Equitability revisited: why the “equitable threat score” is not equitable

In the forecasting of binary events, verification measures that are “equitable” were defined by Gandin and Murphy to satisfy two requirements: 1) they award all random forecasting systems, including those that always issue the same forecast, the same expected score (typically zero), and 2) they are expressible as the linear weighted sum of the elements of the contingency table, where the weights are independent of the entries in the table, apart from the base rate. The authors demonstrate that the widely used “equitable threat score” (ETS), as well as numerous others, satisfies neither of these requirements and only satisfies the first requirement in the limit of an infinite sample size. Such measures are referred to as “asymptotically equitable.” In the case of ETS, the expected score of a random forecasting system is always positive and only falls below 0.01 when the number of samples is greater than around 30. Two other asymptotically equitable measures are the odds ratio skill score and the symmetric extreme dependency score, which are more strongly inequitable than ETS, particularly for rare events; for example, when the base rate is 2% and the sample size is 1000, random but unbiased forecasting systems yield an expected score of around −0.5, reducing in magnitude to −0.01 or smaller only for sample sizes exceeding 25 000. This presents a problem since these nonlinear measures have other desirable properties, in particular being reliable indicators of skill for rare events (provided that the sample size is large enough). A potential way to reconcile these properties with equitability is to recognize that Gandin and Murphy’s two requirements are independent, and the second can be safely discarded without losing the key advantages of equitability that are embodied in the first. This enables inequitable and asymptotically equitable measures to be scaled to make them equitable, while retaining their nonlinearity and other properties such as being reliable indicators of skill for rare events. It also opens up the possibility of designing new equitable verification measures

Accounting for Calibration Uncertainties in X-ray Analysis: Effective Areas in Spectral Fitting

While considerable advance has been made to account for statistical uncertainties in astronomical analyses, systematic instrumental uncertainties have been generally ignored. This can be crucial to a proper interpretation of analysis results because instrumental calibration uncertainty is a form of systematic uncertainty. Ignoring it can underestimate error bars and introduce bias into the fitted values of model parameters. Accounting for such uncertainties currently requires extensive case-specific simulations if using existing analysis packages. Here we present general statistical methods that incorporate calibration uncertainties into spectral analysis of high-energy data. We first present a method based on multiple imputation that can be applied with any fitting method, but is necessarily approximate. We then describe a more exact Bayesian approach that works in conjunction with a Markov chain Monte Carlo based fitting. We explore methods for improving computational efficiency, and in particular detail a method of summarizing calibration uncertainties with a principal component analysis of samples of plausible calibration files. This method is implemented using recently codified Chandra effective area uncertainties for low-resolution spectral analysis and is verified using both simulated and actual Chandra data. Our procedure for incorporating effective area uncertainty is easily generalized to other types of calibration uncertainties.Comment: 61 pages double spaced, 8 figures, accepted for publication in Ap

Study protocol: a randomised controlled trial investigating the effect of exercise training on peripheral blood gene expression in patients with stable angina

Background: Exercise training has been shown to reduce angina and promote collateral vessel development in patients with coronary artery disease. However, the mechanism whereby exercise exerts these beneficial effects is unclear. There has been increasing interest in the use of whole genome peripheral blood gene expression in a wide range of conditions to attempt to identify both novel mechanisms of disease and transcriptional biomarkers. This protocol describes a study in which we will assess the effect of a structured exercise programme on peripheral blood gene expression in patients with stable angina, and correlate this with changes in angina level, anxiety, depression, and exercise capacity. Methods/Design: Sixty patients with stable angina will be recruited and randomised 1: 1 to exercise training or conventional care. Patients randomised to exercise training will attend an exercise physiology laboratory up to three times weekly for supervised aerobic interval training sessions of one hour in total duration. Patients will undergo assessments of angina, anxiety, depression, and peripheral blood gene expression at baseline, after six and twelve weeks of training, and twelve weeks after formal exercise training ceases. Discussion: This study will provide comprehensive data on the effect of exercise training on peripheral blood gene expression in patients with angina. By correlating this with improvement in angina status we will identify candidate peripheral blood transcriptional markers predictive of improvements in angina level in response to exercise training

Influence of individuals’ determinants including vaccine type on cellular and humoral responses to SARS-CoV-2 vaccination

Vaccine development targeting SARS-CoV-2 in 2020 was of critical importance in reducing COVID-19 severity and mortality. In the U.K. during the initial roll-out most individuals either received two doses of Pfizer COVID-19 vaccine (BNT162b2) or the adenovirus-based vaccine from Oxford/AstraZeneca (ChAdOx1-nCoV-19). There are conflicting data as to the impact of age, sex and body habitus on cellular and humoral responses to vaccination, and most studies in this area have focused on determinants of mRNA vaccine immunogenicity. Here, we studied a cohort of participants in a population-based longitudinal study (COVIDENCE UK) to determine the influence of age, sex, body mass index (BMI) and pre-vaccination anti-Spike (anti-S) antibody status on vaccine-induced humoral and cellular immune responses to two doses of BNT162b2 or ChAdOx-n-CoV-19 vaccination. Younger age and pre-vaccination anti-S seropositivity were both associated with stronger antibody responses to vaccination. BNT162b2 generated higher neutralising and anti-S antibody titres to vaccination than ChAdOx1-nCoV-19, but cellular responses to the two vaccines were no different. Irrespective of vaccine type, increasing age was also associated with decreased frequency of cytokine double-positive CD4+T cells. Increasing BMI was associated with reduced frequency of SARS-CoV-2-specific TNF+CD8% T cells for both vaccines. Together, our findings demonstrate that increasing age and BMI are associated with attenuated cellular and humoral responses to SARS-CoV-2 vaccination. Whilst both vaccines induced T cell responses, BNT162b2 induced significantly elevated humoral immune response as compared to ChAdOx-n-CoV-19

Vitamin D Supplementation to Prevent Acute Respiratory Tract Infections: Systematic Review and Meta-Analysis Of Individual Participant Data

OBJECTIVES To assess the overall effect of vitamin D supplementation on risk of acute respiratory tract infection, and to identify factors modifying this effect. DESIGN Systematic review and meta-analysis of individual participant data (IPD) from randomised controlled trials. DATA SOURCES Medline, Embase, the Cochrane Central Register of Controlled Trials, Web of Science, ClinicalTrials.gov, and the International Standard Randomised Controlled Trials Number registry from inception to December 2015. ELIGIBILITY CRITERIA FOR STUDY SELECTION Randomised, double blind, placebo controlled trials of supplementation with vitamin D3 or vitamin D2 of any duration were eligible for inclusion if they had been approved by a research ethics committee and if data on incidence of acute respiratory tract infection were collected prospectively and prespecified as an efficacy outcome. RESULTS 25 eligible randomised controlled trials (total 11 321 participants, aged 0 to 95 years) were identified. IPD were obtained for 10 933 (96.6%) participants. Vitamin D supplementation reduced the risk of acute respiratory tract infection among all participants (adjusted odds ratio 0.88, 95% confidence interval 0.81 to 0.96; P for heterogeneity \u3c0.001). In subgroup analysis, protective effects were seen in those receiving daily or weekly vitamin D without additional bolus doses (adjusted odds ratio 0.81, 0.72 to 0.91) but not in those receiving one or more bolus doses (adjusted odds ratio 0.97, 0.86 to 1.10; P for interaction=0.05). Among those receiving daily or weekly vitamin D, protective effects were stronger in those with baseline 25-hydroxyvitamin D levels \u3c25 nmol/L (adjusted odds ratio 0.30, 0.17 to 0.53) than in those with baseline 25-hydroxyvitamin D levels ≥25 nmol/L (adjusted odds ratio 0.75, 0.60 to 0.95; P for interaction=0.006). Vitamin D did not influence the proportion of participants experiencing at least one serious adverse event (adjusted odds ratio 0.98, 0.80 to 1.20, P=0.83). The body of evidence contributing to these analyses was assessed as being of high quality. CONCLUSIONS Vitamin D supplementation was safe and it protected against acute respiratory tract infection overall. Patients who were very vitamin D deficient and those not receiving bolus doses experienced the most benefit

High prevalence of vitamin D deficiency among women of child-bearing age in Lahore Pakistan, associating with lack of sun exposure and illiteracy

BACKGROUND: Vitamin D status is a key determinant of maternal and neonatal health. Deficiency has been reported to be common in Pakistani women, but information regarding environmental and genetic determinants of vitamin D status is lacking in this population. METHODS: We conducted a cross-sectional study among three groups of healthy women living in Lahore, Pakistan: university students, students or employees of Medrasas or Islamic Institutes, and employees working in office, hospital or domestic settings. Multivariate analysis was performed to identify environmental and genetic determinants of vitamin D status: polymorphisms in genes encoding the vitamin D receptor, vitamin D 25-hydroxylase enzyme CYP2R1 and vitamin D binding protein [DBP] were investigated. We also conducted analyses to identify determinants of body ache and bone pain in this population, and to determine the sensitivity and specificity of testing for hypocalcaemia and raised serum alkaline phosphatase to screen for vitamin D deficiency. RESULTS: Of 215 participants, 156 (73 %) were vitamin D deficient (serum 25[OH]D <50 nmol/L). Risk of vitamin D deficiency was independently associated with illiteracy (adjusted OR 4.0, 95 % CI 1.03–15.52, P = 0.04), <30 min sun exposure per day (adjusted OR 2.13, 95 % CI 1.08–4.19, P = 0.02), sampling in January to March (adjusted OR 2.38, 95 % CI 1.20–4.70), P = 0.01) and lack of regular intake of multivitamins (adjusted OR 2.61, 95 % CI 1.32–5.16, p = 0.005). Participants with the GG genotype of the rs4588 polymorphism in the gene encoding vitamin D binding protein tended to have lower 25(OH)D concentrations than those with GT/TT genotypes (95 % CI for difference 22.7 to −0.13 nmol/L, P = 0.053). Vitamin D deficiency was independently associated with increased risk of body ache or bone pain (adjusted OR 4.43, 95 % CI 2.07 to 9.49, P = 0.001). Hypocalcaemia (serum calcium concentration ≤9.5 mg/dL) and raised alkaline phosphatase concentration (≥280 IU/L) had low sensitivity and very low specificity for identification of vitamin D deficiency. CONCLUSION: Vitamin D deficiency is common among healthy women of child-bearing age in Lahore, Pakistan: illiteracy, decreased sun exposure and lack of multivitamin intake are risk factors

Prevalence and Determinants of Vitamin D Deficiency in 1825 Cape Town Primary Schoolchildren: A Cross-Sectional Study

Vitamin D deficiency (25-hydroxyvitamin D[25(OH)D] &lt;50 nmol/L) is common among adults in Cape Town, South Africa, but studies investigating vitamin D status of children in this setting are lacking. We conducted a cross-sectional study to determine the prevalence and determinants of vitamin D deficiency in 1825 Cape Town schoolchildren aged 6&ndash;11 years. Prevalence of vitamin D deficiency was 7.6% (95% Confidence Interval [CI] 6.5% to 8.9%). Determinants of vitamin D deficiency included month of sampling (adjusted odds ratio [aOR] for July&ndash;September vs. January&ndash;March 10.69, 95% CI 5.02 to 22.77; aOR for October&ndash;December vs. January&ndash;March 6.73, 95% CI 2.82 to 16.08), older age (aOR 1.25 per increasing year, 95% CI: 1.01&ndash;1.53) and higher body mass index (BMI; aOR 1.24 per unit increase in BMI-for-age Z-score, 95% CI: 1.03&ndash;1.49). In a subset of 370 participants in whom parathyroid hormone (PTH) concentrations were measured; these were inversely related to serum 25(OH)D concentrations (p &lt; 0.001). However, no association between participants with hyperparathyroidism (PTH &gt;6.9 pmol/L) and vitamin D deficiency was seen (p = 0.42). In conclusion, we report that season is the major determinant of vitamin D status among Cape Town primary schoolchildren, with prevalence of vitamin D deficiency ranging from 1.4% in January&ndash;March to 22.8% in July&ndash;September

Effect of a test-and-treat approach to vitamin D supplementation on risk of all cause acute respiratory tract infection and covid-19:phase 3 randomised controlled trial (CORONAVIT)

OBJECTIVE: To determine the effect of population level implementation of a test-and-treat approach to correction of suboptimal vitamin D status (25-hydroxyvitamin D (25(OH)D) <75 nmol/L) on risk of all cause acute respiratory tract infection and covid 19. DESIGN: Phase 3 open label randomised controlled trial. SETTING: United Kingdom. PARTICIPANTS: 6200 people aged ≥16 years who were not taking vitamin D supplements at baseline. INTERVENTIONS: Offer of a postal finger prick test of blood 25(OH)D concentration with provision of a six month supply of lower dose vitamin D (800 IU/day, n=1550) or higher dose vitamin D (3200 IU/day, n=1550) to those with blood 25(OH)D concentration <75 nmol/L, compared with no offer of testing or supplementation (n=3100). Follow-up was for six months. MAIN OUTCOME MEASURES: The primary outcome was the proportion of participants with at least one swab test or doctor confirmed acute respiratory tract infection of any cause. A secondary outcome was the proportion of participants with swab test confirmed covid-19. Logistic regression was used to calculate odds ratios and associated 95% confidence intervals. The primary analysis was conducted by intention to treat. RESULTS: Of 3100 participants offered a vitamin D test, 2958 (95.4%) accepted and 2674 (86.3%) had 25(OH)D concentrations <75 nmol/L and received vitamin D supplements (n=1328 lower dose, n=1346 higher dose). Compared with 136/2949 (4.6%) participants in the no offer group, at least one acute respiratory tract infection of any cause occurred in 87/1515 (5.7%) in the lower dose group (odds ratio 1.26, 95% confidence interval 0.96 to 1.66) and 76/1515 (5.0%) in the higher dose group (1.09, 0.82 to 1.46). Compared with 78/2949 (2.6%) participants in the no offer group, 55/1515 (3.6%) developed covid-19 in the lower dose group (1.39, 0.98 to 1.97) and 45/1515 (3.0%) in the higher dose group (1.13, 0.78 to 1.63). CONCLUSIONS: Among people aged 16 years and older with a high baseline prevalence of suboptimal vitamin D status, implementation of a population level test-and-treat approach to vitamin D supplementation was not associated with a reduction in risk of all cause acute respiratory tract infection or covid-19. TRIAL REGISTRATION: ClinicalTrials.gov NCT04579640