Estimating the mean and variance from the median, range, and the size of a sample

BACKGROUND: Usually the researchers performing meta-analysis of continuous outcomes from clinical trials need their mean value and the variance (or standard deviation) in order to pool data. However, sometimes the published reports of clinical trials only report the median, range and the size of the trial. METHODS: In this article we use simple and elementary inequalities and approximations in order to estimate the mean and the variance for such trials. Our estimation is distribution-free, i.e., it makes no assumption on the distribution of the underlying data. RESULTS: We found two simple formulas that estimate the mean using the values of the median (m), low and high end of the range (a and b, respectively), and n (the sample size). Using simulations, we show that median can be used to estimate mean when the sample size is larger than 25. For smaller samples our new formula, devised in this paper, should be used. We also estimated the variance of an unknown sample using the median, low and high end of the range, and the sample size. Our estimate is performing as the best estimate in our simulations for very small samples (n ≤ 15). For moderately sized samples (15 <n ≤ 70), our simulations show that the formula range/4 is the best estimator for the standard deviation (variance). For large samples (n > 70), the formula range/6 gives the best estimator for the standard deviation (variance). We also include an illustrative example of the potential value of our method using reports from the Cochrane review on the role of erythropoietin in anemia due to malignancy. CONCLUSION: Using these formulas, we hope to help meta-analysts use clinical trials in their analysis even when not all of the information is available and/or reported

Effects of long-term low-dose oxygen supplementation on the epithelial function, collagen metabolism and interstitial fibrogenesis in the guinea pig lung

<p>Abstract</p> <p>Background</p> <p>The patient population receiving long-term oxygen therapy has increased with the rising morbidity of COPD. Although high-dose oxygen induces pulmonary edema and interstitial fibrosis, potential lung injury caused by long-term exposure to low-dose oxygen has not been fully analyzed. This study was designed to clarify the effects of long-term low-dose oxygen inhalation on pulmonary epithelial function, edema formation, collagen metabolism, and alveolar fibrosis.</p> <p>Methods</p> <p>Guinea pigs (n = 159) were exposed to either 21% or 40% oxygen for a maximum of 16 weeks, and to 90% oxygen for a maximum of 120 hours. Clearance of inhaled technetium-labeled diethylene triamine pentaacetate (Tc-DTPA) and bronchoalveolar lavage fluid-to-serum ratio (BAL/Serum) of albumin (ALB) were used as markers of epithelial permeability. Lung wet-to-dry weight ratio (W/D) was measured to evaluate pulmonary edema, and types I and III collagenolytic activities and hydroxyproline content in the lung were analyzed as indices of collagen metabolism. Pulmonary fibrotic state was evaluated by histological quantification of fibrous tissue area stained with aniline blue.</p> <p>Results</p> <p>The clearance of Tc-DTPA was higher with 2 week exposure to 40% oxygen, while BAL/Serum Alb and W/D did not differ between the 40% and 21% groups. In the 40% oxygen group, type I collagenolytic activities at 2 and 4 weeks and type III collagenolytic activity at 2 weeks were increased. Hydroxyproline and fibrous tissue area were also increased at 2 weeks. No discernible injury was histologically observed in the 40% group, while progressive alveolar damage was observed in the 90% group.</p> <p>Conclusion</p> <p>These results indicate that epithelial function is damaged, collagen metabolism is affected, and both breakdown of collagen fibrils and fibrogenesis are transiently induced even with low-dose 40% oxygen exposure. However, these changes are successfully compensated even with continuous exposure to low-dose oxygen. We conclude that long-term low-dose oxygen exposure does not significantly induce permanent lung injury in guinea pigs.</p

Optimising the glaucoma signal/noise ratio by mapping changes in spatial summation with area-modulated perimetric stimuli

Identification of glaucomatous damage and progression by perimetry are limited by measurement and response variability. This study tested the hypothesis that the glaucoma damage signal/noise ratio is greater with stimuli varying in area, either solely, or simultaneously with contrast, than with conventional stimuli varying in contrast only (Goldmann III, GIII). Thirty glaucoma patients and 20 age-similar healthy controls were tested with the Method of Constant Stimuli (MOCS). One stimulus modulated in area (A), one modulated in contrast within Ricco's area (C R ), one modulated in both area and contrast simultaneously (AC), and the reference stimulus was a GIII, modulating in contrast. Stimuli were presented on a common platform with a common scale (energy). A three-stage protocol minimised artefactual MOCS slope bias that can occur due to differences in psychometric function sampling between conditions. Threshold difference from age-matched normal (total deviation), response variability, and signal/noise ratio were compared between stimuli. Total deviation was greater with, and response variability less dependent on defect depth with A, AC, and C R stimuli, compared with GIII. Both A and AC stimuli showed a significantly greater signal/noise ratio than the GIII, indicating that area-modulated stimuli offer benefits over the GIII for identifying early glaucoma and measuring progression

Predominant constitutive CFTR conductance in small airways

BACKGROUND: The pathological hallmarks of chronic obstructive pulmonary disease (COPD) are inflammation of the small airways (bronchiolitis) and destruction of lung parenchyma (emphysema). These forms of disease arise from chronic prolonged infections, which are usually never present in the normal lung. Despite the fact that primary hygiene and defense of the airways presumably requires a well controlled fluid environment on the surface of the bronchiolar airway, very little is known of the fluid and electrolyte transport properties of airways of less than a few mm diameter. METHODS: We introduce a novel approach to examine some of these properties in a preparation of minimally traumatized porcine bronchioles of about 1 mm diameter by microperfusing the intact bronchiole. RESULTS: In bilateral isotonic NaCl Ringer solutions, the spontaneous transepithelial potential (TEP; lumen to bath) of the bronchiole was small (mean ± sem: -3 ± 1 mV; n = 25), but when gluconate replaced luminal Cl(-), the bionic Cl(- )diffusion potentials (-58 ± 3 mV; n = 25) were as large as -90 mV. TEP diffusion potentials from 2:1 NaCl dilution showed that epithelial Cl(- )permeability was at least 5 times greater than Na(+ )permeability. The anion selectivity sequence was similar to that of CFTR. The bionic TEP became more electronegative with stimulation by luminal forskolin (5 μM)+IBMX (100 μM), ATP (100 μM), or adenosine (100 μM), but not by ionomycin. The TEP was partially inhibited by NPPB (100 μM), GlyH-101* (5–50 μM), and CFTR(Inh)-172* (5 μM). RT-PCR gave identifying products for CFTR, α-, β-, and γ-ENaC and NKCC1. Antibodies to CFTR localized specifically to the epithelial cells lining the lumen of the small airways. CONCLUSION: These results indicate that the small airway of the pig is characterized by a constitutively active Cl(- )conductance that is most likely due to CFTR

Osteological and Soft-Tissue Evidence for Pneumatization in the Cervical Column of the Ostrich (Struthio camelus) and Observations on the Vertebral Columns of Non-Volant, Semi-Volant and Semi-Aquatic Birds

© 2015 Apostolaki et al. This is an open access article distributed under the terms of the Creative Commons Attribution License [4.0], which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. The attached file is the published version of the article

An evaluation of gender equity in different models of primary care practices in Ontario

Background: The World Health Organization calls for more work evaluating the effect of health care reforms on gender equity in developed countries. We performed this evaluation in Ontario, Canada where primary care models resulting from reforms co-exist. // Methods: This cross sectional study of primary care practices uses data collected in 2005-2006. Healthcare service models included in the study consist of fee for service (FFS) based, salaried, and capitation based. We compared the quality of care delivered to women and men in practices of each model. We performed multi-level, multivariate regressions adjusting for patient socio-demographic and economic factors to evaluate vertical equity, and adjusting for these and health factors in evaluating horizontal equity. We measured seven dimensions of health service delivery (e.g. accessibility and continuity) and three dimensions of quality of care using patient surveys (n = 5,361) and chart abstractions (n = 4,108). // Results: Health service delivery measures were comparable in women and men, with differences ≤ 2.2% in all seven dimensions and in all models. Significant gender differences in the health promotion subjects addressed were observed. Female specific preventive manoeuvres were more likely to be performed than other preventive care. Men attending FFS practices were more likely to receive influenza immunization than women (Adjusted odds ratio: 1.75, 95% confidence intervals (CI) 1.05, 2.92). There was no difference in the other three prevention indicators. FFS practices were also more likely to provide recommended care for chronic diseases to men than women (Adjusted difference of -11.2%, CI -21.7, -0.8). A similar trend was observed in Community Health Centers (CHC). // Conclusions: The observed differences in the type of health promotion subjects discussed are likely an appropriate response to the differential healthcare needs between genders. Chronic disease care is non equitable in FFS but not in capitation based models. We recommend that efforts to monitor and address gender based differences in the delivery of chronic disease management in primary care be pursued.Funding for the original study on which this research is based was provided by the Ontario Ministry of Health and Long Term Care Primary Health Care Transition Fund. The views expressed in this report are the views of the authors and do not necessarily reflect those of the Ontario Ministry of Health and Long Term Care