Red cell distribution width-to-albumin ratio is a simple promising prognostic marker in acute cholangitis requiring biliary drainage

Background: It is crucial to assess the severity of acute cholangitis(AC). There are currently several prognostic markers. However, the accuracies of these markers are not satisfied. The present study aimed to investigate the predictive value of the red cell distribution width(RDW)-to-albumin ratio(RAR) for the prognosis of AC. Methods: We retrospectively evaluated consecutive patients diagnosed with AC between May 2019 and March 2022. RAR was calculated, and its predictive ability for in-hospital mortality, intensive care unit(ICU) admission, bacteremia, and the length of hospitalization were analyzed. Results: Out of 438 patients, 34(7.8%) died. Multivariate analysis showed that malignant etiology [odds ratio(OR) = 4.816, 95% confidence interval(CI): 1.936-11.980], creatinine(OR = 1.649, 95% CI: 1.095-2.484), and RAR(OR = 2.064, 95% CI: 1.494-2.851) were independent risk factors for mortality. When adjusted for relevant covariates, including age, sex, malignant etiology, Tokyo severity grading(TSG), Charlson comorbidity index, and creatinine, RAR significantly predicted mortality(adjusted OR = 1.833, 95% CI: 1.280-2.624). When the cut-off of RAR was set to 3.8, its sensitivity and specificity for mortality were 94.1% and 56.7%, respectively. Patients with an RAR of > 3.8 had a 20.9-fold(OR = 20.9, 95% CI: 4.9-88.6) greater risk of mortality than the remaining patients. The area under the curve value of RAR for mortality was 0.835(95% CI: 0.770-0.901), which was significantly higher than that of TSG and the other prognostic markers, such as C-reactive protein-to-albumin ratio, and procalcitonin-to-albumin ratio. Lastly, RAR was not inferior to TSG in predicting ICU admission, bacteremia, and the length of hospitalization. Conclusions: RAR successfully predicted the in-hospital mortality, ICU admission, bacteremia, and the length of hospitalization of patients with AC, especially in-hospital mortality. RAR is a promising marker that is more convenient than TSG and other prognostic markers for predicting the prognosis of patients with AC.

Red cell distribution width/platelet ratio estimates the 3-year risk of decompensation in Metabolic Dysfunction-Associated Steatotic Liver Disease-induced cirrhosis

BACKGROUND For compensated advanced chronic liver disease(cACLD)patients,the first decompensation represents a dramatically worsening prognostic event.Based on the first decompensation event(DE),the transition to decompensated advanced chronic liver disease(dACLD)can occur through two modalities referred to as acute decompensation(AD)and non-AD(NAD),respectively.Clinically Significant Portal Hypertension(CSPH)is considered the strongest predictor of decompensation in these patients.However,due to its invasiveness and costs,CSPH is almost never evaluated in clinical practice.Therefore,recognizing noninvasively predicting tools still have more appeal across healthcare systems.The red cell distribution width to platelet ratio(RPR)has been reported to be an indicator of hepatic fibrosis in Metabolic Dysfunction-Associated Steatotic Liver Disease(MASLD).However,its predictive role for the decompensation has never been explored.AIM In this observational study,we investigated the clinical usage of RPR in predicting DEs in MASLD-related cACLD patients.METHODS Fourty controls and 150 MASLD-cACLD patients were consecutively enrolled and followed up(FUP)semiannually for 3 years.At baseline,biochemical,clinical,and Liver Stiffness Measurement(LSM),Child-Pugh(CP),Model for End-Stage Liver Disease(MELD),aspartate aminotransferase/platelet count ratio index(APRI),Fibrosis-4(FIB-4),Albumin-Bilirubin(ALBI),ALBI-FIB-4,and RPR were collected.During FUP,DEs(timing and modaities)were recorded.CSPH was assessed at the baseline and on DE occurrence according to the available Clinical Practice Guidelines.RESULTS Of 150 MASLD-related cACLD patients,43(28.6%)progressed to dACLD at a median time of 28.9 months(29 NAD and 14 AD).Baseline RPR values were significantly higher in cACLD in comparison to controls,as well as MELD,CP,APRI,FIB-4,ALBI,ALBI-FIB-4,and LSM in dACLD-progressing compared to cACLD individuals[all P<0.0001,except for FIB-4(P:0.007)and ALBI(P:0.011)].Receiving operator curve analysis revealed RPR>0.472 and>0.894 as the best cut-offs in the prediction respectively of 3-year first DE,as well as its superiority compared to the other non-invasive tools examined.RPR(P:0.02)and the presence of baseline-CSPH(P:0.04)were significantly and independently associated with the DE.Patients presenting baseline-CSPH and RPR>0.472 showed higher risk of decompensation(P:0.0023).CONCLUSION Altogether these findings suggest the RPR as a valid and potentially applicable non-invasive tool in the prediction of timing and modalities of decompensation in MASLD-related cACLD patients.

Application of neutrophil-lymphocyte ratio and red blood cell distribution width in diabetes mellitus complicated with heart failure

BACKGROUND Accumulating clinical evidence has shown that diabetes mellitus(DM)is a serious risk factor for cardiovascular disorders and an important factor for adverse cardiovascular events.AIM To explore the value of the combined determination of the neutrophil-lymphocyte ratio(NLR)and red blood cell distribution width(RDW)in the early diagnosis and prognosis evaluation of DM complicated with heart failure(HF).METHODS We retrospectively analyzed clinical data on 65 patients with type 2 DM(T2DM)complicated with HF(research group,Res)and 60 concurrent patients with uncomplicated T2DM(control group,Con)diagnosed at Zhejiang Provincial People’s Hospital between January 2019 and December 2021.The NLR and RDW values were determined and comparatively analyzed,and their levels in T2DM+HF patients with different cardiac function grades were recorded.The receiver operating characteristic(ROC)curves were plotted to determine the NLR and RDW values(alone and in combination)for the early diagnosis of HF.The correlation between NLR and RDW with the presence or absence of cardiac events was also investigated.RESULTS Higher NLR and RDW levels were identified in the Res vs the Con groups(P<0.05).The NLR and RDW increased gradually and synchronously with the deterioration of cardiac function in the Res group,with marked differences in their levels among patients with grade II,III,and IV HF(P<0.05).ROC curve analysis revealed that NLR combined with RDW detection had an area under the curve of 0.915,a sensitivity of 76.9%,and a specificity of 100%for the early diagnosis of HF.Furthermore,HF patients with cardiac events showed higher NLR and RDW values compared with HF patients without cardiac events.CONCLUSION NLR and RDW were useful laboratory indicators for the early diagnosis of DM complicated with HF,and their joint detection was beneficial for improving diagnostic efficiency.Additionally,NLR and RDW values were directly proportional to patient outcomes.

Using Pearson’s System of Curves to Approximate the Distributions of the Difference between Two Correlated Estimates of Signal-to-Noise Ratios: The Cases of Bivariate Normal and Bivariate Lognormal Distributions

Background: The signal-to-noise ratio (SNR) is recognized as an index of measurements reproducibility. We derive the maximum likelihood estimators of SNR and discuss confidence interval construction on the difference between two correlated SNRs when the readings are from bivariate normal and bivariate lognormal distribution. We use the Pearsons system of curves to approximate the difference between the two estimates and use the bootstrap methods to validate the approximate distributions of the statistic of interest. Methods: The paper uses the delta method to find the first four central moments, and hence the skewness and kurtosis which are important in the determination of the parameters of the Pearsons distribution. Results: The approach is illustrated in two examples;one from veterinary microbiology and food safety data and the other on data from clinical medicine. We derived the four central moments of the target statistics, together with the bootstrap method to evaluate the parameters of Pearsons distribution. The fitted Pearsons curves of Types I and II were recommended based on the available data. The R-codes are also provided to be readily used by the readers.

Probability Distribution of Ratio of China Aviation Network Edge Vertices Degree and Its Evolutionary Trace Based on Complex Network

In order to reveal the complex network characteristics and evolution principle of China aviation network, the probability distribution and evolution trace of ratio of China aviation network edge vertices degree were studied based on the statistics data of China civil aviation network in 1988, 1994, 2001, 2008 and 2015. According to the theory and method of complex network, the network system was constructed with the city where the airport was located as the network node and the route between cities as the edge of the network. Based on the statistical data, the ratio of edge vertices degree in China aviation network in 1988, 1994, 2001, 2008 and 2015 were calculated. Using the probability statistical analysis method and regression analysis approach, it was found that the ratio of edge vertices degree had linear probability distribution and the two parameters of the probability distribution had linear evolution trace.

Red cell distribution width to platelet ratio: New and promising prognostic marker in acute pancreatitis

AIM: To evaluate the accuracy of red cell distribution width (RDW) to platelet ratio (RPR) to predict in-hospital mortality in acute pancreatitis (AP).

NONNULL DISTRIBUTION OF THE LIKELIHOOD RATIO CRITERION FOR TESTING THE EQUALITY OF DIAGONAL BLOCKS WITH BLOCKWISE INDEPENDENCE

In this paper, the nonnull moments and the distributions of the likelihood ratio criterion for testing the equality of diagonal blocks with blockwise independence under certain alternatives have derived.

Influence of porosity distribution on nonlinear free vibration and transient responses of porous functionally graded skew plates

This article deals with the investigation of the effects of porosity distributions on nonlinear free vibration and transient analysis of porous functionally graded skew(PFGS)plates.The effective material properties of the PFGS plates are obtained from the modified power-law equations in which gradation varies through the thickness of the PFGS plate.A nonlinear finite element(FE)formulation for the overall PFGS plate is derived by adopting first-order shear deformation theory(FSDT)in conjunction with von Karman’s nonlinear strain displacement relations.The governing equations of the PFGS plate are derived using the principle of virtual work.The direct iterative method and Newmark’s integration technique are espoused to solve nonlinear mathematical relations.The influences of the porosity distributions and porosity parameter indices on the nonlinear frequency responses of the PFGS plate for different skew angles are studied in various parameters.The effects of volume fraction grading index and skew angle on the plate’s nonlinear dynamic responses for various porosity distributions are illustrated in detail.

R/S ratio in lead Ⅱ, and the prognostic significance of red cell distribution width in acute coronary syndrome

BACKGROUND In spite of developing medical technologies to discover the etiopathogenesis of diseases and developments in the treatment of coronary artery disease, acute coronary syndromes(ACS) continue to be the main cause of mortality and morbidity worldwide. New cardiac biomarkers and techniques are needed to help provide rapid diagnosis in order to evaluate risk in coronary artery patients.AIM To evaluate the effects of R to S ratio(RSR) in the electrocardiograph of patients with ACS, from the point of the arising complication after myocardial infarction(MI), to three-vessel disease(TVD) and mortality.METHODS The data of 1,296 patients with ACS, who presented to the emergency department of our hospital with chest pain between January 2014 and December2018 and were admitted to the cardiology clinic, were retrospectively included in this cross-sectional cohort study. Patients with an RSR value less than I were assigned to group Ⅰ, while those with an RSR value greater than Ⅰ were assigned to group Ⅱ.RESULTS In our study, 466(35.9%) of the 1,296 patients, 357(38.3%) in group 1 and 109(29.9%) in group 2, were female, with a mean age of 61.56 ± 9.42. ST-elevation MI 573(44.2%), unstable angina(UA) 502(38.7%) and non ST-elevation MI 220(17%)were more prevalent in group Ⅰ. Acute anterior MI 263(20.3) in group Ⅰ, and acute inferior MI 184(14.2) in group Ⅱ was higher. Ischemic heart failure was the most common complication. In group Ⅱ, the red cell distribution width(RDW) was 15.42 ± 1.82, the gensini score was 48.39 ± 36.44, the left ventricular ejection fraction was 41.17 ± 10.41, the TVD was 111(8.5), and the mortality rate was 72(5.6), which was significantly higher than group Ⅰ RDW; in MI with ST and nonST-elevation, in TVD, mortality and complications were high and low in UA. In single and multivariate regression analyses, the variables were associated with ACS risk.CONCLUSION RSR levels may be an auxiliary predictive value in ACS in terms of complications developing after MI, TVD, and mortality.

RANGE AMBIGUITY DISTRIBUTION CHARACTERISTIC OF SPACEBORNE SAR AND ITS DESIGN CONSIDERATION

A new approach is proposed which can satisfy the range ambiguity requirement while keep the antenna width not to be enlarged and get the high quality image also. Here the chirp slope of the transmitted linear frequency modulated pulses is reversed alternately. Therefore, during the range compression significant portion of the ambiguous return which is due to the mismatching with the signal reference function is suppressed. The suggested method provides significant improvement in range ambiguity ratio and can be utilized in attaining wider swath.

Distributions of Ratios: From Random Variables to Random Matrices

The ratio R of two random quantities is frequently encountered in probability and statistics. But while for unidimensional statistical variables the distribution of R can be computed relatively easily, for symmetric positive definite random matrices, this ratio can take various forms and its distribution, and even its definition, can offer many challenges. However, for the distribution of its determinant, Meijer G-function often provides an effective analytic and computational tool, applicable at any division level, because of its reproductive property.

Branching ratio and angular distribution of ejected electrons from Eu 4f^76p_(1/2)nd auto-ionizing states

The branching ratios of ions and the angular distributions of electrons ejected from the Eu 4f^76p_（1/2）nd auto-ionizing states are investigated with the velocity-map-imaging technique.To populate the above auto-ionizing states,the relevant bound Rydberg states have to be detected first.Two new bound Rydberg states are identified in the region between41150 cm^（-1）and 44580 cm^（-1）,from which auto-ionization spectra of the Eu 4f^76p_（1/2）nd states are observed with isolated core excitation method.With all preparations above,the branching ratios from the above auto-ionizing states to different final ionic states and the angular distributions of electrons ejected from these processes are measured systematically.Energy dependence of branching ratios and anisotropy parameters within the auto-ionization spectra are carefully analyzed,followed by a qualitative interpretation.

Correlation between hydrocarbon distribution and water-hydrocarbon ratio in Fischer-Tropsch synthesis

In order to shorten the evaluation cycle of cobalt catalyst before the optimized catalyst is fixed on, a mathematical method is proposed to calculate weight percentage of C5＋ hydrocarbons. Based on the carbide polymerization mechanism and the main hydrocarbons being linear alkanes and α-olefins, the correlation between hydrocarbon distribution and the molecular mass ratio of water to hydrocarbons is discussed. The result shows the ratio was within the range of 1.125-1.286 and the lower the ratio, the more gaseous hydrocarbons were obtained. Moreover, a linear equation between the weight percentage of C5＋ hydrocarbons and the weight ratio of C5＋ hydrocarbons to the total water is established. These results are validated by corresponding experiments. The weight percentage of C5＋ hydrocarbons could be immediately calculated by this linear equation without detailed gas chromatography （GC） analysis of them.

THE ASYMPTOTIC DISTRIBUTIONS OF EMPIRICAL LIKELIHOOD RATIO STATISTICS IN THE PRESENCE OF MEASUREMENT ERROR

Suppose that several different imperfect instruments and one perfect instrument are independently used to measure some characteristics of a population. Thus, measurements of two or more sets of samples with varying accuracies are obtained. Statistical inference should be based on the pooled samples. In this article, the authors also assumes that all the imperfect instruments are unbiased. They consider the problem of combining this information to make statistical tests for parameters more relevant. They define the empirical likelihood ratio functions and obtain their asymptotic distributions in the presence of measurement error.

The Distribution of the Concentration Ratio for Samples from a Uniform Population

In the present paper we derived, with direct method, the exact expressions for the sampling probability density function of the Gini concentration ratio for samples from a uniform population of size n = 6, 7, 8, 9 and 10. Moreover, we found some regularities of such distributions valid for any sample size.

A new two-part test based on density ratio model for zero-inflated continuous distributions

In this paper,we consider testing the hypothesis concerning the means of two independent semicontinuous distributions whose observations are zero-inflated,characterized by a sizable number of zeros and positive observations from a continuous distribution.The continuous parts of the two semicontinuous distributions are assumed to follow a density ratio model.A new two-part test is developed for this kind of data.The proposed test takes the sum of one test for equality of proportions of zero values and one conditional test for the continuous distribution.The test is proved to follow a 2 distribution with two degrees of freedom.Simulation studies show that the proposed test controls the type I error rates at the desired level,and is competitive to,and most of the time more powerful than two popular tests.A real data example from a dietary intervention study is used to illustrate the usefulness of the proposed test.

GAS AND OIL POWER DISTRIBUTION RATIO OF A NEW HYDRAULIC BREAKER

The working principle of a new hydraulic breaker operated jointly by gas and hydraulic flow which has a reasonable structure, high efficiency and long piston life-span, is analyzed, and the optimal power distribution ratio of the sealed nitrogen gas to the high-pressure oil in the process of piston impacting is studied. Through theoretical analysis, optimization simulation and detailed calculation, it is determined that the impact system has optimal mechanical performance and highest efficiency when the distribution ratio φ is between 0.3 and 0.5. The theoretical result is also verified by repeated tests.

Study of Ratio of Proton Momentum Distributions with a Chiral Quark Model

The ratio between the anomalous magnetic moments of proton and neutron has recently been suggested to be connected to the ratio of proton momentum fractions carried by the valence quarks inside it. This moment fraction ratio is respectively evaluated by using constituent quark model and chiral quark model in order to check meson cloud effect. Our results show that the meson cloud effect is remarkable to the ratio of the proton momentum fractions, and therefore, this ratiois a sensitive test for the meson cloud effect as well as for the SU(6) symmetry breaking effect.

The Natural Probability Distribution of Load and Unload Response Ratio

In this paper,the Gutenberg-Richter model is used to generate seismic events.The events that satisfy the random distribution are also generated.With those events,the natural probability distribution of Load and Unload Response Ratio(LURR),which measures quantitatively the degree of instability of a nonlinear system,is discussed.The study is based on stress energy release,which is chosen as the response of nonlinear system F3.The comparative results from the observation catalogue and generating data are also studied.It is revealed that the natural probability of LURR is mostly stable when the sample number is sufficient.The lower the natural probability of LURR,the more the precursory is information it may contain.The influence of Y3 resulting from the sample number and the magnitude range of events is also discussed.

The Random Distribution of the Loading and Unloading Response Ratio Under the Assumptions of Poisson Models

This paper discussed the random distribution of the loading and unloading response ratio（LURR） of different definitions（Y1～Y5）using the assumptions that the earthquakes occurfollowing the Poisson process and their magnitudes obey the Gutenberg-Richter law.Theresults show that Y1～Y5 are quite stable or concentrated when the expected number of eventsin the calculation time window is relatively large（】40）;but when this occurrence ratebecomes very small,Y2～Y5 become quite variable or unstable.That is to say,a high value ofthe LURR can be produced not only from seismicity before a large earthquake,but also from arandom sequence of earthquakes that obeys a Poisson process when the expected number ofevents in the window is too small.To check the influence of randomness in the catalogue tothe LURR,the random distribution of the LURR under Poisson models has been calculated bysimulation.90%,95% and 99% confidence ranges of Y1 and Y3 are given in this paper,which is helpful to quantify the random