Denominator Values Research Articles

Industry Payments to Orthopaedic Surgeons: A Geospatial Analysis of the Open Payments Database.

There has been an increasing demand for transparency between industry and physicians. Several studies have evaluated the distribution of payment value and types to orthopaedic surgeons, but little is known about the spending patterns from an industry-centric perspective. The purpose of this study was to describe the payment patterns of top medical device companies in orthopaedics while presenting a geospatial analysis of these trends. The Open Payments database was assessed for all records of industry financial relationships with orthopaedic surgeons from 2015 to 2021. Value of financial relationships was expressed on a per orthopaedic surgeon basis, with the numerator representing total value of payments and denominator representing number of orthopaedic surgeons, and was geographically analyzed according to United States Census Divisions. Based on averages during the study period, the top 10 paying companies were (1) DePuy, (2) Zimmer Biomet, (3) Stryker Corporation, (4) Arthrex, (5) SpineFrontier, (6) Medtronic, (7) Smith and Nephew, (8) Renovis Surgical Technologies, (9) NuVasive, and (10) Paragon 28. Payments in the South Atlantic ($6,854 ± $1,265) Division were significantly greater than all other eight divisions (P < 0.001), with the next leading division being the Pacific Division ($4,114 ± $643). Five companies strongly favored one particular division, directing more than double the amount of payments to this division compared with the next leading division (SpineFrontier, 99% South Atlantic; Renovis Surgical Technologies, 81% Pacific; Paragon 28, 59% South Atlantic; NuVasive, 43% West North Central; DePuy, 35% South Atlantic). Only 3 of 10 companies were headquartered in the same division where most payments were made. From 2015 to 2021, companies preferentially supported surgeons in certain geographic regions, irrespective of where they were headquartered in. Surgeons in the South Atlantic Division received significantly more payments than any other division by a wide margin.

Validating the capture rate of revisions by the New Zealand ACL Registry: An analysis of all-cause reoperation following primary ACL reconstruction.

To validate the New Zealand Anterior Cruciate Ligament(ACL) Registry's capture rate of revisions by cross-referencing Registry data with reoperations data recorded by the Accident Compensation Corporation (ACC) and identify risk factors for all-cause reoperation. Primary ACL reconstructions performed between April 2014 and September 2019 were individually matched on a record-by-record basis between the two databases. The ACC database was used to identify patients who underwent a reoperation with manual review of operation notes to identify whether a revision or other procedure was performed. This was combined with the number of revisions separately recorded in the New Zealand ACL Registry, which was used as the denominator value to calculate the Registry's capture rate of revisions. Patient and surgical data recorded in the Registry were analysed to identify independent predictors for all-cause reoperation. A total of 8046 primary ACL reconstructions were matched between the New Zealand ACL Registry and the ACC databases. The reoperation rate was 8.9% (n = 715) at a mean follow-up of 2.5 years. Meniscal-related procedures were the most common reoperation (n = 299, 3.7%), followed by revision ACL reconstruction (n = 219, 2.7%), arthrofibrosis (n = 185, 2.3%), cartilage (n = 56, 0.7%)and implants (n = 32, 0.4%). The New Zealand ACL Registry captured 96% of revisions. Younger age (hazard ratio [HR] > 1.4, p < 0.001), earlier surgery (HR > 1.3, p = 0.05), concurrent meniscal repair (medial meniscus HR = 1.9, p < 0.001 and lateral meniscus HR = 1.3, p = 0.022)and hamstring tendon autografts (HR = 1.4, p = 0.001) were associated with a higher risk of reoperation. The New Zealand ACL Registry captured 96% of revisions. Risk factors for all-cause reoperation included younger age, earlier surgery, meniscal repairand hamstring tendon autografts. Level III.

Smallest denominators

AbstractWe establish higher dimensional versions of a recent theorem by Chen and Haynes [Int. J. Number Theory 19 (2023), 1405–1413] on the expected value of the smallest denominator of rational points in a randomly shifted interval of small length, and of the closely related 1977 Kruyswijk–Meijer conjecture recently proved by Balazard and Martin [Bull. Sci. Math. 187 (2023), Paper No. 103305]. We express the distribution of smallest denominators in terms of the void statistics of multidimensional Farey fractions and prove convergence of the distribution function and certain finite moments. The latter was previously unknown even in the one‐dimensional setting. We furthermore obtain a higher dimensional extension of Kargaev and Zhigljavsky's work on moments of the distance function for the Farey sequence [J. Number Theory 65 (1997), 130–149] as well as new results on pigeonhole statistics.

Démonstration d'une conjecture de Kruyswijk et Meijer sur le plus petit dénominateur des nombres rationnels d'un intervalle

The average value of the smallest denominator of a rational number belonging to the interval ](j−1)/N,j/N], where j=1,…,N, is proved to be asymptotically equivalent to 16π−2N, when N tends to infinity. The result had been conjectured in 1977 by Kruyswijk and Meijer.

Expected value of the smallest denominator in a random interval of fixed radius

We compute the probability mass function of the random variable which returns the smallest denominator of a reduced fraction in a randomly chosen real interval of radius [Formula: see text]. As an application, we prove that the expected value of the smallest denominator is asymptotic, as [Formula: see text], to [Formula: see text]

Recommendations for reporting measures of diagnostic accuracy.

This article serves as the third in a series that offers recommendations for optimal data reporting, specifically focusing on the statistical methods most frequently reported in Cytopathology articles. Measures of diagnostic accuracy were among the most commonly reported results in Cytopathology, with sensitivity and/or specificity reported in 32% of the reviewed articles. This article will provide a brief overview of common measures of diagnostic accuracy, including sensitivity, specificity, positive and negative predictive values, positive and negative likelihood ratios, overall diagnostic accuracy, receiver operating characteristic (ROC) curve, and area under the curve (AUC). Reporting recommendations for these measures will be reviewed, including the suggestion of providing a 2 × 2 contingency table when possible, or numerator and denominator values for calculations when all values needed for a contingency table are not known, and calculation of ROC and AUC if relevant. Additionally, paired measures should be reported, including sensitivity with specificity, positive with negative predictive values, and positive with negative likelihood ratios. Calculating 95% confidence intervals (CI) for the measures is recommended, with several methods to choose from, including the Wald interval, Wilson interval, Clopper-Pearson interval, Agresti-Coull interval, and Bayesian highest posterior density (HPD) interval. Since there are various methods for CI calculations, the author encourages the reader to consult with a trained statistician to identify the most appropriate method based on the data, which should be reported in the methods section of the resulting write-up.

Bivariate Barycentric and Newton Rational Interpolation Over Rectangular Grids

In this paper, we consider the problem of computing bivariate barycentric and Newton rational interpolation over rectangular grids. Given a set of rectangular grids, under the conditions that the degrees of the numerator and denominator of rational interpolant are prescribed, we provide a matrix method for calculating barycentric weight vector and denominator value vector, which, respectively, induce barycentric and Newton representations of rational interpolants. We aim at constructing the rational interpolants that globally approximate interpolated function. Numerical examples compare the maximum errors of barycentric rational interpolant, Newton rational interpolant, linear interpolant, cubic interpolant and spline interpolant. Numerical results show the higher accuracy of barycentric and Newton rational interpolation.

Development of the Korean Standardized Antimicrobial Administration Ratio as a Tool for Benchmarking Antimicrobial Use in Each Hospital.

BackgroundThe Korea National Antimicrobial Use Analysis System (KONAS), a benchmarking system for antimicrobial use in hospitals, provides Korean Standardized Antimicrobial Administration Ratio (K-SAAR) for benchmarking. This article describes K-SAAR predictive models to enhance the understanding of K-SAAR, an important benchmarking strategy for antimicrobial usage in KONAS.MethodsWe obtained medical insurance claims data for all hospitalized patients aged ≥ 28 days in all secondary and tertiary care hospitals in South Korea (n = 347) from January 2019 to December 2019 from the Health Insurance Review & Assessment Service. Modeling was performed to derive a prediction value for antimicrobial use in each institution, which corresponded to the denominator value for calculating K-SAAR. The prediction values of antimicrobial use were modeled separately for each category, for all inpatients and adult patients (aged ≥ 15 years), using stepwise negative binomial regression.ResultsThe final models for each antimicrobial category were adjusted for different significant risk factors. In the K-SAAR models of all aged patients as well as adult patients, most antimicrobial categories included the number of hospital beds and the number of operations as significant factors, while some antimicrobial categories included mean age for inpatients, hospital type, and the number of patients transferred from other hospitals as significant factors.ConclusionWe developed a model to predict antimicrobial use rates in Korean hospitals, and the model was used as the denominator of the K-SAAR.

Elective abdominal wall hernia repair surgical mortality-A systematic review of the literature and peer review of mortality in Australia.

This study systematically reviewed the literature regarding perioperative mortality in human adults undergoing elective surgical abdominal wall hernia repair, including an audit of the Royal Australasian College of Surgeons (RACS) Australian and New Zealand Audit of Surgical Mortality (ANZASM) database. A systematic review was conducted in accordance with PRISMA guidelines for the reporting of systematic reviews and meta-analysis of observational studies. Cochrane Library, PubMed, MEDLINE and Embase database searches and data extraction were conducted from June 1979 to October 2019. Statistical analysis was undertaken utilising denominator values for elective hernia procedures derived from the Australian Institute of Health and Welfare (AIHW) data. Risk-adjusted perioperative mortality rates for the relevant procedures were also produced, using a binary logistic regression for the risk adjustment. Through systematic review of the literature, it was established that the overall reported perioperative mortality in human adults undergoing elective surgical abdominal wall hernia repair was low (0.1%-0.5%). Using ANZASM and AIHW data, the calculated risk-adjusted mortality rate for Australian patients was found to be significantly lower (0.04%-0.06%, p< 0.001). The risk-adjusted mortality rate for elective abdominal wall hernia surgery in Australia is very low and compares favourably to international cohorts. Despite low absolute numbers, the factors which were most significantly associated with increased perioperative mortality in patients undergoing elective surgical abdominal wall hernia repair were increased age, cardiorespiratory co-morbidity and incisional hernia repair.

Conversion to binary number system of some types of ordinary fractions

The article describes a technique developed by the author for converting a number of ordinary fractions into a binary number system without intermediate conversion to decimal. The technique is generally applicable to two types of fractions: the denominator of which is 2n – 1 or 2n + 1, where n is a natural number, and also for denominator values 2, 4, 8, ... times greater than the indicated values. For fractions with a denominator of the form 2n + 1 and numerators equal to powers of two, an original technique is implemented during translation, which consists in using a conditional negative digit 1 (its designation: 1). The analysis showed that the developed method is more effective than the traditional one. A large number of examples are given and assignments for independent work of students are proposed.

Estimating malaria chemoprevention and vector control coverage using program and campaign data: A scoping review of current practices and opportunities.

BackgroundAccurate estimation of intervention coverage is a vital component of malaria program monitoring and evaluation, both for process evaluation (how well program targets are achieved), and impact evaluation (whether intervention coverage had an impact on malaria burden). There is growing interest in maximizing the utility of program data to generate interim estimates of intervention coverage in the periods between large-scale cross-sectional surveys (the gold standard). As such, this study aimed to identify relevant concepts and themes that may guide future optimization of intervention coverage estimation using routinely collected data, or data collected during and following intervention campaigns, with a particular focus on strategies to define the denominator.MethodsWe conducted a scoping review of current practices to estimate malaria intervention coverage for insecticide-treated nets (ITNs); indoor residual spray (IRS); intermittent preventive treatment in pregnancy (IPTp); mass drug administration (MDA); and seasonal malaria chemoprevention (SMC) interventions; case management was excluded. Multiple databases were searched for relevant articles published from January 1, 2015 to June 1, 2018. Additionally, we identified and included other guidance relevant to estimating population denominators, with a focus on innovative techniques.ResultsWhile program data have the potential to provide intervention coverage data, there are still substantial challenges in selecting appropriate denominators. The review identified a lack of consistency in how coverage was defined and reported for each intervention type, with denominator estimation methods not clearly or consistently reported, and denominator estimates rarely triangulated with other data sources to present the feasible range of denominator values and consequently the range of likely coverage estimates.ConclusionsThough household survey-based estimates of intervention coverage remain the gold standard, efforts should be made to further standardize practices for generating interim measurements of intervention coverage from program data, and for estimating and reporting population denominators. This includes fully describing any projections or adjustments made to existing census or population data, exploring opportunities to validate available data by comparing with other sources, and explaining how the denominator has been restricted (or not) to reflect exclusion criteria.

Completeness and capture rate of publicly funded arthroplasty procedures in the New Zealand Joint Registry.

Registry-based studies have become more common due to the availability of a large study cohort. However, the validity of findings is dependent on the completeness of the registry. This study aimed to validate the capture rate of the New Zealand Joint Registry (NZJR) by matching procedures that have been recorded separately via clinical coding by the New Zealand Government's National Surgical Site Infection Improvement Programme (SSIIP). The National Health Index, a unique identification code for all patients, was combined with the arthroplasty procedure performed (primary total knee arthroplasty (TKA), primary total hip arthroplasty (THA), revision TKA or revision THA) and operation side. Publicly funded procedures recorded in the NZJR were matched with procedures recorded by the SSIIP on a record-by-record basis. This identified the total number of arthroplasty procedures performed in New Zealand, which was used as the denominator value to calculate the procedure capture rate of the NZJR. Between 2013 and 2018, 24 556 primary TKA, 28 970 primary THA, 2107 revision TKA and 4263 revision THA procedures were recorded by both datasets. The NZJR recorded 95.5% of primary TKA procedures, 96.3% of primary THA procedures, 97.1% of revision TKA procedures and 95.2% of revision THA procedures. The NZJR recorded >95% of publicly funded arthroplasty procedures. In contrast, there were inaccuracies in clinical coding by hospitals, particularly with revision procedures, demonstrating the benefits of an arthroplasty registry. However, data recorded by an infection surveillance programme may supplement arthroplasty registry data to strengthen the quality of research.

Prevalence and incidence of diagnosed hypertension in Alberta, Canada

IntroductionThe prevalence of diagnosed hypertension in Canada is projected to increase despite the incidence rate decreasing. Previous work around the world has utilized survey data to provide estimates of prevalence and incidence. Administrative data is population-level, and may provide more reliable estimates of provincial prevalence and incidence than could be achieved using survey data. &#x0D; Objectives and Approach&#x0D; &#x0D; To produce age and sex-specific prevalence and incidence estimates of diagnosed hypertension in Alberta from 2007 to 2015,&#x0D; To project estimates to the fiscal year of 2019/2020.&#x0D; &#x0D; Data from the Discharge Abstract Database, physician claims database, National Ambulatory Care Reporting System, and provincial health insurance registry will be linked using unique anonymous personal identifier and gender. A validated case definition of diagnosed hypertension for use in administrative datasets will be used to identify annual prevalent and incident cases from claims data. Obstetric cases will be excluded. The provincial health insurance registry will be used to estimate denominator values.&#x0D; ResultsResults of this analysis are not available for the time of abstract submission as the timeline for this analysis projects completion in April 2018.&#x0D; Conclusion/ImplicationsMaintained surveillance of diagnosed hypertension is important to inform health policy and spending decisions, to monitor efficacy of public health interventions, and to inform patient care. Furthermore, diagnosis guidelines have been updated since 2017. Providing estimates for the prevalence of diagnosed hypertension in Alberta five years into the future to compare to actual prevalence estimates may indicate whether changes in prevalence are due to actual changes in health status or to changes in diagnosis guidelines.

Chronic Disease Prevalence. A perspective using Administrative Data from Australia

BackgroundPharmaceutical administrative data can provide an alternative method to assess chronic disease prevalence. The data within prescription exchanges includes the specific nature of the medication dispensed which can be utilised for case definition by proxy of certain chronic diseases.&#x0D; ObjectivesThis study examines the potential of Australian administrative pharmaceutical data to define chronic disease and provide population prevalence estimates. The utility of allocated World Health Organization Anatomical Therapeutic Chemical (ATC) codes to the treatment supplied will be assessed and the validity of the results generated compared with other Australian sources of chronic disease prevalence.&#x0D; Methods23 chronic conditions were defined by ATC codes within an Australian (administrative) Pharmaceutical Benefits Scheme (PBS) dataset. This enabled calculation of chronic disease prevalences for the period 2003 to 2014 using Australian census data as denominator values.&#x0D; FindingsPrevalence estimates from PBS data when compared with questionnaire based studies demonstrated homogeneity overall (Mann-Whitney P&gt;0.05). PBS prevalence estimates of diabetes, gout and asthma showed respective correlations of 0.999, 0.8385 and 0.58 to 0.82 with community surveys. In general, the prevalence of most chronic conditions rose. Cardiovascular disorders, iron deficiency treatment, HIV and prescription pain medication however demonstrated notable increases. Prevalence estimates were influenced by artefactual factors including new government regulation in 2012. For diabetes prevalence estimates this improved the correlation associated with community survey data.&#x0D; ConclusionsAustralian pharmaceutical administrative data have potential utility for chronic disease prevalence estimates. Advantages include low costs, speed of analysis, high power and good representation. We consider the technique offers a complimentary perspective of chronic disease prevalence providing new insights into population health.

Introduction to Prediction of Operational Efficiency for a Selected Type of a Military Aircraft / Wprowadzenie Do Prognozy Skuteczności Działania Wybranego Typu Wojskowego Statku Powietrznego

Abstract The study reveals the general outline for a method of determining the operational efficiency of a military aircraft with respect to destruction of targets held by a potential enemy. The method consists in determination of selected probability factors that define the efficiency of an aircraft’s operation on a potential battlefield. The paper is focused on finding a formula for the mathematical expectation for the number of enemy targets that can be eliminated, where the analytical relationships is determined by means of difference equation that is subsequently transformed into the Fokker-Planck partial differential equation. The solution of that equation represents the function of probable density for the number of destroyable targets. When the function is known it can be then used to determine the efficiency factor related to the optimum (most desired) number of enemy targets that are destroyed. For these probabilities the denominator values are equal to one or the optimum values. The efficiency factor, determined in such a way, seems to be useful for determination of the operational potential demonstrated by a military aircraft.

Comprehensive Citation Factor: A novel method in ranking medical journals

The Institute for Scientific Information (ISI) defines substantive articles as source items, which include only research and review (R&R) articles. This policy encourages some Journals to publish a significant number of original reports in the category of letters to the editor and reviews in the category of Editorials. Consequently, the Impact Factor (IF) fails to provide a fair comparison between medical journals. We introduce a new value, the Comprehensive Citation Factor (CCF), which would include in the denominator all original reports and review articles. We reassessed the 2007 ISI IF rankings of 39 dermatology journals using the CCF formula. Along with research and review articles, research letters, editorials and case reports were also included in the denominator value. The CCF was calculated for each journal and then compared with the IF provided by the ISI for 2007. The rank orders of 27/39 journals (69%) were altered by two or more places bi-directionally. Journals with a significant number of editorial and/or letters had a lower CCF. Only 4 of the 39 journals (10%) kept the same rank when evaluated with the new CCF formula. The CCF is a more accurate quantitative representation to use for individual journal comparison. This formula would encourage editors to publish more manuscripts as original or review articles, rather letters or editorials, and eliminate the need for the controversial subjective classification.

Theoretical research of Fernald forward integration method for aerosol backscatter coefficient inversion of airborne atmosphere detecting lidar

Preliminary inversion results show that the Fernald forward integration method (FFIM) can be used to calculate aerosol backscatter coefficient from airborne atmosphere detecting lidar. But the corresponding theoretical explanations have not been found in relevant papers. In this paper,We use the simulated data based on the ground-based atmosphere detecting radar in Hefei lidar data on February 27, 2008, to quantitatively analyze the above inversion results obtained by the FFIM . Results show that there are three main reasons that the FFIM can be used to calculate aerosol backscatter coefficient when the altitude of lidar calibration points is about 10km. First, the inversion error cannot be infinite and negative results will not appear because the difference batween the denominator items in the Fernald forward integration equation is always greater than zero. Second, inversion error is no more than 0.006 when calibration error is 100%, which is 0.6 percent of the denominator value. Third, Molecule backscatter coefficient is dominant in the calibration item of the Fernald forward integration equation. Big fluctuation range of aerosol backscatter coefficient in the calibration points has little influence on the calibration item value. In general, the atmosphere structure that has a small density in the upper layer but a big density in the lowerlayer, and a high calibration position are two basic reasons for which the FFIM can be applied to the aerosol backscatter coefficient inversion through using airborne atmosphere detecting lidar data.

On the denominator values and barycentric weights of rational interpolants

We improve upon the method of Zhu and Zhu [A method for directly finding the denominator values of rational interpolants, J. Comput. Appl. Math. 148 (2002) 341–348] for finding the denominator values of rational interpolants, reducing considerably the number of arithmetical operations required for their computation. In a second stage, we determine the points (if existent) which can be discarded from the rational interpolation problem. Furthermore, when the interpolant has a linear denominator, we obtain a formula for the barycentric weights which is simpler than the one found by Berrut and Mittelmann [Matrices for the direct determination of the barycentric weights of rational interpolation, J. Comput. Appl. Math. 78 (1997) 355–370]. Subsequently, we give a necessary and sufficient condition for the rational interpolant to have a pole.

Systemic scleroderma: a spatiotemporal clustering

The aetiology of systemic scleroderma remains poorly understood. Twin studies suggest a low genetic input. Of the incriminated environmental agents, silica and vinyl chloride monomer exposure appear the most convincing. Spatiotemporal clustering has been demonstrated only three times previously. We now report a fourth cluster around Edenhope, western Victoria in terms of numerator and denominator estimates, cumulative incidence, distribution in time and space, and possible aetiological factors. Prevalence/cumulative incidence numerator and denominator values were obtained and validated. Each case was age-and gender-matched with two controls. A standardized postal questionnaire was used to obtain data on current, past history, family history, and occupational and non-occupational environmental exposure. Six systemic scleroderma cases and one mixed connective tissue disease patient with a predominance of scleroderma features were identified. The 5-year cumulative incidence was 6.1/10,000, tenfold higher than the Sydney estimates for a similar, though non-identical time period. The gender ratio was 1:1. No cases were genetically related. A family history of scleroderma was validated in one instance and a family history of Raynaud's was noted in first degree relatives of two cases and one control. In all instances, Edenhope residence preceded disease onset. No one environmental agent was implicated in all cases. A spatiotemporal cluster of systemic scleroderma was confirmed and validated. It occurred with a tenfold increased cumulative incidence to that expected and also extended beyond the initially defined 50 km radius of Edenhope. The cases identified were not related. Although no one specific environmental agent was identified, the spatiotemporal clustering would be compatible with an agent occurring at relatively high frequency, but with low disease conversion rates, such as silica inhalation (assuming sufficiently small particle size) or reaction to an infective agent.

Genomic DNA as a cohybridization standard for mammalian microarray measurements.

A persistent design problem for ratiometric microarray studies is selecting the 'denominator' RNA cohybridization standard. The ideal standard should be readily available, inexpensive, invariant over time and from laboratory to laboratory, and should represent all genes with a uniform signal. RNA references (both commercial 'universal' and experiment--specific types), fall short of these goals. We show here that mouse genomic DNA is a reliable microarray cohybridization standard which can meet these criteria. Genomic DNA was superior in universality of coverage (>98% of genes from a 16,000 feature mouse 70mer microarray) to the Stratagene Universal Mouse Reference RNA standard. Ratios for genes in very low abundance in the Stratagene standard were more unstable with the Stratagene standard than with genomic DNA. Genes with mid-range, and therefore presumably optimal RNA denominator values, showed comparable reproducibility with both standards. Inferred ratios made between two different experimental RNAs using a genomic DNA standard were found to correlate well with companion, directly measured ratios (Spearman correlation coefficient = 0.98). The advantage in array feature coverage of genomic DNA will likely increase as newer generation microarrays include genes which are expressed exclusively in minor tissue or developmental domains that are not represented in mixed tissue RNA standards.