R-squared Statistic Research Articles

Applying diagnosis and pharmacy-based risk models to predict pharmacy use in Aragon, Spain: The impact of a local calibration

BackgroundIn the financing of a national health system, where pharmaceutical spending is one of the main cost containment targets, predicting pharmacy costs for individuals and populations is essential for budget planning and care management. Although most efforts have focused on risk adjustment applying diagnostic data, the reliability of this information source has been questioned in the primary care setting. We sought to assess the usefulness of incorporating pharmacy data into claims-based predictive models (PMs). Developed primarily for the U.S. health care setting, a secondary objective was to evaluate the benefit of a local calibration in order to adapt the PMs to the Spanish health care system.MethodsThe population was drawn from patients within the primary care setting of Aragon, Spain (n = 84,152). Diagnostic, medication and prior cost data were used to develop PMs based on the Johns Hopkins ACG methodology. Model performance was assessed through r-squared statistics and predictive ratios. The capacity to identify future high-cost patients was examined through c-statistic, sensitivity and specificity parameters.ResultsThe PMs based on pharmacy data had a higher capacity to predict future pharmacy expenses and to identify potential high-cost patients than the models based on diagnostic data alone and a capacity almost as high as that of the combined diagnosis-pharmacy-based PM. PMs provided considerably better predictions when calibrated to Spanish data.ConclusionUnderstandably, pharmacy spending is more predictable using pharmacy-based risk markers compared with diagnosis-based risk markers. Pharmacy-based PMs can assist plan administrators and medical directors in planning the health budget and identifying high-cost-risk patients amenable to care management programs.

Distribution of natural radionuclides in anthrosol-type soil

Taking into account the importance of distribution and transfer of radionuclides in the soil-water-plant system, especially in agricultural fields, in this study, natural radionuclide determination in regosol-type soil was performed. The correlations between main soil properties and the contents of natural isotopes ^{238}U, ^{226}Ra, ^{232}Th, and ^{40}K in agricultural soil and their distribution through the soil depth was studied. For determination of natural radionuclide activity concentration, we used the CANBERRA HPGe detector, applying the gamma spectrometry method. The investigation was performed on an experimental peach tree field characterized by a anthrosol type of soil, derived from the chernozem type of natural soil. The effect of measured soil properties on activity concentration levels was analyzed by simple and multiple linear regression analysis. Considering the linear model, in our soil profiles of 0-80 cm depth, clay content was positively related with ^{238}U, ^{226}Ra, and ^{40}K, and about 30% of the variation of those radionuclides was explained. Sand fraction was negatively related with ^{238}U, ^{226}Ra, ^{232}Th, and ^{40}K and the correlation was medium, except for ^{226}Ra (r = -0.68). The joint effect of pH, carbonates, humus, clay, and sand contents on natural radionuclide distribution in the 0-80 cm layer was found by multiple linear regression analysis. Radionuclide behavior was explained by the R-squared statistic. The investigations of uranium distribution showed that when the soil layers of 0-20 cm and 60-80 cm are considered together, uranium behavior is affected by soil pH and the content of humus, carbonates, and clay. Multiple regression analysis of ^{226}Ra, ^{232}Th, and ^{40}K activities in soil layers of 0-20 cm and 60-80 cm showed that their lower mobility and uniform depth distribution are associated with small variations of carbonates along soil depth and mineral composition of the parent materials, while the soil pH had no effect on their behavior.

Activation and Perceived Expectancies: Correlations with Health Outcomes Among Veterans with Inflammatory Bowel Disease

Inflammatory bowel disease imposes psychosocial stress on the patient. Patients' adaptive capacities may predict quality of life. We examined two adaptive capacity measures and their association with quality of life. Cross-sectional mail survey of patients with inflammatory bowel disease. The Patient Activation Measure (PAM) assesses knowledge, skill, and confidence in self-health management. The Perceived Expectancies Index (PEI) measures perceived competence and dispositional optimism. Four hundred and seventy-seven veterans at VA-Tennessee Valley Healthcare System. Primary outcome was health-related quality of life (measured by the Short Inflammatory Bowel Disease Questionnaire). Bivariate analysis assessed unadjusted correlations. Sequential multivariate linear regression tested theoretical model relationships by calculating the variation in each dependent variable accounted for by independent variables (R-squared statistic). Two hundred and sixty surveys were returned with usable data (54.5%). Median age was 63 years (range 19-91); 90.8% were men and 86.9% self-identified as white. Fifty percent reported having ulcerative colitis, 36.5% Crohn's disease, and 12.3% uncertain type. Unadjusted bivariate analysis revealed positive correlations between the PAM and PEI and the Short Inflammatory Bowel Disease Questionnaire (correlation coefficient = 0.35 and 0.60, respectively; p < 0.0001). Multivariate model including the PAM accounted for 26% of the variation in Short Inflammatory Bowel Disease Questionnaire scores, while the model including the PEI accounted for 50% (p < 0.0001). There are positive, highly significant correlations between adaptive capacities and health-related quality of life in patients with inflammatory bowel disease.

International Staging System (ISS) Is Superior to Durie-Salmon (DS) Staging in Predicting Overall Mortality in Multiple Myeloma (MM)

Background: Despite recent therapeutic advancements, multiple myeloma (MM) remains an incurable disorder. Disease stage is the most commonly used parameter to determine tumor burden, need for treatment initiation and survival outcome. In this context the International Staging System (ISS) proposed in 2005 is considered a good predictor of overall survival (OS) and is reported to be more objective than the previous Durie-Salmon staging system (DSS). To date there has been no direct comparison to determine which of these is superior in predicting OS or mortality. Furthermore, ISS was defined prior to the routine availability of novel agents and primarily included MM patients who had undergone autologous stem cell transplant. Whether ISS has similar predictive value in non-transplant patients has not been reported. We investigated the ability to predict OS and mortality of these two staging systems in non-transplant patients with MM.Methods: All MM patients seen at RPCI between January 2004 and June 2007 were included in the analysis. Clinical staging was done as per the DSS and ISS in all patients. Descriptive baseline demographic data and survival data were collected. A 0.05 nominal significance level was used in all hypothesis testing.Results: A total of 170 consecutive patients were evaluated. None of the patients had undergone a stem cell transplant for their MM diagnosis. Survival data was available on 144 patients which are reported in this analysis. Of these 48% (n=69) were females and 52% (n=75) were males, with a median age of 60 years (range 35–83). The DSS revealed a distribution as follows: stage IA (21; 14.6%), stage IB (1; 0.7%), stage IIA (23; 16%), stage IIB (1; 0.7%), stage IIIA (81; 56.2%) and stage IIIB (17; 11.8%). The distribution as per ISS was stage I (76; 52.8%), stage II (31; 21.5%) and stage III (37; 25.7%). A Cox proportional hazards model was fit to compute a generalized R-square (Gen R2) statistic for the two staging systems and to compute hazard ratios (HR). The Gen R2 for DSS was 0.0259, while for ISS was 0.0461. Thus, by themselves, the two staging systems were not particularly predictive of OS. Comparison was then made by separating stage III (advanced stage disease) from stage I and II for both DSS and ISS. The estimated hazard of death for DSS I/II patients was not significantly different from the estimated hazard of death for DSS III patients (HR=0.48; 95% CI 0.2,1.14; p=0.09), while the estimated hazard of death for ISS I/II patients was significantly different from that for ISS III patients (HR=0.43; 95% CI 0.21,0.85; p=0.01). Exact odds ratios (OR) were computed between dichotomized DSS or ISS stage with patient status at years 1, 2 and 3 of follow up. Survival analysis at 1-year, 2-year and 3-year time point included 112, 93 and 77 patients, respectively. At 1-year, the sample odds of death for stage I/II patients were significantly different from the sample odds of death for stage III patients in both, the DSS (OR=0.32; 95% CI 0.1,0.93; p=0.02) and ISS (OR=0.25; 95% CI 0.08,0.25; p=0.005). At 2-year as well, this difference was significant for both, DSS (OR=0.32; 95% CI 0.1,0.98; p=0.03) and ISS (OR=0.18; 95% CI 0.06,0.63; p=0.002). At 3-year though, the DSS was no longer able to predict a significant difference in the sample odds of death between stage I/II and stage III patients (OR=0.4; 95% CI 0.11,1.34; p=0.11), while the sample odds of death as per the ISS were still significantly different (OR=0.21; 95% CI 0.04, 0.78; p=0.01).Conclusions: Our data from a prospective large cohort of non-transplant MM patients suggests that ISS is more predictive of overall mortality than the DSS. Furthermore, when comparing advanced stage disease (stage III) with early-stage disease (stage I/II), the DSS may only be able to predict short-term survival, while ISS is able to effectively predict survival over a prolonged period. [Display omitted]

MULTIVARIATE ANALYSIS FOR EVALUATING SESAME YIELD AND ITS CONTRIBUTING FACTORS

Two field experiments were carried out in a commercial field at Abo Rawash village, Giza governorate, Egypt during 2004 and 2005 seasons to compare five statistical procedures including: simple correlation, path analysis, multiple linear regression, stepwise regression and factor analysis in determining the relationship between sesame seed yield and its contributing traits. Thirty sesame genotypes were used for this purpose. The studied characters were: flowering date, plant height, number of fruiting branches, stem height to the first capsule, fruiting zone length, number of capsules on main stem, number of capsules per plant, capsule density on main stem, 1000-seed weight and seed yield per plant. The simple correlation coefficients and path analysis of yield components revealed that components with the highest positive correlation to yield also had the highest positive direct effect to yield i.e., number of capsules on main stem and number of capsules per plant. Path analysis showed that, the residual effect (0.433) was high in magnitude which shows that some other important yield contributing characters which contribute to yield have to be included. Stepwise multiple regression analysis showed that 77.25% of the total variation in seed yield could be explained by the variation in number of capsules per plant and flowering date in sesame. The linear regression equation was (Y) = 10.951 - 0.110 X1 + 0.114 X7, where Y, X1 and X7 represent seed yield per plant, flowering date and number of capsules per plant, respectively. Besides, coefficient of determination (R2), adjusted R-squared statistic and standard error of estimate values, mean absolute error (MAE) and Durbin-Watson (DW) statistic test showed no significant differences between the full model regression and stepwise multiple regression analysis technique. However, the efficiency expressed is due to the reduction in number of variables in the fitted model from all variables (full model regression) to two variables only (stepwise multiple regression). Factor analysis indicated that three factors could explain approximately 81.9% of the total variation. The first factor which accounted for about 41% of the variation was strongly associated with fruiting zone length, number of capsules on main stem, number of capsules per plant, and capsule density. The second factor which accounts for about 25% of the variation, was strongly associated and positive effects on days to flowering, 1000-seed weight, plant height and stem height to the first capsule, whereas the third factor had positive effects on number of fruiting branches only, which accounts for about 16% of the variation. Factor analysis technique was more efficient than other used statistical techniques. It provides more information about cluster of inter-correlated variables. It could be concluded that the five of statistical analysis techniques, agreed upon that high yield of sesame plants could be obtained by selecting breeding materials with high number of capsules on main stem, number of capsules per plant, plant height and increasing capsule density on the main stem.

Optimal statistical model for forecasting ozone

The objective of this paper is to apply time series analysis and multiple regression method to ozone data in order to obtain the optimal statistical model for forecasting next day ozone level. The best estimated model is then used to produce one-step ahead point and interval estimates of future values of the ozone series. Ozone data is analyzed using time series analysis, which resulted in an Auto Regressive Moving Average, ARMA (20, 2) with Mean Absolute Percentage Error (MAPE)=42%. Applying multiple regression method and examination of several possible contributing factors, showed that Wind speed, Mixing height where the complex chemical reactions that produce ozone take place, current and predicted next day temperatures and current ozone concentration are influential on the next day ozone concentration levels. Diagnostics tests and statistics including R-square, residual analysis and Durbin-Watson Statistic (DW) were applied in order to select the best fitted model and finally the best prediction model was found using MAPE and Mean Absolute Deviation (MAD) as predictive criteria. Regression analysis of this data, using tomorrow's and today's maximum temperature, today's wind speed and tomorrow's maximum height at 10 am, as explanatory variables results in R-square of 50.7% with MAD=12.423, MAPE=30% and DW=1.66

Genomic characterization of multiple clinical phenotypes of cancer using multivariate linear regression models

The development of gene expression microarray technology has allowed the identification of differentially expressed genes between different clinical phenotypic classes of cancer from a large pool of candidate genes. Although many class comparisons concerned only a single phenotype, simultaneous assessment of the relationship between gene expression and multiple phenotypes would be warranted to better understand the underlying biological structure. We develop a method to select genes related to multiple clinical phenotypes based on a set of multivariate linear regression models. For each gene, we perform model selection based on the doubly-adjusted R-square statistic and use the maximum of this statistic for gene selection. The method can substantially improve the power in gene selection, compared with a conventional method that uses a single model exclusively for gene selection. Application to a bladder cancer study to correlate pre-treatment gene expressions with pathological stage and grade is given. The methods would be useful for screening for genes related to multiple clinical phenotypes. SAS and MATLAB codes are available from author upon request.

Avoiding pitfalls of correlation coefficients in the assessment of measurement instruments in rehabilitation research.

To provide a practical guide on how to avoid the pitfalls of correlated correlation coefficients when comparing multiple instruments in rehabilitation research. An observational study comparing a number of instruments measuring quality of life (QoL) compared with an external criterion. Sixty-eight patients admitted to a rheumatology ward for intensive treatment of rheumatoid arthritis. Patients completed three new (QoL) instruments and an established instrument before and after intensive treatment for rheumatoid arthritis. Correlation coefficients together with their confidence intervals and a test for the difference between a set of correlated correlation coefficients for the change in the EuroQoL Quality of Life scale (EuroQoL), the World Health Organization Quality Of Life-Abbreviated version (WHOQoL-BREF) and the Quality of Life Profile (QLP) against the Stanford Health Assessment Questionnaire (HAQ). Although the range of correlation between the new instruments and the external criterion was between -0.37 and -0.59 and suggested that one new instrument was far more responsive than the others,; an omnibus test for an overall difference could find no difference in responsiveness. It is conceptually simple to use correlation coefficients to assess the properties of multiple instruments measured on the same subjects to find a 'best' instrument. However, proper interpretation of results when correlated correlation coefficients are calculated is complex. We recommend analysis includes: (a) that simple plots of the pairs of analysed variables are shown, (b) that simple linear model-fitting statistics, e.g., the R-squared statistic, accompany the plots, (c) that confidence intervals are presented for correlation coefficients, (d) that an omnibus statistical test for the difference between correlated correlation coefficients is presented, and (e) that normal model assumptions are tested.

Stock Price Synchronicity and Analyst Coverage in Emerging Markets

This paper examines the relationship between the stock price synchronicity and analyst activity in emerging markets. Contrary to conventional wisdom that suggests that security analysts specialize in the production of firm-specific information, we find that the security analysts predominantly produce market-wide information. Using the R-square statistics of the market model as a measure of the synchronicity of stock price movements, we find that more analyst coverage leads to an increase in stock price synchronicity. Furthermore, after controlling for the influence of firm size on the lead-lag relation, we find that returns on high analyst-following portfolio lead returns on low analyst-following portfolio more than vice versa. We also find that the aggregate changes in the earnings forecast of high analyst-following portfolio affect the aggregate returns of the portfolio itself as well as the the low analyst-following portfolio while the aggregate changes in the earnings forecasts of low analyst-following portfolio have no predictive ability. Finally, when the forecast dispersion is high, the effect of analyst coverage on stock price synchronicity is reduced.

Multiple regression modelling of mineral base oil biodegradability based on their physical properties and overall chemical composition

A set of 38 mineral base oils was characterized by a number of chemical (i.e., overall chemical composition) and physical parameters used routinely in industry. Their primary biodegradability was evaluated using the CEC L-33-A-93 test. Multiple (stepwise) linear regression (MLR) analyses were performed to describe the relationships between the biodegradability values and the chemical or physical properties of oils. Chemical, physical, and both types of parameters were successively used as independent variables. Using chemical descriptors as variables, a four-variable model equation was obtained that explained only 68.2% (adjusted R-squared statistic=68.2%) of the variability in biodegradability. The fitting was improved by using either the physical or the whole parameters as variables. MLR analyses led to three-descriptor model equations involving kinematic viscosity (as log), Noack volatility (as log) and either the viscosity index (pure physical model) or the paraffinic carbon percentage (mixed chemical–physical model). These two models displayed very similar adjusted R-squared statistics, of approximately 91%. Their predicting ability was verified using 25 additional base oils or oil blends. For 80% of oils on a total of 63, the absolute percentage error on biodegradability predicted by either model was lower than 20%. Kinematic viscosity was by far the most influential parameter in the two models.

Land surface albedo retrieval via kernel-based BRDF modeling: II. An optimal design scheme for the angular sampling

In this paper, we address some fundamental issues regarding the strategy of inversion of the class of the bi-directional reflectance distribution function (BRDF) models known as kernel-based. We examine two main causes of uncertainty affecting the predicted reflectance values. They are a contribution of the random noise term in the measurements and the model residual after adjustment. For this purpose, we formulate notions of both the experimental design for angular sampling and the kernel response function for an arbitrary set of angular measurements. The Fisher informative matrix is considered to circumscribe the optimal design problem to search for the best angular sampling. Two approaches are presented and discussed: one relates to the random noise term of the BRDF model and is independent on the land cover type (LCT); the other is impacted by the residual term of the BRDF model and is determined by the reflectance peculiarities of the different LCTs. Additionally, we explore the residual terms as a function of the LCT and we analyze the sensitivity of the reflectance predicted by the various BRDF models to the kernel response function. This is achieved by segregating regions of the angular domain that are most responsive to the measurement noise. We further determined the optimal angular sampling distribution for ground-based multi-angular data sets over different LCT and known residual terms. Then, we extend it to the more general case, ignoring the residual term. It is shown that the functions that are associated with the chosen criteria saturate after the selection of five or six observing geometries. These inversion experiments in BRDF modeling confirm the efficiency of certain angular data sets as a solution to the optimal design problem in relation to the negative influence of the redundancy effect of observations. This effect arises from having an excessive number of angular measurements in relation to the number of retrieved parameters. Another manner to prove the optimal design validity is by statistical diagnosis. We carried out a diagnosis study based on the residual standard deviation, the Fisher and R-square statistics. A fast convergence rate is observed with angular measurements determined by the optimal design.

A Statistical Technique for the Development of an Alternate List When Using Constrained Optimization to Make Admission Decisions

Background: In an earlier study it was demonstrated that constrained optimization could be used to accurately translate admission goals. Constrained optimization differs from weighting equations in that it does not assign a rank ordering. Although constrained optimization is conceptually superior, some procedures within the admissions process require a rank ordering of applicants. Purpose: The purpose of this study is to describes and evaluate the use of two discriminant analysis procedures to obtain a rank order list by generating weights that model constrained optimization procedures. This study also evaluates the usefulness of an additional method that does not require a rank ordering. Methods: Premium Solvera selected a class from the 1998/99 applicant pool. A discriminant analysis was used to generate a discriminant function for modeling the dichotomous group classification selection variable. These weights were then applied and the discriminant function values calculated. The success of the procedure was evaluated by examining rank orders and the magnitude of the correlation and R-square statistic. Results: Discriminant analysis accounted for 70% of the decision variance generated by the constrained optimization procedure. Using real data allowed an estimate of the number of students impacted by inconsistent outcomes. Conclusion: Discriminant analysis could be used to manage an alternate list, however it will be based on somewhat different criteria than the initial selection procedure. Each method evaluated has advantages and disadvantages and the selection of one method over another depends on what outcomes are most valued by the college.

A methodology for fitting and validating metamodels in simulation

This paper proposes a methodology that replaces the usual ad hoc approach to metamodeling. This methodology considers validation of a metamodel with respect to both the underlying simulation model and the problem entity. It distinguishes between fitting and validating a metamodel, and covers four types of goal: (i) understanding, (ii) prediction, (iii) optimization, and (iv) verification and validation. The methodology consists of a metamodeling process with 10 steps. This process includes classic design of experiments (DOE) and measuring fit through standard measures such as R-square and cross-validation statistics. The paper extends this DOE to stagewise DOE, and discusses several validation criteria, measures, and estimators. The methodology covers metamodels in general (including neural networks); it also gives a specific procedure for developing linear regression (including polynomial) metamodels for random simulation.

Unit Trusts in Singapore: Degree of Diversification

This study examines the degree of diversification of the funds in Singapore. The R-square statistic was employed as a measure for the degree of diversification. The findings generally indicated that the local funds were not well-diversified. Various explanations are given to account for this low level of diversification, as indicated by a low R-square statistic. This study also addresses some definitional and conceptual issues relating to diversification that affect the propriety of using the R-square statistic as a measure of diversification. More specifically, Markowitz’s Modern Portfolio Theory is introduced to illustrate the difference between naive and efficient diversification.

Utilization of image processing to quantitate surface metmyoglobin on fresh beef

Ground beef patties were manufactured with various combinations of ascorbic acid and mechanically recovered neck bone lean (MRNL) to study the use of image processing in predicting percentage surface metmyoglobin (metMb) on fresh beef. Ascorbic acid and MRNL cause various color phenomena that resulted in a wide range of variation in surface color. Patties were also stored over six days of retail display to cause further color changes. Surface color was assessed by several different accepted methods. A prediction equation for percentage surface metMb included mean values for hue, saturation and intensity. Root mean square error, R-square and Mallow's Cp statistic were used as selection criteria for choosing the best predictive model. Image processing hue, saturation and intensity accounted for 93% of the variation in percentage surface metMb. Since hue, saturation and intensity each contribute to overall color profile it is logical that these parameters are good predictors. These data indicate that image processing is capable of objectively measuring percentage surface metMb.

A Kernel Test for Neglected Nonlinearity

This paper develops a new kernel test for neglected nonlinearity in the conditional expectation function, and compares this test to the Ramsey RESET test (1969) and the Neural Net test of Lee, White, and Granger (1993). Like the Neural Test and the Ramsey Reset Test, this Kernel test is a Lagrange Multiplier test based on the R-Square statistic from a regression of the estimated residuals on the regressors, and an additional nonlinear function of the regressors. Unlike the other tests, our test has a two stage approach where in the first stage we estimate the structure of the misspecification and in the second stage we test for whether or not the estimate of the misspecification can better predict the residuals than their mean. This two stage approach can give the researcher guidance on the nature of the misspecification, and should improve the power of the test since the added function in the regression of the residuals is itself an estimate of the conditional expectation of the residuals given the independent variables. In addition, because it uses simple, well known estimation methods it can be implemented by researchers when using linear models.

Site Redundancy in Urban Ozone Monitoring

This article describes two statistical methods that enable air pollution control agencies to assess the effectiveness of the spatial distribution of current stationary ozone monitoring networks by providing measures of site redundancy. These methods analyze site redundancy by determining the degree to which ozone measurements at one site can be successfully predicted from data collected at other monitoring sites. The first method, the similarity (SIM) measure, calculates redundancy based on the percentage of common operational days during which two monitoring stations report similar daily maximum ozone concentrations. The second method, a modeling technique, relates site redundancy in ozone measurement to an R-squared statistic from an autoregressive model. The model uses meteorological components recorded at a central location and ozone concentrations reported by the network’s other monitoring stations. Both techniques can assist in effective allocation of limited monitoring resources and offer a statist...