On the stick-breaking representation of normalized inverse Gaussian priors

Random probability measures are the main tool for Bayesian nonparametric inference, with their laws acting as prior distributions. Many well-known priors used in practice admit different, though equivalent, representations. In terms of computational convenience, stick-breaking representations stand out. In this paper we focus on the normalized inverse Gaussian process and provide a completely explicit stick-breaking representation for it. This result is of interest both from a theoretical viewpoint and for statistical practice

Laplace approximation of Lauricella functions F A and F D

The Lauricella functions, which are generalizations of the Gauss hypergeometric function 2 F 1, arise naturally in many areas of mathematics and statistics. So far as we are aware, there is little or nothing in the literature on how to calculate numerical approximations for these functions outside those cases in which a simple one-dimensional integral representation or a one-dimensional series representation is available. In this paper we present first-order and second-order Laplace approximations to the Lauricella functions F(n)A and F(n)D. Our extensive numerical results show that these approximations achieve surprisingly good accuracy in a wide variety of examples, including cases well outside the asymptotic framework within which the approximations were derived. Moreover, it turns out that the second-order Laplace approximations are usually more accurate than their first-order versions. The numerical results are complemented by theoretical investigations which suggest that the approximations have good relative error properties outside the asymptotic regimes within which they were derived, including in certain cases where the dimension n goes to infinity

Can Clinical and Surgical Parameters Be Combined to Predict How Long It Will Take a Tibia Fracture to Heal? A Prospective Multicentre Observational Study: The FRACTING Study

Healing of tibia fractures occurs over a wide time range of months, with a number of risk factors contributing to prolonged healing. In this prospective, multicentre, observational study, we investigated the capability of FRACTING (tibia FRACTure prediction healING days) score, calculated soon after tibia fracture treatment, to predict healing time. Methods: The study included 363 patients. Information on patient health, fracture morphology, and surgical treatment adopted were combined to calculate the FRACTING score. Fractures were considered healed when the patient was able to fully weight-bear without pain. Results: 319 fractures (88%) healed within 12 months from treatment. Forty-four fractures healed after 12 months or underwent a second surgery. FRACTING score positively correlated with days to healing: r = 0.63 (p < 0.0001). Average score value was 7.3 ± 2.5; ROC analysis showed strong reliability of the score in separating patients healing before versus after 6 months: AUC = 0.823. Conclusions: This study shows that the FRACTING score can be employed both to predict months needed for fracture healing and to identify immediately after treatment patients at risk of prolonged healing. In patients with high score values, new pharmacological and nonpharmacological treatments to enhance osteogenesis could be tested selectively, which may finally result in reduced disability time and health cost savings

Risk of Early-Onset Neonatal Group B Streptococcal Disease With Maternal Colonization Worldwide: Systematic Review and Meta-analyses.

Background: Early-onset group B streptococcal disease (EOGBS) occurs in neonates (days 0-6) born to pregnant women who are rectovaginally colonized with group B Streptococcus (GBS), but the risk of EOGBS from vertical transmission has not been systematically reviewed. This article, the seventh in a series on the burden of GBS disease, aims to estimate this risk and how it varies with coverage of intrapartum antibiotic prophylaxis (IAP), used to reduce the incidence of EOGBS. Methods: We conducted systematic reviews (Pubmed/Medline, Embase, Latin American and Caribbean Health Sciences Literature (LILACS), World Health Organization Library Information System [WHOLIS], and Scopus) and sought unpublished data from investigator groups on maternal GBS colonization and neonatal outcomes. We included articles with ≥200 GBS colonized pregnant women that reported IAP coverage. We did meta-analyses to determine pooled estimates of risk of EOGBS, and examined the association in risk of EOGBS with IAP coverage. Results: We identified 30 articles including 20328 GBS-colonized pregnant women for inclusion. The risk of EOGBS in settings without an IAP policy was 1.1% (95% confidence interval [CI], .6%-1.5%). As IAP increased, the risk of EOGBS decreased, with a linear association. Based on linear regression, the risk of EOGBS in settings with 80% IAP coverage was predicted to be 0.3% (95% CI, 0-.9). Conclusions: The risk of EOGBS among GBS-colonized pregnant women, from this first systematic review, is consistent with previous estimates from single studies (1%-2%). Increasing IAP coverage was linearly associated with decreased risk of EOGBS disease

Cardiac tumours in children

Cardiac tumours are benign or malignant neoplasms arising primarily in the inner lining, muscle layer, or the surrounding pericardium of the heart. They can be primary or metastatic. Primary cardiac tumours are rare in paediatric practice with a prevalence of 0.0017 to 0.28 in autopsy series. In contrast, the incidence of cardiac tumours during foetal life has been reported to be approximately 0.14%. The vast majority of primary cardiac tumours in children are benign, whilst approximately 10% are malignant. Secondary malignant tumours are 10–20 times more prevalent than primary malignant tumours. Rhabdomyoma is the most common cardiac tumour during foetal life and childhood. It accounts for more than 60% of all primary cardiac tumours. The frequency and type of cardiac tumours in adults differ from those in children with 75% being benign and 25% being malignant. Myxomas are the most common primary tumours in adults constituting 40% of benign tumours. Sarcomas make up 75% of malignant cardiac masses. Echocardiography, Computing Tomography (CT) and Magnetic Resonance Imaging (MRI) of the heart are the main non-invasive diagnostic tools. Cardiac catheterisation is seldom necessary. Tumour biopsy with histological assessment remains the gold standard for confirmation of the diagnosis. Surgical resection of primary cardiac tumours should be considered to relieve symptoms and mechanical obstruction to blood flow. The outcome of surgical resection in symptomatic, non-myxomatous benign cardiac tumours is favourable. Patients with primary cardiac malignancies may benefit from palliative surgery but this approach should not be recommended for patients with metastatic cardiac tumours. Surgery, chemotherapy and radiotherapy may prolong survival. The prognosis for malignant primary cardiac tumours is generally extremely poor