Statnote 32 : the partial correlation coefficient

In previous statnotes, the application of correlation and regression methods to the analysis of two variables (X,Y) was described. The most important statistic used to measure the degree of correlation between two variables is Pearson’s ‘product moment correlation coefficient’ (‘r’). The correlation between two variables may be due to their common relation to other variables. Hence, investigators using correlation studies need to be alert to the possibilities of spurious correlation and the methods of ‘partial correlation’ are one method of taking this into account. This statnote applies the methods of partial correlation to three scenarios. First, to a fairly obvious example of a spurious correlation resulting from the ‘size effect’ involving the relationship between the number of general practitioners (GP) and the number of deaths of patients in a town. Second, to the relationship between the abundance of the nitrogen-fixing bacterium Azotobacter in soil and three soil variables, and finally, to a more complex scenario, first introduced in Statnote 24involving the relationship between the growth of lichens in the field and climate.

The effect of intrinsic soil properties on soil quality assessments

The assessment of soil quality is based on indicators and indices derived from soil properties. However, intrinsic soil properties may interfere with other soil properties that vary under different land uses and are used to calculate the indices. The aim of this study was to assess the extent to which intrinsic soil properties (clay and iron oxide contents) explain variable soil properties (sum of bases, potential acidity, organic carbon, total porosity, and bulk density) under different land uses (native forest, no-tillage and conventional agriculture) on small family farms in Southern Brazil. The results showed that the five properties evaluated can be included in soil quality assessments and are not influenced by the clay and iron oxide contents. It was concluded that for little weathered 1:1 and 2:1 phyllosilicate rich-soils, if the difference between the maximum and the minimum clay content under the different land uses is less than about 200 g kg-1 and the iron oxide content less than about 15 g kg-1, the physico-chemical soil properties in the surface layer are determined mostly by the land use.

Análisis composicional de datos en Ciencias Geoambientales

Compositional data (concentrations) are common in geosciences. Neglecting its character mey lead to erroneous conclusions. Spurious correlation (K. Pearson, 1897) has disastrous consequences. On the basis of the pioneering work by J. Aitchison in the 1980s, a methodology free of these drawbacks is now available. The geometry of the símplex allows the representation of compositions using orthogonal co-ordinares, to which usual statistical methods can be applied, thus facilating computation ans analysis. The use of (log) ratios precludes the interpretation of single concentrations disregarding their relative character. A hydro-chemical data set is used to illustrate the point

Ratiomuuttujat ja näennäinen korrelaatio

Eri tieteenalojen tutkijat ovat kiistelleet jo yli vuosisadan ajan ratiomuodossa olevien muuttujien käytön vaikutuksista korrelaatio- ja regressioanalyysien tuloksiin ja niiden oikeaan tulkintaan. Strategiatutkimuksen piirissä aiheeseen ei ole kuitenkaan kiinnitetty suuresti huomiota. Tämä on yllättävää, sillä ratiomuuttujat ovat hyvin yleisesti käytettyjä empiirisen strategiatutkimuksen piirissä. Tässä työssä luodaan katsaus ratiomuuttujien ympärillä käytyyn debattiin. Lisäksi selvitetään artikkelikatsauksen avulla niiden käytön yleisyyttä nykypäivän strategiatutkimuksessa. Työssä tutkitaan Monte Carlo –simulaatioiden avulla ratiomuuttujien ominaisuuksien vaikutuksia korrelaatio- ja regressioanalyysin tuloksiin erityisesti yhteisen nimittäjän tapauksissa.

Cointegration: Bayesian Significance Test

To estimate causal relationships, time series econometricians must be aware of spurious correlation, a problem first mentioned by Yule (1926). To deal with this problem, one can work either with differenced series or multivariate models: VAR (VEC or VECM) models. These models usually include at least one cointegration relation. Although the Bayesian literature on VAR/VEC is quite advanced, Bauwens et al. (1999) highlighted that "the topic of selecting the cointegrating rank has not yet given very useful and convincing results". The present article applies the Full Bayesian Significance Test (FBST), especially designed to deal with sharp hypotheses, to cointegration rank selection tests in VECM time series models. It shows the FBST implementation using both simulated and available (in the literature) data sets. As illustration, standard non informative priors are used.

Car ownership modeling and forecasts for China

A great increase of private car ownership took place in China from 1980 to 2009 with the development of the economy. To explain the relationship between car ownership and economic and social changes, an ordinary least squares linear regression model is developed using car ownership per capita as the dependent variable with GDP, savings deposits and highway mileages per capita as the independent variables. The model is tested and corrected for econometric problems such as spurious correlation and cointegration. Finally, the regression model is used to project oil consumption by the Chinese transportation sector through 2015. The result shows that about 2.0 million barrels of oil will be consumed by private cars in conservative scenario, and about 2.6 million barrels of oil per day in high case scenario in 2015. Both of them are much higher than the consumption level of 2009, which is 1.9 million barrels per day. It also shows that the annual growth rate of oil demand by transportation is 2.7% - 3.1% per year in the conservative scenario, and 6.9% - 7.3% per year in the high case forecast scenario from 2010 to 2015. As a result, actions like increasing oil efficiency need to be taken to deal with challenges of the increasing demand for oil.

Radiomics of NSCLC: Quantitative CT Image Feature Characterization and Tumor Shrinkage Prediction

Radiomics is the high-throughput extraction and analysis of quantitative image features. For non-small cell lung cancer (NSCLC) patients, radiomics can be applied to standard of care computed tomography (CT) images to improve tumor diagnosis, staging, and response assessment. The first objective of this work was to show that CT image features extracted from pre-treatment NSCLC tumors could be used to predict tumor shrinkage in response to therapy. This is important since tumor shrinkage is an important cancer treatment endpoint that is correlated with probability of disease progression and overall survival. Accurate prediction of tumor shrinkage could also lead to individually customized treatment plans. To accomplish this objective, 64 stage NSCLC patients with similar treatments were all imaged using the same CT scanner and protocol. Quantitative image features were extracted and principal component regression with simulated annealing subset selection was used to predict shrinkage. Cross validation and permutation tests were used to validate the results. The optimal model gave a strong correlation between the observed and predicted shrinkages with . The second objective of this work was to identify sets of NSCLC CT image features that are reproducible, non-redundant, and informative across multiple machines. Feature sets with these qualities are needed for NSCLC radiomics models to be robust to machine variation and spurious correlation. To accomplish this objective, test-retest CT image pairs were obtained from 56 NSCLC patients imaged on three CT machines from two institutions. For each machine, quantitative image features with concordance correlation coefficient values greater than 0.90 were considered reproducible. Multi-machine reproducible feature sets were created by taking the intersection of individual machine reproducible feature sets. Redundant features were removed through hierarchical clustering. The findings showed that image feature reproducibility and redundancy depended on both the CT machine and the CT image type (average cine 4D-CT imaging vs. end-exhale cine 4D-CT imaging vs. helical inspiratory breath-hold 3D CT). For each image type, a set of cross-machine reproducible, non-redundant, and informative image features was identified. Compared to end-exhale 4D-CT and breath-hold 3D-CT, average 4D-CT derived image features showed superior multi-machine reproducibility and are the best candidates for clinical correlation.

High Diagnostic Accuracy And Reproducibility Of Fine-needle Aspiration Cytology For Diagnosing Salivary Gland Tumors: Cytohistologic Correlation In 182 Cases.

The purpose of this study was to assess the efficacy and reproducibility of the cytologic diagnosis of salivary gland tumors (SGTs) using fine-needle aspiration cytology (FNAC). The study aimed to determine diagnostic accuracy, sensitivity, and specificity and to evaluate the extent of interobserver agreement. We retrospectively evaluated SGTs from the files of the Division of Pathology at the Clinics Hospital of São Paulo and Piracicaba Dental School between 2000 and 2006. We performed cytohistologic correlation in 182 SGTs. The sensitivity, specificity, positive predictive value, negative predictive value, and diagnostic accuracy were 94%, 100%, 100%, 100%, and 99%, respectively. The interobserver cytologic reproducibility showed significant statistical concordance (P < .0001). FNAC is an effective tool for performing a reliable preoperative diagnosis in SGTs and shows high diagnostic accuracy and consistent interobserver reproducibility. Further FNAC studies analyzing large samples of malignant SGTs and reactive salivary lesions are needed to confirm their accuracy.

Core-valence Correlation Effects On Ir Calculations: The Bf3 And Bcl3 Cases.

The first theoretical results of core-valence correlation effects are presented for the infrared wavenumbers and intensities of the BF3 and BCl3 molecules, using (double- and triple-zeta) Dunning core-valence basis sets at the CCSD(T) level. The results are compared with those calculated in the frozen core approximation with standard Dunning basis sets at the same correlation level and with the experimental values. The general conclusion is that the effect of core-valence correlation is, for infrared wavenumbers and intensities, smaller than the effect of adding augmented diffuse functions to the basis set, e.g., cc-pVTZ to aug-cc-pVTZ. Moreover, the trends observed in the data are mainly related to the augmented functions rather than the core-valence functions added to the basis set. The results obtained here confirm previous studies pointing out the large descrepancy between the theoretical and experimental intensities of the stretching mode for BCl3.

Measuring The Hydrodynamic Radius Of Quantum Dots By Fluorescence Correlation Spectroscopy.

Fluorescence Correlation Spectroscopy (FCS) is an optical technique that allows the measurement of the diffusion coefficient of molecules in a diluted sample. From the diffusion coefficient it is possible to calculate the hydrodynamic radius of the molecules. For colloidal quantum dots (QDs) the hydrodynamic radius is valuable information to study interactions with other molecules or other QDs. In this chapter we describe the main aspects of the technique and how to use it to calculate the hydrodynamic radius of quantum dots (QDs).

Correlation Between Cephalometric Data And Severity Of Sleep Apnea.

Obstructive sleep apnea syndrome has a high prevalence among adults. Cephalometric variables can be a valuable method for evaluating patients with this syndrome. To correlate cephalometric data with the apnea-hypopnea sleep index. We performed a retrospective and cross-sectional study that analyzed the cephalometric data of patients followed in the Sleep Disorders Outpatient Clinic of the Discipline of Otorhinolaryngology of a university hospital, from June 2007 to May 2012. Ninety-six patients were included, 45 men, and 51 women, with a mean age of 50.3 years. A total of 11 patients had snoring, 20 had mild apnea, 26 had moderate apnea, and 39 had severe apnea. The distance from the hyoid bone to the mandibular plane was the only variable that showed a statistically significant correlation with the apnea-hypopnea index. Cephalometric variables are useful tools for the understanding of obstructive sleep apnea syndrome. The distance from the hyoid bone to the mandibular plane showed a statistically significant correlation with the apnea-hypopnea index.

Histologic Correlation Of Expression Of Ki-67 In Squamous Cell Carcinoma Of The Glottis According To The Degree Of Cell Differentiation.

Squamous cell carcinoma is the most common neoplasm of the larynx and glottis, and its prognosis depends on the size of the lesion, level of local invasion, cervical lymphatic spread, and presence of distant metastases. Ki-67 (MKI67) is a protein present in the core, whose function is related to cell proliferation. To evaluate the expression of marker Ki-67 in squamous cell carcinoma of the larynx and glottis and its correlation to pathological findings. Experimental study with immunohistochemistry analysis of Ki-67, calculating the percentage of the cell proliferation index in glottic squamous cell carcinomas. Sixteen cases were analyzed, with six well-differentiated and 10 poorly/moderately differentiated tumors. There was a correlation between cell proliferation index and degree of cell differentiation, with higher proliferation in poorly/moderately differentiated tumors. The cell proliferation index, as measured by Ki-67, may be useful in the characterization of histological degree in glottic squamous cell tumors.

Correlation Between Testosterone And Psa Kinetics In Metastatic Prostate Cancer Patients Treated With Diverse Chemical Castrations.

To assess total testosterone and prostatic-specific antigen (PSA) kinetics among diverse chemical castrations, advanced-stage prostate cancer patients were randomized into three groups of 20: Group 1, Leuprolide 3.75 mg; Group 2, Leuprolide 7.5 mg; and Group 3, Goserelin 3.6 mg. All groups were treated with monthly application of the respective drugs. The patients' levels of serum total testosterone and PSA were evaluated at two time periods: before the treatment and 3 months after the treatment. Spearman's rank correlation coefficient was utilized to verify the hypothesis of linear correlation between total testosterone and PSA levels. At the beginning the patients' age, stage, grade, PSA, and total testosterone were similar within the three groups, with median age 72, 70, and 70 years in Groups 1, 2, and 3, respectively. Three months after the treatment, patients who received Leuprolide 7.5 mg presented significantly lower median total testosterone levels compared with Goserelin 3.6 mg and Leuprolide 3.75 mg (9.5 ng/dL vs. 20.0 ng/dL vs. 30.0 ng/dL, respectively; p = .0072), while those who received Goserelin 3.6 mg presented significantly lower PSA levels compared with Leuprolide 7.5 mg and Leuprolide 3.75 mg (0.67 vs. 1.86 vs. 2.57, respectively; p = .0067). There was no linear correlation between total testosterone and PSA levels. Overall, regarding castration levels of total testosterone, 28.77% of patients did not obtain levels ≤50 ng/dL and 47.80% did not obtain levels ≤20 ng/dL. There was no correlation between total testosterone and PSA kinetics and no equivalence among different pharmacological castrations.

Human Herpesvirus-6 And Cytomegalovirus Dna In Liver Donor Biopsies And Their Correlation With Hla Matches And Acute Cellular Rejection.

Herpesvirus reactivation is common after liver transplantation. Analyze the presence of cytomegalovirus (HCMV) and human herpesvirus-6 (HHV-6) DNA in liver donor biopsies, seeking to better understand issues involving human donor leukocyte antigens (HLA)-A, B and DR, as well as correlations with acute cellular rejection. Fifty-nine liver transplantation patients were investigated for the presence of HCMV and HHV-6 DNA in liver donor biopsies, using the Nested-PCR technique. The clinical donor information and HLA matches were obtained from the São Paulo State Transplant System. The recipients' records regarding acute cellular rejection were studied. Seven (11.8%) biopsies were positive for HCMV DNA and 29 (49%) were positive for HHV-6 DNA. In 14 donors with HLA-DR 15 nine had HHV-6 DNA positive liver biopsy with a tendency for significant association (p=0.09), 22 recipients developed acute cellular rejection and 9/22 were positive for HLA-DR 15 (p=0.03; χ(2)=4.51), which was statistically significant in univariate analysis and showed a tendency after multivariate analysis (p=0.08). HHV-6 DNA was prevalent in liver donors studied as well as HLA-DR 15. These findings suggest that patients with HLA-DR 15 in liver donor biopsies develop more rejection after liver transplantation.

Correlation Between Vascular Endothelial Growth Factor Expression And Presence Of Lymph Node Metastasis In Advanced Squamous Cell Carcinoma Of The Larynx.

Squamous cell carcinoma is the most common neoplasm of the larynx, and its evolution depends on tumor staging. Vascular endothelial growth factor is a marker of angiogenesis, and its expression may be related to increased tumor aggressiveness, as evidenced by the presence of cervical lymphatic metastases. To evaluate the expression of the vascular endothelial growth factor marker in non-glottic advanced squamous cell carcinoma of the larynx (T3/T4) and correlate it with the presence of cervical lymph node metastases. Retrospective clinical study and immunohistochemical analysis of vascular endothelial growth factor through the German scale of immunoreactivity in products of non-glottic squamous cell carcinomas. This study analyzed 15 cases of advanced non-glottic laryngeal tumors (T3/T4), four of which exhibited cervical lymphatic metastases. There was no correlation between vascular endothelial growth factor expression and the presence of cervical metastases. Although vascular endothelial growth factor was expressed in a few cases, there was no correlation with the spread of cervical lymph metastases.