Voting Power and Probability

Voting power is commonly measured using a probability. But what kind of probability is this? Is it a degree of belief or an objective chance or some other sort of probability? The aim of this paper is to answer this question. The answer depends on the use to which a measure of voting power is put. Some objectivist interpretations of probabilities are appropriate when we employ such a measure for descriptive purposes. By contrast, when voting power is used to normatively assess voting rules, the probabilities are best understood as classical probabilities, which count possibilities. This is so because, from a normative stance, voting power is most plausibly taken to concern rights and thus possibilities. The classical interpretation also underwrites the use of the Bernoulli model upon which the Penrose/Banzhaf measure is based.

Five-year results of lumbar disc prostheses in the SWISSspine registry

PURPOSE The Swiss Federal Office of Public Health demanded a nationwide HTA registry for lumbar total disc arthroplasty (TDA), to decide about its reimbursement. The goal of the SWISS spine registry is to generate evidence about the safety and efficiency of lumbar TDA. METHODS Two hundred forty-eight cases treated between 3-2005 and 6-2006, who were eligible for the 5-year follow-up were included in the study. Follow-up rates for 3-6 months, 1, 2 and 5 years were 85.9, 77.0, 44.0 and 51.2 %, respectively. Outcome measures were back and leg pain, medication consumption, quality of life, intraoperative and postoperative complication and revision rates. Additionally, segmental mobility, ossification, adjacent and distant segment degeneration were analysed at the 5-year follow-up. RESULTS There was a significant, clinically relevant and lasting reduction of back (preop/postop 73/29 VAS points) and leg pain (preop/postop VAS 55/22) and a consequently decreased analgesics consumption and quality of life improvement (preop/postop 0.30/0.76 EQ-5D score points) until 5 years after surgery. The rates for intraoperative and early postoperative complications were 4.4 and 3.2 %, respectively. The overall complication rate during five postoperative years was 23.4 %, and the adjacent segment degeneration rate was 10.7 %. In 4.4 % of patients, a revision surgery was performed. Cumulative survivorship probability for a revision/re-intervention-free 5-year postoperative course was 90.4 %. At the 5-year follow-up, the average range of motion of the mobile segments (86.8 %) was 9.7°. In 43.9 % of patients, osteophytes at least potentially affecting the range of motion were seen. CONCLUSIONS Lumbar TDA appeared as efficient in long-term pain alleviation, consequent reduction of pain medication consumption and improvement of quality of life. The procedure also appeared sufficiently safe, but surgeons have to be aware of a list of potential adverse events. The outcome is stable over the 5-year postoperative period. The vast majority of treated segments remained mobile after 5 years, although almost half of patients showed osteophytes.

Diagnostic Performance and Additional Value of Elastosonography in Focal Breast Lesions: Statistical Correlation between Size-Dependant Strain Index Measurements, Multimodality-BI-RADS Score, and Histopathology in a Clinical Routine Setting

Objective. To evaluate the diagnostic benefit of real-time elastography (RTE) in clinical routine. Strain indices (SI) for benign and malignant tumors were assessed. Methods. 100 patients with 110 focal breast lesions were retrieved. Patients had mammography (MG), ultrasound (US), and, if necessary, MRI. RTE was conducted after ultrasound. Lesions were assessed with BI-RADS for mammography and ultrasound. Diagnosis was established with histology or follow-up. Results. SI for BI-RADS 2 was 1.71 ± 0.86. Higher SI (2.21 ± 1.96) was observed for BI-RADS 3 lesions. SI of BI-RADS 4 and 5 lesions were significantly higher (16.92 ± 20.89) and (19.54 ± 10.41). 31 malignant tumors exhibited an average SI of 16.13 ± 14.67; SI of benign lesions was 5.29 ± 11.87 (P value <0.0001). ROC analysis threshold was >3.8 for malignant disease. Sensitivity of sonography was 90.3% (specificity 78.5%). RTE showed a sensitivity of 87.1% (specificity 79.7%). Accuracy of all modalities combined was 96.8%. In BI-RADS 3 lesions RTE was able to detect all malignant lesions (sensitivity 100%, specificity 92.9%, and accuracy 93.9%). Conclusions. RTE increased sensitivity and specificity for breast cancer detection when used in combination with ultrasound.

A clinical prediction model to identify patients at high risk of death in the emergency department.

PURPOSE Rapid assessment and intervention is important for the prognosis of acutely ill patients admitted to the emergency department (ED). The aim of this study was to prospectively develop and validate a model predicting the risk of in-hospital death based on all available information available at the time of ED admission and to compare its discriminative performance with a non-systematic risk estimate by the triaging first health-care provider. METHODS Prospective cohort analysis based on a multivariable logistic regression for the probability of death. RESULTS A total of 8,607 consecutive admissions of 7,680 patients admitted to the ED of a tertiary care hospital were analysed. Most frequent APACHE II diagnostic categories at the time of admission were neurological (2,052, 24 %), trauma (1,522, 18 %), infection categories [1,328, 15 %; including sepsis (357, 4.1 %), severe sepsis (249, 2.9 %), septic shock (27, 0.3 %)], cardiovascular (1,022, 12 %), gastrointestinal (848, 10 %) and respiratory (449, 5 %). The predictors of the final model were age, prolonged capillary refill time, blood pressure, mechanical ventilation, oxygen saturation index, Glasgow coma score and APACHE II diagnostic category. The model showed good discriminative ability, with an area under the receiver operating characteristic curve of 0.92 and good internal validity. The model performed significantly better than non-systematic triaging of the patient. CONCLUSIONS The use of the prediction model can facilitate the identification of ED patients with higher mortality risk. The model performs better than a non-systematic assessment and may facilitate more rapid identification and commencement of treatment of patients at risk of an unfavourable outcome.

A logarithmic efficient estimator of the probability of ruin with recuperation for spectrally negative Lévy risk processes

This article provides an importance sampling algorithm for computing the probability of ruin with recuperation of a spectrally negative Lévy risk process with light-tailed downwards jumps. Ruin with recuperation corresponds to the following double passage event: for some t∈(0,∞)t∈(0,∞), the risk process starting at level x∈[0,∞)x∈[0,∞) falls below the null level during the period [0,t][0,t] and returns above the null level at the end of the period tt. The proposed Monte Carlo estimator is logarithmic efficient, as t,x→∞t,x→∞, when y=t/xy=t/x is constant and below a certain bound.

The Initial Slope of the Variogram, Foundation of the Trabecular Bone Score, Is Not or Poorly Associated With Vertebral Strength

Trabecular bone score (TBS) rests on the textural analysis of DXA to reflect the decay in trabecular structure characterising osteoporosis. Yet, its discriminative power in fracture studies remains incomprehensible as prior biomechanical tests found no correlation with vertebral strength. To verify this result possibly due to an unrealistic set-up and to cover a wide range of loading scenarios, the data from three previous biomechanical studies using different experimental settings was used. They involved the compressive failure of 62 human lumbar vertebrae loaded 1) via intervertebral discs to mimic the in vivo situation (“full vertebra”), 2) via the classical endplate embedding (“vertebral body”) or 3) via a ball joint to induce anterior wedge failure (“vertebral section”). HR-pQCT scans acquired prior testing were used to simulate anterior-posterior DXA from which areal bone mineral density (aBMD) and the initial slope of the variogram (ISV), the early definition of TBS, were evaluated. Finally, the relation of aBMD and ISV with failure load (Fexp) and apparent failure stress (σexp) was assessed and their relative contribution to a multi-linear model was quantified via ANOVA. We found that, unlike aBMD, ISV did not significantly correlate with Fexp and σexp, except for the “vertebral body” case (r2 = 0.396, p = 0.028). Aside from the “vertebra section” set-up where it explained only 6.4% of σexp (p = 0.037), it brought no significant improvement to aBMD. These results indicate that ISV, a replica of TBS, is a poor surrogate for vertebral strength no matter the testing set-up, which supports the prior observations and raises a fortiori the question of the deterministic factors underlying the statistical relationship between TBS and vertebral fracture risk.

Saddlepoint Approximations to the Probability of Ruin in Finite Time for the Compound Poisson Risk Process Perturbed by Diffusion

A large deviations type approximation to the probability of ruin within a finite time for the compound Poisson risk process perturbed by diffusion is derived. This approximation is based on the saddlepoint method and generalizes the approximation for the non-perturbed risk process by Barndorff-Nielsen and Schmidli (Scand Actuar J 1995(2):169–186, 1995). An importance sampling approximation to this probability of ruin is also provided. Numerical illustrations assess the accuracy of the saddlepoint approximation using importance sampling as a benchmark. The relative deviations between saddlepoint approximation and importance sampling are very small, even for extremely small probabilities of ruin. The saddlepoint approximation is however substantially faster to compute.

Glucose-Induced Temporary Visual Recovery in Primary Open-Angle Glaucoma: A Double-Blind, Randomized Study

Purpose To investigate the effect of topical glucose on visual parameters in individuals with primary open-angle glaucoma (POAG). Design Double-blind, randomized, crossover study. Participants Nondiabetic pseudophakic patients with definite POAG were recruited; 29 eyes of 16 individuals participated in study 1. A follow-up study (study 2) included 14 eyes of 7 individuals. Intervention Eyes were randomly allocated to receive 50% glucose or saline eye drops every 5 minutes for 60 minutes. Main Outcome Measures The contrast sensitivity and best-corrected logarithm of the minimum angle of resolution (logMAR). Results The 50% glucose reached the vitreous in pseudophakic but not phakic individuals. Glucose significantly improved the mean contrast sensitivity at 12 cycles/degree compared with 0.9% saline by 0.26 log units (95% confidence interval [CI], 0.13–0.38; P < 0.001) and 0.40 log units (95% CI, 0.17–0.60; P < 0.001) in the follow-up study. The intraocular pressure, refraction, and central corneal thickness were not affected by glucose; age was not a significant predictor of the response. Conclusions Topical glucose temporarily improves psychophysical visual parameters in some individuals with POAG, suggesting that neuronal energy substrate delivery to the vitreous reservoir may recover function of “sick” retinal neurons.