Socio-demographic factors, smoking, symptoms, morbidities and pulmonary function and quality of life in individuals with a heavy smoking history

Objective: To determine which socio-demographic, exposure, morbidity and symptom variables are associated with health-related quality of life among former and current heavy smokers. Methods: Cross sectional data from 2537 participants were studied. All participants were at ≥2% risk of developing lung cancer within 6 years. Linear and logistic regression models utilizing a multivariable fractional polynomial selection process identified variables associated with health-related quality of life, measured by the EQ-5D. Results: Upstream and downstream associations between smoking cessation and higher health-related quality of life were evident. Significant upstream associations, such as education level and current working status and were explained by the addition of morbidities and symptoms to regression models. Having arthritis, decreased forced expiratory volume in one second, fatigue, poor appetite or dyspnea were most highly and commonly associated with decreased HRQoL. Discussion: Upstream factors such as educational attainment, employment status and smoking cessation should be targeted to prevent decreased health-related quality of life. Practitioners should focus treatment on downstream factors, especially symptoms, to improve health-related quality of life.

Fractional polynomial response surface models

Second-order polynomial models have been used extensively to approximate the relationship between a response variable and several continuous factors. However, sometimes polynomial models do not adequately describe the important features of the response surface. This article describes the use of fractional polynomial models. It is shown how the models can be fitted, an appropriate model selected, and inference conducted. Polynomial and fractional polynomial models are fitted to two published datasets, illustrating that sometimes the fractional polynomial can give as good a fit to the data and much more plausible behavior between the design points than the polynomial model. © 2005 American Statistical Association and the International Biometric Society.

DNA Topoisomerase I Gene Copy Number and mRNA Expression Assessed as Predictive Biomarkers for Adjuvant Irinotecan in Stage II/III Colon Cancer.

PURPOSE: Prospective-retrospective assessment of theTOP1gene copy number andTOP1mRNA expression as predictive biomarkers for adjuvant irinotecan in stage II/III colon cancer. EXPERIMENTAL DESIGN: Formalin-fixed, paraffin-embedded tissue microarrays were obtained from an adjuvant colon cancer trial (PETACC3) where patients were randomized to 5-fluorouracil/folinic acid with or without additional irinotecan.TOP1copy number status was analyzed by fluorescencein situhybridization (FISH) using aTOP1/CEN20 dual-probe combination.TOP1mRNA data were available from previous analyses. RESULTS: TOP1FISH and follow-up data were obtained from 534 patients.TOP1gain was identified in 27% using a single-probe enumeration strategy (≥4TOP1signals per cell) and in 31% when defined by aTOP1/CEN20 ratio ≥ 1.5. The effect of additional irinotecan was not dependent onTOP1FISH status.TOP1mRNA data were available from 580 patients with stage III disease. Benefit of irinotecan was restricted to patients characterized byTOP1mRNA expression ≥ third quartile (RFS: HRadjusted, 0.59;P= 0.09; OS: HRadjusted, 0.44;P= 0.03). The treatment byTOP1mRNA interaction was not statistically significant, but in exploratory multivariable fractional polynomial interaction analysis, increasingTOP1mRNA values appeared to be associated with increasing benefit of irinotecan. CONCLUSIONS: In contrast to theTOP1copy number, a trend was demonstrated for a predictive property ofTOP1mRNA expression. On the basis ofTOP1mRNA, it might be possible to identify a subgroup of patients where an irinotecan doublet is a clinically relevant option in the adjuvant setting of colon cancer.Clin Cancer Res; 22(7); 1621-31. ©2015 AACR.

Crescita volumetrica dei miomi uterini: analisi dei fattori di rischio

I miomi uterini sono la neoplasia uterina più comune e colpiscono fino al 30% delle donne in età fertile. Nonostante l’elevata prevalenza, pochi studi in Letteratura hanno analizzato i fattori di rischio per la crescita dei miomi uterini, mostrando spesso dei risultati contrastanti. Nel nostro studio osservazionale prospettico sono state arruolate pazienti che rispettassero i criteri di inclusione e di esclusione, con diagnosi di miomi uterini evidenziati mediante ecografia eseguita presso i nostri ambulatori, a partire da giugno 2017. A partire da gennaio 2019, sono state ricercate mensilmente le pazienti precedentemente arruolate che erano tornate presso i nostri ambulatori per esecuzione di ulteriore ecografia, a distanza di 24 ± 5 mesi, fino a raggiungere il campione designato, cioè 450 pazienti totali. È stato, quindi, valutato il tasso di crescita annuo del mioma di maggiori dimensioni ed è stato utilizzato l'approccio polinomiale frazionario multivariabile per selezionare i fattori di rischio anamnestici ed ecografici legati all’incremento volumetrico. Circa la metà dei miomi uterini analizzati ha mostrato stabilità dimensionale nel corso del follow-up (crescita ≤10%), mentre la restante metà ha mostrato una crescita > 10%. Il solo fattore di rischio associato alla crescita volumetrica dei miomi uterini è risultato essere il volume del mioma durante l’ecografia di arruolamento (P = 0.001), quindi miomi di piccole dimensioni presentano un tasso di crescita maggiore rispetto ai miomi di grandi dimensioni. Lo studio ha raccolto la più ampia casistica in Letteratura nella valutazione del naturale andamento di modifica dimensionale dei miomi uterini. Sebbene siano necessari ulteriori studi con campione più ampio, questi dati possono fornire un utile supporto per eseguire un adeguato counselling con le pazienti nella pratica clinica quotidiana.

A general model to predict individual exposure to solar UV by using ambient irradiance data

Excessive exposure to solar ultraviolet (UV) is the main cause of skin cancer. Specific prevention should be further developed to target overexposed or highly vulnerable populations. A better characterisation of anatomical UV exposure patterns is however needed for specific prevention. To develop a regression model for predicting the UV exposure ratio (ER, ratio between the anatomical dose and the corresponding ground level dose) for each body site without requiring individual measurements. A 3D numeric model (SimUVEx) was used to compute ER for various body sites and postures. A multiple fractional polynomial regression analysis was performed to identify predictors of ER. The regression model used simulation data and its performance was tested on an independent data set. Two input variables were sufficient to explain ER: the cosine of the maximal daily solar zenith angle and the fraction of the sky visible from the body site. The regression model was in good agreement with the simulated data ER (R(2)=0.988). Relative errors up to +20% and -10% were found in daily doses predictions, whereas an average relative error of only 2.4% (-0.03% to 5.4%) was found in yearly dose predictions. The regression model predicts accurately ER and UV doses on the basis of readily available data such as global UV erythemal irradiance measured at ground surface stations or inferred from satellite information. It renders the development of exposure data on a wide temporal and geographical scale possible and opens broad perspectives for epidemiological studies and skin cancer prevention.

J-shaped association between serum glucose and functional outcome in acute ischemic stroke.

BACKGROUND AND PURPOSE: Hyperglycemia after stroke is associated with larger infarct volume and poorer functional outcome. In an animal stroke model, the association between serum glucose and infarct volume is described by a U-shaped curve with a nadir ≈7 mmol/L. However, a similar curve in human studies was never reported. The objective of the present study is to investigate the association between serum glucose levels and functional outcome in patients with acute ischemic stroke. METHODS: We analyzed 1446 consecutive patients with acute ischemic stroke. Serum glucose was measured on admission at the emergency department together with multiple other metabolic, clinical, and radiological parameters. National Institutes of Health Stroke Scale (NIHSS) score was recorded at 24 hours, and Rankin score was recorded at 3 and 12 months. The association between serum glucose and favorable outcome (Rankin score ≤2) was explored in univariate and multivariate analysis. The model was further analyzed in a robust regression model based on fractional polynomial (-2-2) functions. RESULTS: Serum glucose is independently correlated with functional outcome at 12 months (OR, 1.15; P=0.01). Other predictors of outcome include admission NIHSS score (OR, 1.18; P<0001), age (OR, 1.06; P<0.001), prestroke Rankin score (OR, 20.8; P=0.004), and leukoaraiosis (OR, 2.21; P=0.016). Using these factors in multiple logistic regression analysis, the area under the receiver-operator characteristic curve is 0.869. The association between serum glucose and Rankin score at 12 months is described by a J-shaped curve with a nadir of 5 mmol/L. Glucose values between 3.7 and 7.3 mmol/L are associated with favorable outcome. A similar curve was generated for the association of glucose and 24-hour NIHSS score, for which glucose values between 4.0 and 7.2 mmol/L are associated with a NIHSS score <7. Discussion-Both hypoglycemia and hyperglycemia are dangerous in acute ischemic stroke as shown by a J-shaped association between serum glucose and 24-hour and 12-month outcome. Initial serum glucose values between 3.7 and 7.3 mmol/L are associated with favorable outcome.

Polinômios fracionários em modelos de regressão

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

HAART and the heart: changes in coronary risk factors and implications for coronary risk in men starting antiretroviral therapy

OBJECTIVES: To estimate changes in coronary risk factors and their implications for coronary heart disease (CHD) rates in men starting highly active antiretroviral therapy (HAART). METHODS: Men participating in the Swiss HIV Cohort Study with measurements of coronary risk factors both before and up to 3 years after starting HAART were identified. Fractional polynomial regression was used to graph associations between risk factors and time on HAART. Mean risk factor changes associated with starting HAART were estimated using multilevel models. A prognostic model was used to predict corresponding CHD rate ratios. RESULTS: Of 556 eligible men, 259 (47%) started a nonnucleoside reverse transcriptase inhibitor (NNRTI) and 297 a protease inhibitor (PI) based regimen. Levels of most risk factors increased sharply during the first 3 months on HAART, then more slowly. Increases were greater with PI- than NNRTI-based HAART for total cholesterol (1.18 vs. 0.98 mmol L(-1)), systolic blood pressure (3.6 vs. 0 mmHg) and BMI (1.04 vs. 0.55 kg m(2)) but not HDL cholesterol (0.24 vs. 0.32 mmol L(-1)) or glucose (1.02 vs. 1.03 mmol L(-1)). Predicted CHD rate ratios were 1.40 (95% CI 1.13-1.75) and 1.17 (0.95-1.47) for PI- and NNRTI-based HAART respectively. CONCLUSIONS: Coronary heart disease rates will increase in a majority of patients starting HAART: however the increases corresponding to typical changes in risk factors are relatively modest and could be offset by lifestyle changes.

Assessment of the effect on statistical power of regression model misspecification by using techniques of mathematical statistics and simulation study

Objectives. This paper seeks to assess the effect on statistical power of regression model misspecification in a variety of situations. ^ Methods and results. The effect of misspecification in regression can be approximated by evaluating the correlation between the correct specification and the misspecification of the outcome variable (Harris 2010).In this paper, three misspecified models (linear, categorical and fractional polynomial) were considered. In the first section, the mathematical method of calculating the correlation between correct and misspecified models with simple mathematical forms was derived and demonstrated. In the second section, data from the National Health and Nutrition Examination Survey (NHANES 2007-2008) were used to examine such correlations. Our study shows that comparing to linear or categorical models, the fractional polynomial models, with the higher correlations, provided a better approximation of the true relationship, which was illustrated by LOESS regression. In the third section, we present the results of simulation studies that demonstrate overall misspecification in regression can produce marked decreases in power with small sample sizes. However, the categorical model had greatest power, ranging from 0.877 to 0.936 depending on sample size and outcome variable used. The power of fractional polynomial model was close to that of linear model, which ranged from 0.69 to 0.83, and appeared to be affected by the increased degrees of freedom of this model.^ Conclusion. Correlations between alternative model specifications can be used to provide a good approximation of the effect on statistical power of misspecification when the sample size is large. When model specifications have known simple mathematical forms, such correlations can be calculated mathematically. Actual public health data from NHANES 2007-2008 were used as examples to demonstrate the situations with unknown or complex correct model specification. Simulation of power for misspecified models confirmed the results based on correlation methods but also illustrated the effect of model degrees of freedom on power.^

LOGITCPRPLOT: Stata module to graph component-plus-residual plot for logistic regression

logitcprplot can be used after logistic regression for graphing a component-plus-residual plot (a.k.a. partial residual plot) for a given predictor, including a lowess, local polynomial, restricted cubic spline, fractional polynomial, penalized spline, regression spline, running line, or adaptive variable span running line smooth

Algorithm to determine the intersection curves between bezier surfaces by the solution of multivariable polynomial system and the differential marching method

The determination of the intersection curve between Bézier Surfaces may be seen as the composition of two separated problems: determining initial points and tracing the intersection curve from these points. The Bézier Surface is represented by a parametric function (polynomial with two variables) that maps a point in the tridimensional space from the bidimensional parametric space. In this article, it is proposed an algorithm to determine the initial points of the intersection curve of Bézier Surfaces, based on the solution of polynomial systems with the Projected Polyhedral Method, followed by a method for tracing the intersection curves (Marching Method with differential equations). In order to allow the use of the Projected Polyhedral Method, the equations of the system must be represented in terms of the Bernstein basis, and towards this goal it is proposed a robust and reliable algorithm to exactly transform a multivariable polynomial in terms of power basis to a polynomial written in terms of Bernstein basis .

Discrete fractional order system vibrations

A theory of free vibrations of discrete fractional order (FO) systems with a finite number of degrees of freedom (dof) is developed. A FO system with a finite number of dof is defined by means of three matrices: mass inertia, system rigidity and FO elements. By adopting a matrix formulation, a mathematical description of FO discrete system free vibrations is determined in the form of coupled fractional order differential equations (FODE). The corresponding solutions in analytical form, for the special case of the matrix of FO properties elements, are determined and expressed as a polynomial series along time. For the eigen characteristic numbers, the system eigen main coordinates and the independent eigen FO modes are determined. A generalized function of visoelastic creep FO dissipation of energy and generalized forces of system with no ideal visoelastic creep FO dissipation of energy for generalized coordinates are formulated. Extended Lagrange FODE of second kind, for FO system dynamics, are also introduced. Two examples of FO chain systems are analyzed and the corresponding eigen characteristic numbers determined. It is shown that the oscillatory phenomena of a FO mechanical chain have analogies to electrical FO circuits. A FO electrical resistor is introduced and its constitutive voltage–current is formulated. Also a function of thermal energy FO dissipation of a FO electrical relation is discussed.

Efficient Legendre spectral tau algorithm for solving two-sided space-time Caputo fractional advection-dispersion equation

In this paper we present the operational matrices of the left Caputo fractional derivative, right Caputo fractional derivative and Riemann–Liouville fractional integral for shifted Legendre polynomials. We develop an accurate numerical algorithm to solve the two-sided space–time fractional advection–dispersion equation (FADE) based on a spectral shifted Legendre tau (SLT) method in combination with the derived shifted Legendre operational matrices. The fractional derivatives are described in the Caputo sense. We propose a spectral SLT method, both in temporal and spatial discretizations for the two-sided space–time FADE. This technique reduces the two-sided space–time FADE to a system of algebraic equations that simplifies the problem. Numerical results carried out to confirm the spectral accuracy and efficiency of the proposed algorithm. By selecting relatively few Legendre polynomial degrees, we are able to get very accurate approximations, demonstrating the utility of the new approach over other numerical methods.

Comparison of the polynomial model against explicit measurements of noise components for different mammography systems.

Given the adverse impact of image noise on the perception of important clinical details in digital mammography, routine quality control measurements should include an evaluation of noise. The European Guidelines, for example, employ a second-order polynomial fit of pixel variance as a function of detector air kerma (DAK) to decompose noise into quantum, electronic and fixed pattern (FP) components and assess the DAK range where quantum noise dominates. This work examines the robustness of the polynomial method against an explicit noise decomposition method. The two methods were applied to variance and noise power spectrum (NPS) data from six digital mammography units. Twenty homogeneously exposed images were acquired with PMMA blocks for target DAKs ranging from 6.25 to 1600 µGy. Both methods were explored for the effects of data weighting and squared fit coefficients during the curve fitting, the influence of the additional filter material (2 mm Al versus 40 mm PMMA) and noise de-trending. Finally, spatial stationarity of noise was assessed.Data weighting improved noise model fitting over large DAK ranges, especially at low detector exposures. The polynomial and explicit decompositions generally agreed for quantum and electronic noise but FP noise fraction was consistently underestimated by the polynomial method. Noise decomposition as a function of position in the image showed limited noise stationarity, especially for FP noise; thus the position of the region of interest (ROI) used for noise decomposition may influence fractional noise composition. The ROI area and position used in the Guidelines offer an acceptable estimation of noise components. While there are limitations to the polynomial model, when used with care and with appropriate data weighting, the method offers a simple and robust means of examining the detector noise components as a function of detector exposure.

Mathematical modelling and optimal multivariable control of chemical processes

This work reports the developnent of a mathenatical model and distributed, multi variable computer-control for a pilot plant double-effect climbing-film evaporator. A distributed-parameter model of the plant has been developed and the time-domain model transformed into the Laplace domain. The model has been further transformed into an integral domain conforming to an algebraic ring of polynomials, to eliminate the transcendental terms which arise in the Laplace domain due to the distributed nature of the plant model. This has made possible the application of linear control theories to a set of linear-partial differential equations. The models obtained have well tracked the experimental results of the plant. A distributed-computer network has been interfaced with the plant to implement digital controllers in a hierarchical structure. A modern rnultivariable Wiener-Hopf controller has been applled to the plant model. The application has revealed a limitation condition that the plant matrix should be positive-definite along the infinite frequency axis. A new multi variable control theory has emerged fram this study, which avoids the above limitation. The controller has the structure of the modern Wiener-Hopf controller, but with a unique feature enabling a designer to specify the closed-loop poles in advance and to shape the sensitivity matrix as required. In this way, the method treats directly the interaction problems found in the chemical processes with good tracking and regulation performances. Though the ability of the analytical design methods to determine once and for all whether a given set of specifications can be met is one of its chief advantages over the conventional trial-and-error design procedures. However, one disadvantage that offsets to some degree the enormous advantages is the relatively complicated algebra that must be employed in working out all but the simplest problem. Mathematical algorithms and computer software have been developed to treat some of the mathematical operations defined over the integral domain, such as matrix fraction description, spectral factorization, the Bezout identity, and the general manipulation of polynomial matrices. Hence, the design problems of Wiener-Hopf type of controllers and other similar algebraic design methods can be easily solved.