Estimation of Sample Size and Power For Quantile Regression

Quantile regression (QR) was first introduced by Roger Koenker and Gilbert Bassett in 1978. It is robust to outliers which affect least squares estimator on a large scale in linear regression. Instead of modeling mean of the response, QR provides an alternative way to model the relationship between quantiles of the response and covariates. Therefore, QR can be widely used to solve problems in econometrics, environmental sciences and health sciences. Sample size is an important factor in the planning stage of experimental design and observational studies. In ordinary linear regression, sample size may be determined based on either precision analysis or power analysis with closed form formulas. There are also methods that calculate sample size based on precision analysis for QR like C.Jennen-Steinmetz and S.Wellek (2005). A method to estimate sample size for QR based on power analysis was proposed by Shao and Wang (2009). In this paper, a new method is proposed to calculate sample size based on power analysis under hypothesis test of covariate effects. Even though error distribution assumption is not necessary for QR analysis itself, researchers have to make assumptions of error distribution and covariate structure in the planning stage of a study to obtain a reasonable estimate of sample size. In this project, both parametric and nonparametric methods are provided to estimate error distribution. Since the method proposed can be implemented in R, user is able to choose either parametric distribution or nonparametric kernel density estimation for error distribution. User also needs to specify the covariate structure and effect size to carry out sample size and power calculation. The performance of the method proposed is further evaluated using numerical simulation. The results suggest that the sample sizes obtained from our method provide empirical powers that are closed to the nominal power level, for example, 80%.

Hierarchical Reconstruction Method for Solving Ill-posed Linear Inverse Problems

We present a detailed analysis of the application of a multi-scale Hierarchical Reconstruction method for solving a family of ill-posed linear inverse problems. When the observations on the unknown quantity of interest and the observation operators are known, these inverse problems are concerned with the recovery of the unknown from its observations. Although the observation operators we consider are linear, they are inevitably ill-posed in various ways. We recall in this context the classical Tikhonov regularization method with a stabilizing function which targets the specific ill-posedness from the observation operators and preserves desired features of the unknown. Having studied the mechanism of the Tikhonov regularization, we propose a multi-scale generalization to the Tikhonov regularization method, so-called the Hierarchical Reconstruction (HR) method. First introduction of the HR method can be traced back to the Hierarchical Decomposition method in Image Processing. The HR method successively extracts information from the previous hierarchical residual to the current hierarchical term at a finer hierarchical scale. As the sum of all the hierarchical terms, the hierarchical sum from the HR method provides an reasonable approximate solution to the unknown, when the observation matrix satisfies certain conditions with specific stabilizing functions. When compared to the Tikhonov regularization method on solving the same inverse problems, the HR method is shown to be able to decrease the total number of iterations, reduce the approximation error, and offer self control of the approximation distance between the hierarchical sum and the unknown, thanks to using a ladder of finitely many hierarchical scales. We report numerical experiments supporting our claims on these advantages the HR method has over the Tikhonov regularization method.

Resource use and greenhouse gas emissions from grain-finishing beef cattle in seven Australian feedlots: a life cycle assessment

Grain finishing of cattle has become increasingly common in Australia over the past 30 years. However, interest in the associated environmental impacts and resource use is increasing and requires detailed analysis. In this study we conducted a life cycle assessment (LCA) to investigate impacts of the grain-finishing stage for cattle in seven feedlots in eastern Australia, with a particular focus on the feedlot stage, including the impacts from producing the ration, feedlot operations, transport, and livestock emissions while cattle are in the feedlot (gate-to-gate). The functional unit was 1 kg of liveweight gain (LWG) for the feedlot stage and results are included for the full supply chain (cradle-to-gate), reported per kilogram of liveweight (LW) at the point of slaughter. Three classes of cattle produced for different markets were studied: short-fed domestic market (55–80 days on feed), mid-fed export (108–164 days on feed) and long-fed export (>300 days on feed). In the feedlot stage, mean fresh water consumption was found to vary from 171.9 to 672.6 L/kg LWG and mean stress-weighted water use ranged from 100.9 to 193.2 water stress index eq. L/kg LWG. Irrigation contributed 57–91% of total fresh water consumption with differences mainly related to the availability of irrigation water near the feedlot and the use of irrigated feed inputs in rations. Mean fossil energy demand ranged from 16.5 to 34.2 MJ lower heating values/kg LWG and arable land occupation from 18.7 to 40.5 m2/kg LWG in the feedlot stage. Mean greenhouse gas (GHG) emissions in the feedlot stage ranged from 4.6 to 9.5 kg CO2-e/kg LWG (excluding land use and direct land-use change emissions). Emissions were dominated by enteric methane and contributions from the production, transport and milling of feed inputs. Linear regression analysis showed that the feed conversion ratio was able to explain >86% of the variation in GHG intensity and energy demand. The feedlot stage contributed between 26% and 44% of total slaughter weight for the classes of cattle fed, whereas the contribution of this phase to resource use varied from 4% to 96% showing impacts from the finishing phase varied considerably, compared with the breeding and backgrounding. GHG emissions and total land occupation per kilogram of LWG during the grain finishing phase were lower than emissions from breeding and backgrounding, resulting in lower life-time emissions for grain-finished cattle compared with grass finishing.

RELATIONSHIP BETWEEN COLUMN DENSITY AND SURFACE MIXING RATIO FOR O3 AND NO2: IMPLICATIONS FOR SATELLITE OBSERVATIONS AND THE IMPACTS OF VERTICAL MIXING

Satellites have great potential for diagnosis of surface air quality conditions, though reduced sensitivity of satellite instrumentation to the lower troposphere currently impedes their applicability. One objective of the NASA DISCOVER-AQ project is to provide information relevant to improving our ability to relate satellite-observed columns to surface conditions for key trace gases and aerosols. In support of DISCOVER-AQ, this dissertation investigates the degree of correlation between O3 and NO2 column abundance and surface mixing ratio during the four DISCOVER-AQ deployments; characterize the variability of the aircraft in situ and model-simulated O3 and NO2 profiles; and use the WRF-Chem model to further investigate the role of boundary layer mixing in the column-surface connection for the Maryland 2011 deployment, and determine which of the available boundary layer schemes best captures the observations. Simple linear regression analyses suggest that O3 partial column observations from future satellite instruments with sufficient sensitivity to the lower troposphere may be most meaningful for surface air quality under the conditions associated with the Maryland 2011 campaign, which included generally deep, convective boundary layers, the least wind shear of all four deployments, and few geographical influences on local meteorology, with exception of bay breezes. Hierarchical clustering analysis of the in situ O3 and NO2 profiles indicate that the degree of vertical mixing (defined by temperature lapse rate) associated with each cluster exerted an important influence on the shapes of the median cluster profiles for O3, as well as impacted the column vs. surface correlations for many clusters for both O3 and NO2. However, comparisons to the CMAQ model suggest that, among other errors, vertical mixing is overestimated, causing too great a column-surface connection within the model. Finally, the WRF-Chem model, a meteorology model with coupled chemistry, is used to further investigate the impact of vertical mixing on the O3 and NO2 column-surface connection, for an ozone pollution event that occurred on July 26-29, 2011. Five PBL schemes were tested, with no one scheme producing a clear, consistent “best” comparison with the observations for PBLH and pollutant profiles; however, despite improvements, the ACM2 scheme continues to overestimate vertical mixing.

Effect of investigation intensity and treatment differences on prostate cancer survivor's physical symptoms, psychological well-being and health-related quality of life: a two country cross-sectional study.

Aim: To investigate effects on men's health and well-being of higher prostate cancer (PCa) investigation and treatment levels in similar populations. Participants: PCa survivors in Ireland where the Republic of Ireland (RoI) has a 50% higher PCa incidence than Northern Ireland (NI). Method: A cross-sectional postal questionnaire was sent to PCa survivors 2–18 years post-treatment, seeking information about current physical effects of treatment, health-related quality of life (HRQoL; EORTC QLQ-C30; EQ-5D-5L) and psychological well-being (21 question version of the Depression, Anxiety and Stress Scale, DASS-21). Outcomes in RoI and NI survivors were compared, stratifying into ‘late disease’ (stage III/IV and any Gleason grade (GG) at diagnosis) and ‘early disease’ (stage I/II and GG 2–7). Responses were weighted by age, jurisdiction and time since diagnosis. Between-country differences were investigated using multivariate logistic and linear regression. Results: 3348 men responded (RoI n=2567; NI n=781; reflecting population sizes, response rate 54%). RoI responders were younger; less often had comorbidities (45% vs 38%); were more likely to present asymptomatically (66%; 41%) or with early disease (56%; 35%); and less often currently used androgen deprivation therapy (ADT; 2%; 28%). Current prevalence of incontinence (16%) and impotence (56% early disease, 67% late disease) did not differ between RoI and NI. In early disease, only current bowel problems (RoI 12%; NI 21%) differed significantly in multivariate analysis. In late disease, NI men reported significantly higher levels of gynaecomastia (23% vs 9%) and hot flashes(41% vs 19%), but when ADT users were analysed separately, differences disappeared. For HRQoL, in multivariate analysis, only pain (early disease: RoI 11.1, NI 19.4) and financial difficulties (late disease: RoI 10.4, NI 7.9) differed significantly between countries. There were no significant between-country differences in DASS-21 or index ED-5D-5L score. Conclusions: Treatment side effects were commonly reported and increased PCa detection in RoI has left more men with these side effects. We recommended that men be offered a PSA test only after informed discussion.

Adapting The Sniffin' Sticks Olfactory Test To Diagnose Parkinson's Disease In Estonia.

The aim of the study was to develop a culturally adapted translation of the 12-item smell identification test from Sniffin' Sticks (SS-12) for the Estonian population in order to help diagnose Parkinson's disease (PD). A standard translation of the SS-12 was created and 150 healthy Estonians were questioned about the smells used as response options in the test. Unfamiliar smells were replaced by culturally familiar options. The adapted SS-12 was applied to 70 controls in all age groups, and thereafter to 50 PD patients and 50 age- and sex-matched controls. 14 response options from 48 used in the SS-12 were replaced with familiar smells in an adapted version, in which the mean rate of correct response was 87% (range 73-99) compared to 83% with the literal translation (range 50-98). In PD patients, the average adapted SS-12 score (5.4/12) was significantly lower than in controls (average score 8.9/12), p < 0.0001. A multiple linear regression using the score in the SS-12 as the outcome measure showed that diagnosis and age independently influenced the result of the SS-12. A logistic regression using the SS-12 and age as covariates showed that the SS-12 (but not age) correctly classified 79.0% of subjects into the PD and control category, using a cut-off of <7 gave a sensitivity of 76% and specificity of 86% for the diagnosis of PD. The developed SS-12 cultural adaption is appropriate for testing olfaction in Estonia for the purpose of PD diagnosis.

Relationship Between Orofacial Function, Dentofacial Morphology, And Bite Force In Young Subjects.

The aim was to evaluate the relationship between orofacial function, dentofacial morphology, and bite force in young subjects. Three hundred and sixteen subjects were divided according to dentition stage (early, intermediate, and late mixed and permanent dentition). Orofacial function was screened using the Nordic Orofacial Test-Screening (NOT-S). Orthodontic treatment need, bite force, lateral and frontal craniofacial dimensions and presence of sleep bruxism were also assessed. The results were submitted to descriptive statistics, normality and correlation tests, analysis of variance, and multiple linear regression to test the relationship between NOT-S scores and the studied independent variables. The variance of NOT-S scores between groups was not significant. The evaluation of the variables that significantly contributed to NOT-S scores variation showed that age and presence of bruxism related to higher NOT-S total scores, while the increase in overbite measurement and presence of closed lip posture related to lower scores. Bite force did not show a significant relationship with scores of orofacial dysfunction. No significant correlations between craniofacial dimensions and NOT-S scores were observed. Age and sleep bruxism were related to higher NOT-S scores, while the increase in overbite measurement and closed lip posture contributed to lower scores of orofacial dysfunction.

Exploratory Study Of The Effect Of Lifestyle Counselling On Bone Mineral Density And Body Composition In Users Of The Contraceptive Depot-medroxyprogesterone Acetate.

To compare variations in bone mineral density (BMD) and body composition (BC) in depot-medroxyprogesterone acetate (DMPA) users and nonusers after providing counselling on healthy lifestyle habits. An exploratory study in which women aged 18 to 40 years participated: 29 new DMPA users and 25 new non-hormonal contraceptive users. All participants were advised on healthy lifestyle habits: sun exposure, walking and calcium intake. BMD and BC were assessed at baseline and 12 months later. Statistical analysis included the Mann-Whitney test or Student's t-test followed by multiple linear regression analysis. Compared to the controls, DMPA users had lower BMD at vertebrae L1 and L4 after 12 months of use. They also had a mean increase of 2 kg in total fat mass and an increase of 2.2% in body fat compared to the non-hormonal contraceptive users. BMD loss at L1 was less pronounced in DMPA users with a calcium intake ≥ 1 g/day compared to DMPA users with a lower calcium intake. DMPA use was apparently associated with lower BMD and an increase in fat mass at 12 months of use. Calcium intake ≥ 1 g/day attenuates BMD loss in DMPA users. Counselling on healthy lifestyle habits failed to achieve its aims.

Evolution Of The Deaths Registry System In Brazil: Associations With Changes In The Mortality Profile, Under-registration Of Death Counts, And Ill-defined Causes Of Death.

This paper examines the spatial pattern of ill-defined causes of death across Brazilian regions, and its relationship with the evolution of completeness of the deaths registry and changes in the mortality age profile. We make use of the Brazilian Health Informatics Department mortality database and population censuses from 1980 to 2010. We applied demographic methods to evaluate the quality of mortality data for 137 small areas and correct for under-registration of death counts when necessary. The second part of the analysis uses linear regression models to investigate the relationship between, on the one hand, changes in death counts coverage and age profile of mortality, and on the other, changes in the reporting of ill-defined causes of death. The completeness of death counts coverage increases from about 80% in 1980-1991 to over 95% in 2000-2010 at the same time the percentage of ill-defined causes of deaths reduced about 53% in the country. The analysis suggests that the government's efforts to improve data quality are proving successful, and they will allow for a better understanding of the dynamics of health and the mortality transition.

Storage At Low Temperature Differentially Affects The Colour And Carotenoid Composition Of Two Cultivars Of Banana.

Different storage conditions can induce changes in the colour and carotenoid profiles and levels in some fruits. The goal of this work was to evaluate the influence of low temperature storage on the colour and carotenoid synthesis in two banana cultivars: Prata and Nanicão. For this purpose, the carotenoids from the banana pulp were determined by HPLC-DAD-MS/MS, and the colour of the banana skin was determined by a colorimeter method. Ten carotenoids were identified, of which the major carotenoids were all-trans-lutein, all-trans-α-carotene and all-trans-β-carotene in both cultivars. The effect of the low temperatures was subjected to linear regression analysis. In cv. Prata, all-trans-α-carotene and all-trans-β-carotene were significantly affected by low temperature (p<0.01), with negative estimated values (β coefficients) indicating that during cold storage conditions, the concentrations of these carotenoids tended to decrease. In cv. Nanicão, no carotenoid was significantly affected by cold storage (p>0.05). The accumulation of carotenoids in this group may be because the metabolic pathways using these carotenoids were affected by storage at low temperatures. The colour of the fruits was not negatively affected by the low temperatures (p>0.05).

Clinical Influence Of Different Intracanal Medications On Th1-type And Th2-type Cytokine Responses In Apical Periodontitis.

This clinical study assessed the influence of different intracanal medications on Th1-type and Th2-type cytokine responses in apical periodontitis and monitored the levels of bacteria from primarily infection during endodontic procedures. Thirty primarily infected teeth were randomly divided into 3 groups according to the medication selected: chlorhexidine (CHX), 2% CHX gel; Ca(OH)2/SSL, Ca(OH)2 + SSL; and Ca(OH)2/CHX, Ca(OH)2 + 2% CHX gel (all, n = 10). Bacterial sample was collected from root canals, and the interstitial fluid was sampled from lesions. Culture techniques were used to determine bacterial counts (colony-forming units/mL). Th1 (tumor necrosis factor-α, interferon-γ, and interleukin [IL]-2) and Th2 cytokines (IL-4, IL-5, and IL-13) were measured by enzyme-linked immunosorbent assay. All intracanal medication protocols were effective in reducing the bacterial load from root canals (all P < .05) and lowering the levels of Th1-type cytokines in apical lesions (all P < .05), with no differences between them (P > .05). Both Ca(OH)2 treatment protocols significantly increased the levels of Th2-type cytokines (P < .05), with no differences between them (P > .05). Thus, chlorhexidine medication showed the lowest effectiveness in increasing the levels of Th2-type cytokine. After treatment, regardless of the type of medication, the linear regression analysis indicated the down-regulation of Th2-type cytokines by Th1-type cytokines. All intracanal medication protocols were effective in reducing bacterial load and lowering the levels of Th1-type cytokines. Thus, the use of Ca(OH)2 medications contributed to the increase in the Th2-type cytokine response in apical periodontitis.

Estatística aplicada à química: dez dúvidas comuns

Ten common doubts of chemistry students and professionals about their statistical applications are discussed. The use of the N-1 denominator instead of N is described for the standard deviation. The statistical meaning of the denominators of the root mean square error of calibration (RMSEC) and root mean square error of validation (RMSEV) are given for researchers using multivariate calibration methods. The reason why scientists and engineers use the average instead of the median is explained. Several problematic aspects about regression and correlation are treated. The popular use of triplicate experiments in teaching and research laboratories is seen to have its origin in statistical confidence intervals. Nonparametric statistics and bootstrapping methods round out the discussion.

Modelos de regressão lineares para estimativa de produtividade da soja no oeste do Paraná, utilizando dados espectrais

The main objective of this work was to evaluate the linear regression between spectral response and soybean yield in regional scale. In this study were monitored 36 municipalities from the west region of the states of Parana using five images of Landsat 5/TM during 2004/05 season. The spectral response was converted in physical values, apparent and surface reflectances, by radiometric transformation and atmospheric corrections and both used to calculate NDVI and GVI vegetation indices. Those ones were compared by multiple and simple regression with government official yield values (IBGE). Diagnostic processing method to identify influents values or collinearity was applied to the data too. The results showed that the mean surface reflectance value from all images was more correlated with yield than individual dates. Further, the multiple regressions using all dates and both vegetation indices gave better results than simple regression.

Determinação do máximo déficit acumulado de oxigênio: efeito da duração dos testes submáximos para predição da demanda de oxigênio

The aim of this study was to investigate the influence of different assessment time periods of submaximal tests on the determination of the maximal accumulated oxygen deficit (MAOD), through the adoption of different time slots of 4 to 6, 6 to 8 and 8 to 10 min. Ten cyclists with mean age of 27.5 ± 4.1 years, body mass 74.4 ± 12.7 kg and time experience of 9.8 ± 4.7 years participated in this study. The athletes underwent an incremental exercise test to determine the peak oxygen consumption (VO2peak), and four submaximal constant work-load test sessions (60, 70, 80 and 90% VO2peak) of 10 min in order to estimate the O2 demand (DEO2). The mean VO2 values obtained on each constant work-load for the 4 to 6, 6 to 8 and 8 to 10 min time-periods intervals were used to perform a linear regression between the intensity and O2 consumption for each time-period. In addition, the subjects performed one supramaximal rectangular test (110% VO2peak) for the quantification of MAOD. There was no significant difference in VO2 between the different time-periods for all submaximal tests (P> 0.05). Similarly, no significant difference was found in DEAO2 and MAOD (P> 0.05). Furthermore, the values of MAOD for the three time-periods intervals showed good agreement and strong correlation. Thus, the data suggest that the submaximal tests used to estimate the values of MAOD can be reduced, at least in this type of sample, and with the use of a cycle simulator.

Patient education in glaucoma: what do patients know about glaucoma?

PURPOSE: To evaluate the knowledge glaucoma patients have about their disease and its treatment. METHODS: One hundred and eighty-three patients were interviewed at the Glaucoma Service of Wills Eye Hospital (Philadelphia, USA, Group 1) and 100 at the Glaucoma Service of University of Campinas (Campinas, Brazil, Group 2). An informal, relaxed atmosphere was created by the interviewer before asking a list of 18 open-ended questions. RESULTS: In Group 1, 44% of the 183 patients did not have an acceptable idea about what glaucoma is, 30% did not know the purpose of the medications they were taking, 47% were not aware of what was an average intraocular pressure, and 45% did not understand why visual fields were examined. In Group 2, 54% gave unsatisfactory answers to the question What is glaucoma?, 54% did not know the purpose of the medications they were taking, 80% were not aware of what was an average intraocular pressure, and 94% did not understand why visual fields were examined (p<0.001). Linear regression analysis demonstrated that level of education was positively correlated to knowledge about glaucoma in both groups (r=0.65, p=0.001). CONCLUSION: This study showed that patients' knowledge about glaucoma varies greatly, and that in an urban, American setting, around one third of the patients have minimal understanding, whereas in an urban setting in Brazil around two thirds of patients were lacking basic information about glaucoma. Innovative and effective methods are needed to correct this situation.