traits are assumed to be random variables and a convenient distribution is assigned to them. A very common choice for such a distribution has been the standard normal. Recently, Azevedo et al. [Bayesian inference for a skew-normal IRT model under the centred parameterization, Comput. Stat. Data Anal. 55 (2011), pp. 353-365] proposed a skew-normal distribution under the centred parameterization (SNCP) as had been studied in [R. B. Arellano-Valle and A. Azzalini, The centred parametrization for the multivariate skew-normal distribution, J. Multivariate Anal. 99(7) (2008), pp. 1362-1382], to model the latent trait distribution. This approach allows one to represent any asymmetric behaviour concerning the latent trait distribution. Also, they developed a Metropolis-Hastings within the Gibbs sampling (MHWGS) algorithm based on the density of the SNCP. They showed that the algorithm recovers all parameters properly. Their results indicated that, in the presence of asymmetry, the proposed model and the estimation algorithm perform better than the usual model and estimation methods. Our main goal in this paper is to propose another type of MHWGS algorithm based on a stochastic representation (hierarchical structure) of the SNCP studied in [N. Henze, A probabilistic representation of the skew-normal distribution, Scand. J. Statist. 13 (1986), pp. 271-275]. Our algorithm has only one Metropolis-Hastings step, in opposition to the algorithm developed by Azevedo et al., which has two such steps. This not only makes the implementation easier but also reduces the number of proposal densities to be used, which can be a problem in the implementation of MHWGS algorithms, as can be seen in [R.J. Patz and B.W. Junker, A straightforward approach to Markov Chain Monte Carlo methods for item response models, J. Educ. Behav. Stat. 24(2) (1999), pp. 146-178; R. J. Patz and B. W. Junker, The applications and extensions of MCMC in IRT: Multiple item types, missing data, and rated responses, J. Educ. Behav. Stat. 24(4) (1999), pp. 342-366; A. Gelman, G.O. Roberts, and W.R. Gilks, Efficient Metropolis jumping rules, Bayesian Stat. 5 (1996), pp. 599-607]. Moreover, we consider a modified beta prior (which generalizes the one considered in [3]) and a Jeffreys prior for the asymmetry parameter. Furthermore, we study the sensitivity of such priors as well as the use of different kernel densities for this parameter. Finally, we assess the impact of the number of examinees, number of items and the asymmetry level on the parameter recovery. Results of the simulation study indicated that our approach performed equally as well as that in [3], in terms of parameter recovery, mainly using the Jeffreys prior. Also, they indicated that the asymmetry level has the highest impact on parameter recovery, even though it is relatively small. A real data analysis is considered jointly with the development of model fitting assessment tools. The results are compared with the ones obtained by Azevedo et al. The results indicate that using the hierarchical approach allows us to implement MCMC algorithms more easily, it facilitates diagnosis of the convergence and also it can be very useful to fit more complex skew IRT models.

Mitochondrial localization and structure-based phosphate activation mechanism of Glutaminase C with implications for cancer metabolism

Glutamine is an essential nutrient for cancer cell proliferation, especially in the context of citric acid cycle anaplerosis. In this manuscript we present results that collectively demonstrate that, of the three major mammalian glutaminases identified to date, the lesser studied splice variant of the gene gls, known as Glutaminase C (GAC), is important for tumor metabolism. We show that, although levels of both the kidney-type isoforms are elevated in tumor vs. normal tissues, GAC is distinctly mitochondrial. GAC is also most responsive to the activator inorganic phosphate, the content of which is supposedly higher in mitochondria subject to hypoxia. Analysis of X-ray crystal structures of GAC in different bound states suggests a mechanism that introduces the tetramerization-induced lifting of a "gating loop" as essential for the phosphate-dependent activation process. Surprisingly, phosphate binds inside the catalytic pocket rather than at the oligomerization interface. Phosphate also mediates substrate entry by competing with glutamate. A greater tendency to oligomerize differentiates GAC from its alternatively spliced isoform and the cycling of phosphate in and out of the active site distinguishes it from the liver-type isozyme, which is known to be less dependent on this ion.

Optic Disc Margin Anatomy in Patients with Glaucoma and Normal Controls with Spectral Domain Optical Coherence Tomography

Objective: To characterize optic nerve head (ONH) anatomy related to the clinical optic disc margin with spectral domain-optical coherence tomography (SD-OCT). Design: Cross-sectional study. Participants: Patients with open-angle glaucoma with focal, diffuse, and sclerotic optic disc damage, and age-matched normal controls. Methods: High-resolution radial SD-OCT B-scans centered on the ONH were analyzed at each clock hour. For each scan, the border tissue of Elschnig was classified for obliqueness (internally oblique, externally oblique, or nonoblique) and the presence of Bruch's membrane overhanging the border tissue. Optic disc stereophotographs were co-localized to SD-OCT data with customized software. The frequency with which the disc margin identified in stereophotographs coincided with (1) Bruch's membrane opening (BMO), defined as the innermost edge of Bruch's membrane; (2) Bruch's membrane/border tissue, defined as any aspect of either outside BMO or border tissue; or (3) border tissue, defined as any aspect of border tissue alone, in the B-scans was computed at each clock hour. Main Outcome Measures: The SD-OCT structures coinciding with the disc margin in stereophotographs. Results: There were 30 patients (10 with each type of disc damage) and 10 controls, with a median (range) age of 68.1 (42-86) years and 63.5 (42-77) years, respectively. Although 28 patients (93%) had 2 or more border tissue configurations, the most predominant one was internally oblique, primarily superiorly and nasally, frequently with Bruch's membrane overhang. Externally oblique border tissue was less frequent, observed mostly inferiorly and temporally. In controls, there was predominantly internally oblique configuration around the disc. Although the configurations were not statistically different between patients and controls, they were among the 3 glaucoma groups. At most locations, the SD-OCT structure most frequently identified as the disc margin was some aspect of Bruch's membrane and border tissue external to BMO. Bruch's membrane overhang was regionally present in the majority of patients with glaucoma and controls; however, in most cases it was not visible as the disc margin. Conclusions: The clinically perceived disc margin is most likely not the innermost edge of Bruch's membrane detected by SD-OCT. These findings have important implications for the automated detection of the disc margin and estimates of the neuroretinal rim. Financial Disclosure(s): Proprietary or commercial disclosure may be found after the references. Ophthalmology 2012;119:738-747 (C) 2012 by the American Academy of Ophthalmology.