Multivariate Multiple Regression Models Research Articles

Prenatal co-exposure to manganese and depression and 24-months neurodevelopment

BackgroundNormal prenatal neurodevelopment follows stages that are potentially influenced by both chemical and psychosocial environments. Exposure to elevated manganese during this critically vulnerable period has been found to be neurotoxic. Independently, maternal prenatal depression has been associated with subsequent neurodevelopmental decrements in children. The association between child neurodevelopment and prenatal co-exposure to manganese and maternal depression has not been sufficiently studied. MethodsDuring pregnancy and at birth, we measured maternal blood and cord blood manganese levels respectively. Maternal depression was assessed in the 3rd trimester of pregnancy using the Edinburgh Depression Scale. Neurodevelopment was evaluated at 24 months of age with the Bayley Scales of Infant Development. A multivariate multiple regression model was used to analyze cognitive, language and motor scores simultaneously for 473 children from the PROGRESS birth cohort in Mexico City. ResultsOver 25% of our study participants reported having depressive symptoms. 3rd trimester blood manganese as well as depressive symptoms were independently negatively associated with all neurodevelopment scores in adjusted models. In stratified analyses, the negative association between manganese (maternal as well as cord blood) and 24-month language scores was stronger among women with depressive symptoms. Receptive language was mostly affected. Inverted U-shaped curves were seen for the association between with cord blood manganese and neurodevelopment scores. ConclusionsOur findings are in line with previous studies of manganese and depression neurotoxicity. The prenatal period may be particularly sensitive to manganese and depression co-exposures and should be of interest for public health interventions to promote healthy emotional and nutritional pregnancies.

Comparison of the timing of intervention and treatment modality of poor-grade aneurysmal subarachnoid hemorrhage

Objectives: The timing and modality of intervention in the treatment of poor-grade aneurysmal subarachnoid haemorrhage (aSAH) has not been defined. The purpose of the study is to analyse whether early treatment and type of intervention influence the clinical outcomes of poor-grade aSAH patients.Material and methods: Patients with poor-grade aSAH were retrieved. Demographics, Fisher grade, radiological characteristics and clinical outcomes were recorded. Outcomes were compared using the modified Rankin Scale (mRS), for groups treated early within 24 hours of aSAH or later and by clipping or endovascular therapy. Multivariate multiple regression model and logistic regression were used to assess factors affecting outcomes at discharge in mRS and length of stay.Results: The study was conducted on 79 patients. 47 (59%) were treated by clipping, 38 (48%) received intervention within 24 hours of aSAH. Patients treated <24h had significantly lower mortality (n = 5; 13% vs. n = 14; 37%; p < .023), higher rate of 0-3 mRS (n = 22;58% vs. n = 9; 22%; p < .039) and were younger (49.5 ± 6.1 vs. 65.8 ± 7.4 years; p < .038). There were no significant differences in mRS between clipping and endovascular therapy. Predictors of length of stay were ICH, MLS, endovascular therapy, location in posterior circulation, Fisher grade and time to intervention <24h. Early intervention, <24h significantly influenced the favourable results in mRS (0-3); (OR 4,14; Cl95% 3.82-4.35). Posterior circulation aneurysms, midline shift and intracerebral hematoma were correlated with poor outcomes.Conclusions: Early treatment, within 24 h, of poor-grade aSAH confirmed better clinical outcome compared to later aneurysm securement. There was no significant difference between clipping and endovascular treatment.

Analysis of road transportation energy consumption demand in China

In this paper, we first analyze the historical trends in road transportation energy consumption and GDP in developed economies to find out the development characteristics of road energy consumption. The two indexes present obvious ‘S’ type patterns. Then, in order to explore the current status and future trend of road energy transportation in China, we employ path analysis to analyze the impact mechanism of the factors related to road transportation energy consumption. Next, we adopt the BMA model to select the core factors related to road transportation energy consumption in China, and on the basis of the model selection as well as univariate (ETS & ARIMA models) and multivariate (multiple regression) models, the road transportation energy consumption is analyzed and forecast. The results showed that the road transportation energy consumption rises by 0.33 percent for every percent increase in GDP and by 1.26 percentage points for every percent increase in urbanization. The road transportation energy consumption in China is expected to reach around 226181.1ktoe by the end of 2015, and about 347,363ktoe by 2020.

Irregular breakfast habits are associated with children’s increased adiposity and children’s and parents’ lifestyle-related behaviors: a population-based cross-sectional study

Abstract Background Skipping meals, especially breakfast, is related to an increase in adiposity indicators, and this behavior is related to metabolic changes that predispose to the development of chronic diseases, recognized as major causes of death worldwide. The objective of the present paper was estimated the association between irregular breakfast habits with adiposity indices in schoolchildren and other lifestyle factors. Methods A population-based cross-sectional study was conducted in 2009–2010, including schoolchildren (n = 10,243) between 6 and 9 years old (51.3 % girls) from 18 districts of mainland Portugal. Breakfast habits were ascertained by asking a yes/no question (“Does your child eat breakfast regularly?”). An index estimated by performing principal component analysis was used to assess body adiposity from three different adiposity indicators (body mass index (BMI), waist circumference (WC), and the triceps, subscapular, and suprailiac skinfolds (used to estimate body fat percentage (BFP))). Multivariate logistic regression and multiple linear regression models were used to estimate the association of irregular breakfast habits with anthropometric indicators (BMI, BMI z score, WC, BFP, and adiposity index) and with children’s and parents’ lifestyle and socioeconomic characteristics. Results A total of 3.5 % of the children did not have breakfast regularly (girls 3.9 %; boys 3.1 %; P = 0.02). Among boys, irregular breakfast habits were associated with lower fathers’ education level, television time ≥2 h/day, and soft drink consumption ≥2 times/week. For girls, irregular breakfast habits were associated with lower mothers’ education level and physical inactivity, soft drink consumption ≥2 times/week, and &lt;1 portion of milk/day. Multivariate linear models revealed a positive association between irregular breakfast habits with increased adiposity indicators among boys (BMI (kg/m2): β = 1.33; BMI z score: β = 0.48; WC (cm): β = 2.00; BFP (%): β = 2.20; adiposity index: β = 0.37; P &lt; 0.01 for all). No significant association was found for girls. Conclusions Irregular breakfast habits were positively associated with boys’ increased global adiposity and were significantly affected by children’s and parents’ lifestyle-related behaviors.

Is it Necessary to Fuse to S1 for the Tilted L5 in the Treatment of Adult Degenerative Scoliosis?

IntroductionThe extension of fusion to S1 compared with L5 and lower thoracic levels compared with L1 remains a highly controversial topic in the surgical treatment for adult degenerative scoliosis (ADS). As one of the criterion, if the tilted L5 were over 15°, the distal fusion level should extend to the sacrum. Could the tilted L5 be neutralized and the L5S1 be saved in the ADS correction? Material and MethodsPosterior one stage of facetectomy and interbody release combined with key segment anterior structural column support were used to treat 32 ADS cases. The thoroughly interbody release and fusion were done with both side in all involved segment, a little bigger inserter were inserted into L3,4 and L4,5 cave side to neutralize the tilted L5 maximally. The operating time and the blood loss were recorded. Mean follow-up was at least two years. All the subjects were analyzed by visual analog scale, Oswestry Disability Index (ODI), and SF-36 scores, SRS 22 before and after surgery and at follow-up. The scoliotic curve, thoracic kyphosis, lumbar lordosis, pelvic incidence (PI), pelvic tilt (PT), sacral slope, and C7 plumb line were measured. For the statistical analysis, multivariate multiple regression models were formulated, considering as significant (p < 0.05). ResultsThe average operating time were 150min and the mean blood loss were 520ml. A statistically significant clinical and radiological amelioration was noted after surgery and at final follow-up. The ODI, and SF-36 scores, SRS 22 improved. The Cobb angle of lumbar lordosis (7 plumb line) and spino-pelvic parameters (PI, PT, sacral slope) returned to the normal range after surgery. L5S1 radiological adjacent segment pathology (RASP) happened in two cases at the follow-up, one was extended to the S1,there is no symptom in another case. ConclusionThe tilted L5 can be neutralized and the L5S1 can be saved in the ADS correction. Even with a little movement, the saved L5S1 is important for a whole body to balance.

College Towns, Vacation Spots, and Tech Hubs: Using Geo-Social Media to Model and Compare Locations

In this paper, we explore the potential of geo-social media to construct location-based interest profiles to uncover the hidden relationships among disparate locations. Through an investigation of millions of geo-tagged Tweets, we construct a per-city interest model based on fourteen high-level categories (e.g., technology, art, sports). These interest models support the discovery of related locations that are connected based on these categorical perspectives (e.g., college towns or vacation spots) but perhaps not on the individual tweet level. We then connect these city-based interest models to underlying demographic data. By building multivariate multiple linear regression (MMLR) and neural network (NN) models we show how a location's interest profile may be estimated based purely on its demographics features.

Can the Social Vulnerability Index Be Used for More Than Emergency Preparedness? An Examination Using Youth Physical Fitness Data

The Social Vulnerability Index (SVI), a publicly available dataset, is used in emergency preparedness to identify communities in greatest need of resources. The SVI includes multiple socioeconomic, demographic, and geographic indicators that also are associated with physical fitness and physical activity. This study examined the utility of using the SVI to explain variation in youth fitness, including aerobic capacity and body mass index. FITNESSGRAM data from 2,126 Georgia schools were matched at the census tract level with SVI themes of socioeconomic, household composition, minority status and language, and housing and transportation. Multivariate multiple regression models were used to test whether SVI factors explained fitness outcomes, controlling for grade level (ie, elementary, middle, high school) and stratified by gender. SVI themes explained the most variation in aerobic fitness and body mass index for both boys and girls (R2 values 11.5% to 26.6%). Socioeconomic, Minority Status and Language, and Housing and Transportation themes were salient predictors of fitness outcomes. Youth fitness in Georgia was related to socioeconomic, demographic, and geographic themes. The SVI may be a useful needs assessment tool for health officials and researchers examining multilevel influences on health behaviors or identifying communities for prevention efforts.

Family Chaos and Child Functioning in Relation to Sleep Problems Among Children at Risk for Obesity

This study evaluated the influence of child and family functioning on child sleep behaviors in low-income minority families who are at risk for obesity. A cross-sectional study was utilized to measure child and family functioning from 2013 to 2014. Participants were recruited from Head Start classrooms while data were collected during home visits. A convenience sample of 72 low-income Hispanic (65%) and African American (32%) families of preschool-aged children were recruited for this study. We assessed the association of child and family functioning with child sleep behaviors using a multivariate multiple linear regression model. Bootstrap mediation analyses examined the effects of family chaos between child functioning and child sleep problems. Poorer child emotional and behavioral functioning related to total sleep behavior problems. Chaos associated with bedtime resistance significantly mediated the relationship between Behavioral and Emotional Screening System (BESS) and Bedtime Resistance. Families at high risk for obesity showed children with poorer emotional and behavioral functioning were at higher risk for problematic sleep behaviors, although we found no link between obesity and child sleep. Family chaos appears to play a significant role in understanding part of these relationships. Future longitudinal studies are necessary to establish causal relationships between child and family functioning and sleep problems to further guide obesity interventions aimed at improving child sleep routines and increasing sleep duration.

Likelihood Based Finite Sample Inference for Singly Imputed Synthetic Data Under the Multivariate Normal and Multiple Linear Regression Models

In this paper we develop likelihood-based finite sample inference based on singly imputed partially synthetic data, when the original data follow either a multivariate normal or a multiple linear regression model. We assume that the synthetic data are generated by using the plug-in sampling method, where unknown parameters in the data model are set equal to observed values of their point estimators based on the original data, and synthetic data are drawn from this estimated version of the model. Empirical studies are presented to show that the proposed methods do indeed perform as the theory predicts, and to compare the proposed methods for singly imputed synthetic data with the combining rules that are used to analyze multiply imputed partially synthetic data. Some theoretical comparisons between singly and multiply imputed partially synthetic data inference are also provided. A data analysis example and disclosure risk evaluation of singly and multiply imputed partially synthetic data is presented based on public use data from the Current Population Survey. We discuss the specific conditions under which the proposed methodology will yield valid inference, and evaluate the performance of the methodology when certain conditions do not hold. We outline some ways to extend the proposed methodology for certain scenarios where the required set of conditions do not hold.

Association of peripheral inflammation with body mass index and depressive relapse in bipolar disorder

Bipolar I disorder (BD) is associated with increased inflammation, which is believed to be central to disease etiology and progression. However, BD patients also have high rates of obesity, itself an inflammatory condition, and the relative contributions of mood illness and obesity to inflammation are unknown. Moreover, the impact of inflammation on clinical illness course has not been well studied. The objectives of this analysis were therefore: (1) to determine if inflammation in BD is mood illness-related or secondary to elevated body mass index (BMI), and (2) to investigate the impact of inflammation on prospectively-ascertained relapse into depression and mania. We measured the serum levels of 7 inflammatory cytokines (TNF-α, γ-interferon, monocyte chemoattractant protein-1 [MCP-1], IL-1α, IL-2, IL-6, and IL-8) and 2 anti-inflammatory cytokines (IL-4 and IL-10) in 52 early-stage BD patients and 22 healthy subjects. In patients, a multivariate multiple regression model that controlled for psychotropic medications found that higher BMI, but not recent (past-6-month) mood episodes, predicted greater inflammatory cytokines (p=.05). Healthy subjects also had a BMI-related increase in inflammatory cytokines (p<.01), but it was counter-balanced by a compensatory increase in anti-inflammatory cytokines (p=.02), reducing their total inflammatory burden from higher BMI. In patients, linear regression showed that two inflammatory cytokines predicted depressive relapse in the 12 months after cytokine measurement: IL-1α (p<.01) and MCP-1 (p<.01). These results suggest that elevated BMI is a significant contributor to inflammation in BD, more so even than recent mood illness severity. They also point to inflammation as an important predictor of illness course, particularly depressive relapse.

Inference for Singly Imputed Synthetic Data Based on Posterior Predictive Sampling under Multivariate Normal and Multiple Linear Regression Models

Likelihood-based finite sample inference for singly imputed synthetic data generated via posterior predictive sampling is developed in this paper for multivariate normal and multiple linear regression models. Currently available methodology for drawing valid inference on population parameters using synthetic data is based on concepts of multiple imputation for missing data, and therefore requires the release of multiple synthetic datasets. The methodology developed in this paper demonstrates that, contrary to the usual belief, valid inference about meaningful model parameters can indeed be drawn based on a singly imputed synthetic dataset under the multivariate normal and multiple linear regression models, by fully utilizing the model structure.

Exploring the Relationship of Innovation Intensity, Knowledge Production and Productivity in Greek SMEs Before the Eruption of Debt Crisis

In the context of this paper, we examine the relationship of innovation density, labour productivity and knowledge production in terms of new to the market products for Greece, before the eruption of debt crisis. This paper extends prior research (Hatzikian 2013a, b) and the main question of this study is, “What was the most effective innovation intensity that a firm needs to have for its firm performance before the Greek debt Crisis?” To this end, we use productivity and knowledge production or growth as metrics of firm performance and we explore their behaviour with regard to a firm’s innovation intensity. We test the hypotheses that there is a U-shaped relationship between innovation intensity and productivity, and there is an inverted U-shaped relationship between innovation intensity and knowledge production in the short-term period. We apply the method for examining nonlinearities, that is, the introduction of squared terms as independent variables. The collected variables are used in a multivariate multiple regression model formulation to evaluate the relative performance associated with them. For this reason, a number of variables are used, like the innovation intensity, the squared term of innovation intensity, the research and development (R&D) personnel, as well as the firm size. We rely on the final results of a research project on women in innovation, technology and science, based on 372 questionnaires selected on a 2-year time period (2004–2006) before the eruption of the debt crisis in Greece.

Evidence for early neurodegeneration in the cervical cord of patients with primary progressive multiple sclerosis.

Spinal neurodegeneration is an important determinant of disability progression in patients with primary progressive multiple sclerosis. Advanced imaging techniques, such as single-voxel (1)H-magnetic resonance spectroscopy and q-space imaging, have increased pathological specificity for neurodegeneration, but are challenging to implement in the spinal cord and have yet to be applied in early primary progressive multiple sclerosis. By combining these imaging techniques with new clinical measures, which reflect spinal cord pathology more closely than conventional clinical tests, we explored the potential for spinal magnetic resonance spectroscopy and q-space imaging to detect early spinal neurodegeneration that may be responsible for clinical disability. Data from 21 patients with primary progressive multiple sclerosis within 6 years of disease onset, and 24 control subjects were analysed. Patients were clinically assessed on grip strength, vibration perception thresholds and postural stability, in addition to the Expanded Disability Status Scale, Nine Hole Peg Test, Timed 25-Foot Walk Test, Multiple Sclerosis Walking Scale-12, and Modified Ashworth Scale. All subjects underwent magnetic resonance spectroscopy and q-space imaging of the cervical cord and conventional brain and spinal magnetic resonance imaging at 3 T. Multivariate analyses and multiple regression models were used to assess the differences in imaging measures between groups and the relationship between magnetic resonance imaging measures and clinical scores, correcting for age, gender, spinal cord cross-sectional area, brain T2 lesion volume, and brain white matter and grey matter volume fractions. Although patients did not show significant cord atrophy when compared with healthy controls, they had significantly lower total N-acetyl-aspartate (mean 4.01 versus 5.31 mmol/l, P = 0.020) and glutamate-glutamine (mean 4.65 versus 5.93 mmol/l, P = 0.043) than controls. Patients showed an increase in q-space imaging-derived indices of perpendicular diffusivity in both the whole cord and major columns compared with controls (P < 0.05 for all indices). Lower total N-acetyl-aspartate was associated with higher disability, as assessed by the Expanded Disability Status Scale (coefficient = -0.41, 0.01 < P < 0.05), Modified Ashworth Scale (coefficient = -3.78, 0.01 < P < 0.05), vibration perception thresholds (coefficient = -4.37, P = 0.021) and postural sway (P < 0.001). Lower glutamate-glutamine predicted increased postural sway (P = 0.017). Increased perpendicular diffusivity in the whole cord and columns was associated with increased scores on the Modified Ashworth Scale, vibration perception thresholds and postural sway (P < 0.05 in all cases). These imaging findings indicate reduced structural integrity of neurons, demyelination, and abnormalities in the glutamatergic pathways in the cervical cord of early primary progressive multiple sclerosis, in the absence of extensive spinal cord atrophy. The observed relationship between imaging measures and disability suggests that early spinal neurodegeneration may underlie clinical impairment, and should be targeted in future clinical trials with neuroprotective agents to prevent the development of progressive disability.

White matter structure in youth with behavioral and emotional dysregulation disorders: a probabilistic tractographic study.

Psychiatric disorders in youth characterized by behavioral and emotional dysregulation are often comorbid and difficult to distinguish. An alternative approach to conceptualizing these disorders is to move toward a diagnostic system based on underlying pathophysiologic processes that may cut across conventionally defined diagnoses. Neuroimaging techniques have potentials for the identification of these processes. To determine whether diffusion imaging, a neuroimaging technique examining white matter (WM) structure, can identify neural correlates of emotional dysregulation in a sample of youth with different psychiatric disorders characterized by behavioral and emotional dysregulation. Using global probabilistic tractography, we examined relationships between WM structure in key tracts in emotional regulation circuitry (ie, cingulum, uncinate fasciculus, and forceps minor) and (1) broader diagnostic categories of behavioral and emotional dysregulation disorders (DDs) and (2) symptom dimensions cutting across conventional diagnoses in 120 youth with behavioral and/or emotional DDs, a referred sample of the Longitudinal Assessment of Manic Symptoms (LAM) study. Thirty age- and sex-matched typically developing youth (control participants) were included. Multivariate multiple regression models were used. The study was conducted from July 1, 2010, to February 28, 2014. Fractional anisotropy as well as axial and radial diffusivity were estimated and imported into a well-established statistical package. We hypothesized that (1) youth with emotional DDs and those with both behavioral and emotional DDs would show significantly lower fractional anisotropy compared with youth with behavioral DDs in these WM tracts and (2) that there would be significant inverse relationships between dimensional measures of affective symptom severity and fractional anisotropy in these tracts across all participants. Multivariate multiple regression analyses revealed decreased fractional anisotropy and decreased axial diffusivity within the uncinate fasciculus in youth with emotional DDs vs those with behavioral DDs, those with both DDs, and the controls (F6,160 = 2.4; P = .032; all pairwise comparisons, P < .002). In the same model, greater severity of manic symptoms was positively associated with higher fractional anisotropy across all affected youth (F3,85 = 2.8; P = .044). These findings suggest that abnormal uncinate fasciculus and cingulum WM structure may underlie emotional, but not behavioral, dysregulation in pediatric psychiatric disorders and that a different neural mechanism may exist for comorbid emotional and behavioral DDs.

Probabilistic Multisite Statistical Downscaling for Daily Precipitation Using a Bernoulli–Generalized Pareto Multivariate Autoregressive Model

Abstract A Bernoulli–generalized Pareto multivariate autoregressive (BMAR) model is proposed in this paper for multisite statistical downscaling of daily precipitation. The proposed model relies on a probabilistic framework to describe the conditional probability density function of precipitation at each station for a given day and handles multivariate dependence in both time and space using a multivariate autoregressive model. Within a probabilistic framework, BMAR employs a regression model whose outputs are parameters of the mixed Bernoulli–generalized Pareto distribution. As a stochastic component, the BMAR employs a latent multivariate autoregressive Gaussian field to preserve lag-0 and lag-1 cross correlations of precipitation at multiple sites. The proposed model is applied for the downscaling of AOGCM data to daily precipitation in the southern part of Québec, Canada. Reanalysis products are used in this study to assess the potential of the proposed method. Based on the mean errors (MEs), the root-mean-square errors (RMSEs), precipitation indices, and the ability to preserve lag-0 and lag-1 cross correlation, results of the study indicate the superiority of the proposed model over a multivariate multiple linear regression (MMLR) model and a multisite hybrid statistical downscaling procedure that combines MMLR and stochastic generator schemes.

Multivariate sparse group lasso for the multivariate multiple linear regression with an arbitrary group structure.

We propose a multivariate sparse group lasso variable selection and estimation method for data with high-dimensional predictors as well as high-dimensional response variables. The method is carried out through a penalized multivariate multiple linear regression model with an arbitrary group structure for the regression coefficient matrix. It suits many biology studies well in detecting associations between multiple traits and multiple predictors, with each trait and each predictor embedded in some biological functional groups such as genes, pathways or brain regions. The method is able to effectively remove unimportant groups as well as unimportant individual coefficients within important groups, particularly for large p small n problems, and is flexible in handling various complex group structures such as overlapping or nested or multilevel hierarchical structures. The method is evaluated through extensive simulations with comparisons to the conventional lasso and group lasso methods, and is applied to an eQTL association study.

Adult scoliosis: age-related deformity and surgery.

We retrospectively analyzed our results in thoracolumbar and lumbar adolescent idiopathic scoliosis treated during adulthood. Fifty-two thoracolumbar and 30 lumbar idiopathic scoliosis surgically treated were reviewed. Mean follow-up was 9.5±6.6years. All the subjects were analyzed by visual analog scale, Oswestry Disability Index (ODI), and SF-36 scores before and after surgery and at follow-up. The scoliotic curve, thoracic kyphosis, lumbar lordosis, pelvic incidence (PI), pelvic tilt (PT), sacral slope, and C7 plumb line were measured. For the statistical analysis, multivariate multiple regression models were formulated, considering as significative a P<0.05. A statistically significant clinical and radiological amelioration was noted after surgery and at final follow-up. According to the logistic regression model, ODI was related to lumbar lordosis and spino-pelvic parameters at follow-up. The only determinant of failure was age. Spino-pelvic recovery is easier in patients aged less than 60years with PI<55° and PT<25°.

RWA Web: A Free, Comprehensive, Web-Based, and User-Friendly Tool for Relative Weight Analyses

Over the last 15 years, a number of methodological developments have enabled researchers to draw more accurate inferences concerning the relative contribution (i.e., relative importance) among multiple (often correlated) predictor variables in a regression analysis. One such development has been relative weight analysis (RWA). Researchers can use a RWA to decompose the total variance predicted in a regression model (R 2) into weights that accurately reflect the proportional contribution of the various predictor variables. Prior to RWA, researchers were forced to rely on traditional statistics (e.g., correlations; standardized regression weights), which are known to yield faulty or misleading information concerning variable importance (especially when predictor variables are correlated with one another, which is often the case in organizational research). Although there has been a surge of interest in RWA over the last 10 years, integration of this statistical tool into organizational research has been hampered by the lack of a user-friendly statistical package for implementing RWA. Indeed, most popular statistical packages (e.g., SPSS, SAS) have yet to include RWA protocols into their regression modules. The purpose of this paper is to present a new, free, comprehensive, web-based, user-friendly resource, RWA-Web, which may be used by anyone having simple access to the internet. Our paper is structured as a tutorial on using RWA-Web to examine relative importance in the classic multiple regression model, the multivariate multiple regression model, and the logistic regression model. We also illustrate how RWA-Web may be used to conduct null hypothesis significance tests using advanced bootstrapping procedures.

Vector regression introduced

AbstractThis study formulates regression of vector data that will enable statistical analysis of various geodetic phenomena such as, polar motion, ocean currents, typhoon/hurricane tracking, crustal deformations, and precursory earthquake signals. The observed vector variable of an event (dependent vector variable) is expressed as a function of a number of hypothesized phenomena realized also as vector variables (independent vector variables) and/or scalar variables that are likely to impact the dependent vector variable. The proposed representation has the unique property of solving the coefficients of independent vector variables (explanatory variables) also as vectors, hence it supersedes multivariate multiple regression models, in which the unknown coefficients are scalar quantities. For the solution, complex numbers are used to rep- resent vector information, and the method of least squares is deployed to estimate the vector model parameters after transforming the complex vector regression model into a real vector regression model through isomorphism. Various operational statistics for testing the predictive significance of the estimated vector parameter coefficients are also derived. A simple numerical example demonstrates the use of the proposed vector regression analysis in modeling typhoon paths.

Molecular Signatures of Epithelial Ovarian Cancer: Analysis of Associations with Tumor Characteristics and Epidemiologic Risk Factors

Six gene expression subtypes of invasive epithelial ovarian cancer were recently defined using microarrays by Tothill and colleagues. The Cancer Genome Atlas (TCGA) project subsequently replicated these subtypes and identified a signature predictive of survival in high-grade serous (HGS) cancers. We previously validated these signatures for use in formalin-fixed paraffin-embedded tissues. The aim of the present study was to determine whether these signatures are associated with specific ovarian cancer risk factors, which would add to the evidence that they reflect the heterogeneous etiology of this disease. We modeled signature-specific tumor characteristics and epidemiologic risk factor relationships using multiple regression and multivariate response multiple regression models in 193 patients from a case-control study of epithelial ovarian cancer. We observed associations between the Tothill gene expression subtype signatures and both age at diagnosis (P = 0.0008) and race (P = 0.008). Although most established epidemiologic risk factors were not associated with molecular signatures, there was an association between breast feeding (P = 0.024) and first-degree family history of breast or ovarian cancer (P = 0.034) among the 106 HGS cases. Some of the above associations were validated using gene expression microarray data from the TCGA project. Weak associations were seen with age at menarche and duration of oral contraceptive use and the TCGA survival signature. These data support the potential for genomic characterization to elucidate the etiologic heterogeneity of epithelial ovarian cancer. This study suggests that molecular signatures may augment the ability to define etiologic subtypes of epithelial ovarian cancer.