Assumption Of Proportionality Research Articles

Application of De Novo Programming Approach for Optimizing the Business Process

The linear programming model is sometimes difficult to apply in real business situations due to its assumption of proportionality. This paper shows an example of how to use De Novo programming approach instead of linear programming. In the De Novo programming, resources are not fixed like in linear programming but resource quantities depend only on available budget. Budget is a new, important element of the De Novo approach. Two different production situations are presented: increasing costs and quantity discounts of raw materials. The focus of this paper is on advantages of the De Novo approach in the optimization of production plan for production company which produces souvenirs made from famous stone from the island of Brac, one of the greatest islands from Croatia.

Age stratification corrects bias in estimated hazard of APOE genotype for Alzheimer's disease

IntroductionThe apolipoprotein E (APOE) e4 allele is a major genetic risk factor of late-onset Alzheimer's disease. However, its interaction with two other canonical risk factors, age and sex, is not clear. Previous studies have reported conflicting results on its differential effects in men and women, its association with young-onset AD before the age of 65 years, and its significance in genetic admixture populations. In these studies, the hazard of the e4 allele was assumed to be constant during aging. However, this hypothesis has not been tested and its violation may lead to significant biases and contribute to such discrepant findings. MethodsIn a prospective cohort of 4727 subjects, we performed Cox regression analysis of the association of the e4 allele with AD age of onset. We then performed diagnostics on the resulting model and tested if the hazard of the e4 allele violated the assumption of proportionality during aging. We examined whether incorporating age stratifications and time-dependent coefficients could restore the proportionality. We then validated our findings in four independent cohorts. ResultsHazard of the e4 allele for AD was nonproportional. It took a stepwise decline around the age of 80 years for men and around the age of 75 years for women. By stratifying subjects into a younger group and an older group, we detected more consistent effects of the e4 allele across multiple independent cohorts. We also found that the e4 allele was a significant risk factor for young-onset AD with age of onset before 65 years. DiscussionAge compositions of study cohorts can significantly bias the estimated effect of the APOE genotype. Studies of AD should consider hidden age structures among subjects and routinely employ appropriate age and sex stratification strategies or nonparametric modeling in experimental designs and data analysis. Finally, we argue that the e4 allele is a risk factor not only for late-onset AD but also for young-onset AD.

Flexible modeling of the hazard rate and treatment effects in long-term survival studies.

The effects of predictors on time to failure may be difficult to assess in cancer studies with longer follow-up, as the commonly used assumption of proportionality of hazards holding over an extended period is often questionable. Motivated by a long-term prostate cancer clinical trial, we contrast and compare four powerful methods for estimation of the hazard rate. These four methods allow for varying degrees of smoothness as well as covariates with effects that vary over time. We pay particular attention to an extended multiresolution hazard estimator, which is a flexible, semi-parametric, Bayesian method for joint estimation of predictor effects and the hazard rate. We compare the results of the extended multiresolution hazard model to three other commonly used, comparable models: Aalen's additive model, Kooperberg's hazard regression model, and an extended Cox model. Through simulations and the analysis of a large-scale randomized prostate cancer clinical trial, we use the different methods to examine patterns of biochemical failure and to estimate the time-varying effects of androgen deprivation therapy treatment and other covariates.

Survival analysis in the presence of competing risks

Survival analysis in the presence of competing risks imposes additional challenges for clinical investigators in that hazard function (the rate) has no one-to-one link to the cumulative incidence function (CIF, the risk). CIF is of particular interest and can be estimated non-parametrically with the use cuminc() function. This function also allows for group comparison and visualization of estimated CIF. The effect of covariates on cause-specific hazard can be explored using conventional Cox proportional hazard model by treating competing events as censoring. However, the effect on hazard cannot be directly linked to the effect on CIF because there is no one-to-one correspondence between hazard and cumulative incidence. Fine-Gray model directly models the covariate effect on CIF and it reports subdistribution hazard ratio (SHR). However, SHR only provide information on the ordering of CIF curves at different levels of covariates, it has no practical interpretation as HR in the absence of competing risks. Fine-Gray model can be fit with crr() function shipped with the cmprsk package. Time-varying covariates are allowed in the crr() function, which is specified by cov2 and tf arguments. Predictions and visualization of CIF for subjects with given covariate values are allowed for crr object. Alternatively, competing risk models can be fit with riskRegression package by employing different link functions between covariates and outcomes. The assumption of proportionality can be checked by testing statistical significance of interaction terms involving failure time. Schoenfeld residuals provide another way to check model assumption.

A meta-analysis of fecundity in rockfishes (genus Sebastes)

Estimates of fecundity at size are a key component of age-structured population dynamics models such as those used for stock assessment purposes. Fecundity-length relationships for many exploited fish stocks are often poorly understood due to small sample sizes and high levels of intrinsic variability among individuals. Several species in the genus Sebastes match this description, and are important components of commercial and recreational fisheries off the U.S. West Coast. We used a hierarchical Bayesian modeling framework for simultaneous estimation of parameters in the fecundity-length relationships for 29 species of rockfish while accounting for variability within and among subgenera. Hierarchical models that account for subgeneric phylogenetic structure and variability among species outperformed models that treat all species in the genus as exchangeable or ignored variation among species within a subgenus, based on a predictive information criterion. Our results confirm that weight-specific fecundity increases with size in nearly all Sebastes species, and that the assumption of proportionality between mature female biomass and total egg production is inappropriate for most Sebastes stock assessments. Benefits of the hierarchical framework include prediction of fecundity-length parameters at the genus, subgenus, and species level, as well as predictive distributions for unobserved Sebastes species.

A special case of reduced rank models for identification and modelling of time varying effects in survival analysis.

Flexible survival models are in need when modelling data from long term follow-up studies. In many cases, the assumption of proportionality imposed by a Cox model will not be valid. Instead, a model that can identify time varying effects of fixed covariates can be used. Although there are several approaches that deal with this problem, it is not always straightforward how to choose which covariates should be modelled having time varying effects and which not. At the same time, it is up to the researcher to define appropriate time functions that describe the dynamic pattern of the effects. In this work, we suggest a model that can deal with both fixed and time varying effects and uses simple hypotheses tests to distinguish which covariates do have dynamic effects. The model is an extension of the parsimonious reduced rank model of rank 1. As such, the number of parameters is kept low, and thus, a flexible set of time functions, such as b-splines, can be used. The basic theory is illustrated along with an efficient fitting algorithm. The proposed method is applied to a dataset of breast cancer patients and compared with a multivariate fractional polynomials approach for modelling time-varying effects. Copyright © 2016 John Wiley & Sons, Ltd.

A proportional odds transition model for ordinal responses with an application to pig behaviour

ABSTRACTCategorical data are quite common in many fields of science including in behaviour studies in animal science. In this article, the data concern the degree of lesions in pigs, related to the behaviour of these animals. The experimental design corresponded to two levels of environmental enrichment and four levels of genetic lineages in a completely randomized factorial with data collected longitudinally over four time occasions. The transition models used for the data analysis are based on stochastic processes and Generalized Linear Models. In general, these are not used for analysis of longitudinal data but they are useful in many situations as in this study. We present some aspects of this class of models for the stationary case. The proportional odds transition model is used to construct the matrix of transition probabilities and a function was developed in the R system to fit this model. The likelihood ratio test was used to verify the assumption of odds ratio proportionality and to select the structure of the linear predictor. The methodology used allowed for the choice of a model that can be used to explain the relationship between the severity of lesions in pigs and the use of the environmental enrichment.

Test for additive interaction in proportional hazard model applied to Pitot sensors reliability and survivability

Abstract Cox proportional hazards model is one of the most common methods used in analysis of time to event data. Estimation of proportional hazards models when covariates are time independent increase the power of significance of the model. Techniques to release this assumption of proportionality allow researchers to test whether the effects of covariates change over time and also permit a more nuanced understanding of the phenomenon being studied. The current paper presents an extension for the Cox model in case of non-proportional risk. This new model will be applied in the Pitot Sensor's reliability function to study the covariates interaction with time. A simulation study is used to illustrate the model and to show its new performances. This paper focuses in the determination of the Pitot sensor reliability and survivability Function. However, the same process can be generalized to study the reliability function of other standby systems.

SOME PROPERTIES OF THE VARIATIONAL PROBLEMS OF OPTIMAL CONTROL OF CONSUMPTION

ARTICLE RETRACTED In this paper we study the General patterns of models based on variational methods in various problems of optimal control of consumption: decisionmaking in the management of the household, as well as models of the economic dynamics of the Harrod–Domar and Solow. The role of optimal control in these tasks is played by the consumption function: in the first task is a function of consumption of the household, the model of Harrod–Domar is the aggregate consumption, as in the Solow model is per capita consumption. The role of the equation of when the first task is the equation of the dynamic balance between income, expenses, and accumulated savings, the model of Harrod–Domar – equation dynamic balance between income and investment, with the assumption of proportionality of investment and derivative income, as in the Solow model the role of the equation of the relationship is played by the equation of dynamic balance between the capitallabor ratio, economic productivity and per capita consumption. In all considered processes, the optimal control problem is formulated as a maximization problem of the functional expressing the integrated discounted utility of consumption under the equity equation.

Inference in a model of successive failures with shape-adjusted hazard rates

For successive failure times of components in a technical system, a flexible model based on sequential order statistics is proposed. Beyond the common assumption of proportionality, this model allows for structural adjustments of the hazard rates of the underlying lifetime distributions in situations, where failures have an impact on the entire shape of the hazard rate of remaining components. The hazard rates may be chosen, e.g., as strictly ordered bathtub curves. The general structure is analysed, and maximum likelihood estimators are stated for both, unrestricted and order restricted model parameters, as well as for parameters connected by a linear link function. Several properties of the estimators are obtained. Utilizing the maximum likelihood estimators, simultaneous confidence regions based on the Jeffreys–Kullback–Leibler distance and the Hellinger distance are examined.

Sensitivity Analysis of Environmental Process Modeling in a Life Cycle Context: A Case Study of Hemp Crop Production

SummaryThe aim of this article is to develop a methodological approach allowing to assess the influence of parameters of one or more elementary processes in the foreground system, on the outcomes of a life cycle assessment (LCA) study. From this perspective, the method must be able to: (1) include foreground process modeling in order to avoid the assumption of proportionality between inventory data and reference flows; (2) quantify influences of foreground processes’ parameters (and, possibly, interactions between parameters); and (3) identify trends (either increasing or decreasing) for each parameter on each indicator in order to determine the most favorable direction for parametric variation. These objectives can be reached by combining foreground system modeling, a set of two different sensitivity analysis methods (each one providing different and complementary information), and LCA. The proposed method is applied to a case study of hemp‐based insulation materials for buildings. The present study will focus on the agricultural stage as a foreground system and as a first step encompassing the entire life cycle. A set of technological recommendations were identified for hemp farmers in order to reduce the crop's environmental impacts (from –11% to –89% according to the considered impact category). One of the main limitations of the approach is the need for a detailed model of the foreground process. Further, the method is, at present, rather time‐consuming. However, it offers long‐term advantages given that the higher level of model detail adds robustness to the LCA results.

Anthropogenic black carbon emissions to the atmosphere: Surface distribution through Russian territory

Official statistical data from the Ministry of Natural Resources and Ecology of the Russian Federation on anthropogenic pollutant emissions from Russian cities and regions for 2010 are analyzed, and the black carbon (BC) emission distribution through the Russian territory is estimated. The lack of this information makes it difficult to study the long-range atmospheric transport of BC and forecast the related climate and ecological effects. Calculations are based on available data on carbon monoxide (CO) and BC emissions from Russian cities and regions under the assumption of proportionality of the BC and CO emissions, indepen-dently of transport and stationary sources. The analysis includes 54 regions and almost 100 cities in an area within (50–72° N × 20–180° E), which covers about 94% of the Russian territory. The spatial distribution of the annual BC emission through the territory under study is modeled on a (1° × 1°) grid for the first time. The total annual BC emission from this area is estimated at (210 ± 30) Gg. The main anthropogenic BC sources are located in industrial regions of the central European part of Russia, Southern Ural, Western Siberia, and on the large sparsely populated territories of the Western Siberia with natural oil/gas extraction industry.

Dependence of dislocation damping on helium-3 concentration in helium-4 crystals

The mechanical properties of crystals are strongly affected by dislocation mobility. Impurities can bind to dislocations and interfere with their motion, causing changes in the crystal's shear modulus and mechanical dissipation. In 4He crystals, the only impurities are 3He atoms, and they can move through the crystal at arbitrarily low temperatures by quantum tunneling. When dislocations in 4He vibrate at speeds v < 45 μm/sec, bound 3He impurities move with the dislocations and exert a damping force B3v on them. In order to characterize 4He dislocation networks and determine the 3He binding energy, it is usually assumed that B3 is proportional to the concentration of 3He bound to the dislocations. In this preliminary report, we determine B3 in a crystal with 2.32 ppm 3He and compare with our previous measurements of B3 in natural purity 4He crystals to verify the assumption of proportionality.

A discrimination index for selecting markers of tumor growth dynamic across multiple cancer studies with a cure fraction

To identify genomic markers with consistent effect on tumor dynamics across multiple cancer series, discrimination indices based on proportional hazards models can be used since they do not depend heavily on the sample size. However, the underlying assumption of proportionality of the hazards does not always hold, especially when the studied population is a mixture of cured and uncured patients, like in early-stage cancers.We propose a novel index that quantifies the capability of a genomic marker to separate uncured patients, according to their time-to-event outcomes. It allows to identify genomic markers characterizing tumor growth dynamic across multiple studies.Simulation results show that our index performs better than classical indices based on the Cox model. It is neither affected by the sample size nor the cure rate fraction.In a cross-study of early-stage breast cancers, the index allows to select genomic markers with a potential consistent effect on tumor growth dynamics.

Effects of blood ΔR2* non-linearity on absolute perfusion quantification using DSC-MRI: Comparison with Xe-133 SPECT

PurposeTo evaluate whether a non-linear blood ΔR2*-versus-concentration relationship improves quantitative cerebral blood flow (CBF) estimates obtained by dynamic susceptibility contrast (DSC) MRI in a comparison with Xe-133 SPECT CBF in healthy volunteers. Material and MethodsLinear as well as non-linear relationships between ΔR2* and contrast agent concentration in blood were applied to the arterial input function (AIF) and the venous output function (VOF) from DSC-MRI. To reduce partial volume effects in the AIF, the arterial time integral was rescaled using a corrected VOF scheme. ResultsUnder the assumption of proportionality between the two modalities, the relationship CBF(MRI)=0.58CBF(SPECT) (r=0.64) was observed using the linear relationship and CBF(MRI)=0.51CBF(SPECT) (r=0.71) using the non-linear relationship. DiscussionA smaller ratio of the VOF time integral to the AIF time integral and a somewhat better correlation between global DSC-MRI and Xe-133 SPECT CBF estimates were observed using the non-linear relationship. The results did not, however, confirm the superiority of one model over the other, potentially because realistic AIF signal data may well originate from a combination of blood and surrounding tissue.

Erythrocyte Storage Duration Is Not Associated with Increased Mortality in Noncardiac Surgical Patients

More than 5 million patients receive erythrocyte transfusions in the United States every year. Previous studies linked the storage duration of allogeneic erythrocytes to the risk of severe postoperative complications, especially after cardiac or trauma surgery. Limited data are available for noncardiac surgical patients. We therefore evaluated the association between storage duration of transfused erythrocytes and postoperative all-cause mortality among general surgery patients. Perioperative data corresponding to 63,319 adult, general surgery patients were obtained from our registry and merged with blood product data. Patients receiving solely leukocyte-reduced, allogeneic erythrocyte transfusions were included. Multivariable Cox proportional hazards regression was used to characterize the relationship between median erythrocyte storage duration and postoperative mortality rate, adjusting for characteristics plausibly influencing the storage duration of erythrocytes. Of the 6,994 patients included in the final analysis, 23, 44, 11, 9, and 13% received 1, 2, 3, 4, and ≥5 erythrocyte units, respectively. The authors found no evidence that increasing median storage duration was associated with a difference in the risk of postoperative mortality (hazard ratio, 0.99 [0.94-1.04]; P = 0.64). Analyzing the mean storage duration of erythrocyte units as a function of year of transfusion, the authors demonstrate a relevant decrease in utilization of the oldest blood units, whereas young blood storage duration remains nearly unchanged. The authors' study supports the recent literature in surgical and medical patients and underlines the importance of sufficiently powered randomized trials to finally resolve the erythrocyte storage duration debate.

Annealing of ion irradiation damage in nuclear graphite

Changes in Raman spectra of polished and ion-irradiated Gilsocarbon and Highly Orientated Pyrolytic Graphite (HOPG) during annealing have been investigated and compared with changes reported during stored energy release in fast neutron irradiated graphite. It is postulated that the change in the Raman spectra of polished, ion-irradiated and neutron irradiated graphite can be attributed to crystalline structural changes due to the annealing of lattice defects. This is illustrated in this work by changes in the kinetic parameters, in terms of the decrease of the Raman ID/IG ratio, during the thermal annealing of polished and ion-irradiated Gilsocarbon and HOPG graphite. Several kinetic models are investigated in terms of activation energy and order of reaction. The most suitable model to explain Raman annealing kinetics was found to be, a two reaction model for polished Gilsocarbon graphite, and a two and possibly three reaction model for ion-irradiated Gilsocarbon graphite and ion-irradiated HOPG. The kinetics parameters obtained using both the two and three reaction models reveal similarities with kinetic models obtained for neutron irradiated graphite. The assumption that the Raman intensity ratio ID/IG is proportional to the square root of the defect quantity provided a better fit than the assumption of direct proportionality.

Bone Marrow Dosimetry Using 124I-PET

Bone marrow is usually dose-limiting for radioimmunotherapy. In this study, we directly estimated red marrow activity concentration and the self-dose component of absorbed radiation dose to red marrow based on PET/CT of 2 different (124)I-labeled antibodies (cG250 and huA33) and compared the results with plasma activity concentration and plasma-based dose estimates. Two groups of patients injected with (124)I-labeled monoclonal antibodies (11 patients with renal cancer receiving (124)I-cG250 and 5 patients with colorectal cancer receiving (124)I- huA33) were imaged by PET or PET/CT on 2 or 3 occasions after infusion. Regions of interest were drawn over several lumbar vertebrae, and red marrow activity concentration was quantified. Plasma activity concentration was also quantified using multiple patient blood samples. The red marrow-to-plasma activity concentration ratio (RMPR) was calculated at the times of imaging. The self-dose component of the absorbed radiation dose to the red marrow was estimated from the images, from the plasma measurements, and using a combination of both sets of measurements. RMPR was observed to increase with time for both groups of patients. Mean (±SD) time-dependent RMPR (RMPR(t)) for the cG250 group increased from 0.13 ± 0.06 immediately after infusion to 0.23 ± 0.09 at approximately 6 d after infusion. For the huA33 group, mean RMPR(t) was 0.10 ± 0.04 immediately after infusion, 0.13 ± 0.05 approximately 2 d after infusion, and 0.20 ± 0.09 approximately 7 d after infusion. Plasma-based estimates of red marrow self-dose tended to be greater than image-based values by, on average, 11% and 47% for cG250 and huA33, respectively, but by as much as -73% to 62% for individual patients. The hybrid method combining RMPR(t) and plasma activity concentration provided a closer match to the image-based dose estimates (average discrepancies, -2% and 18% for cG250 and huA33, respectively). These results suggest that the assumption of time-independent proportionality between red marrow and plasma activity concentration may be too simplistic. Individualized imaged-based dosimetry is probably required for the optimal therapeutic delivery of radiolabeled antibodies, which does not compromise red marrow and may allow, for some patients, a substantial increase in administered activity and thus tumor dose.

Correlation between arterial blood volume obtained by arterial spin labelling and cerebral blood volume in intracranial tumours

To compare measurements of the arterial blood volume (aBV), a perfusion parameter calculated from arterial spin labelling (ASL), and cerebral blood volume (CBV), calculated from dynamic susceptibility contrast (DSC) MRI. In the clinic, CBV is used for grading of intracranial tumours. Estimates of aBV from the model-free ASL technique quantitative STAR labelling of arterial regions (QUASAR) experiment and of DSC-CBV were obtained at 3T in ten patients with eleven tumours (three grade III gliomas, four glioblastomas and four meningiomas, two in one patient). Parametric values of aBV and CBV were determined in the tumour as well as in normal grey matter (GM), and tumour-to-GM aBV and CBV ratios were calculated. In a 4-pixel ROI representing maximal tumour values, the coefficient of determination R (2) was 0.61 for the comparison of ASL-based aBV tumour-to-GM ratios and DSC-MRI-based CBV tumour-to-GM ratios and 0.29 for the comparison of parametric values of ASL-aBV and DSC-CBV, under the assumption of proportionality. Both aBV and CBV showed a non-significant tendency to increase when going from grade III gliomas to glioblastomas to meningiomas. These results suggest that measurement of aBV is a potential tool for non-invasive assessment of blood volume in intracranial tumours.

Quantitative Analysis of Tat Peptide Binding to Import Carriers Reveals Unconventional Nuclear Transport Properties

A detailed study of nuclear import mediated by the HIV-1 Tat peptide (47YGRKKRRQRRR57, TatRRR) is reported. Fluorescence-based measurements, calibration of protein concentrations, and binding assays are exploited to address the physicochemical mechanisms of Tat peptide recognition by the classical importin α (Impα) and importin β (Impβ) receptors both in vitro and in intact cells. We show that TatRRR is an unconventional nuclear localization sequence that binds directly to both Impα and Impβ carriers in the absence of competitors (in vitro), whereas this property is silenced in the actual cellular environment. In the latter case, Impα/β-dependent nuclear import can be successfully restored by replacing the "RRR" stretch with "GGG". We apply a recently developed method to determine quantitatively TatGGG affinity for each receptor. Based on these results, we can rationalize previous controversial reports on the Tat peptide and provide coherent guidelines for the design of novel intracellular targeting sequences.