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Concept: Kendall tau rank correlation coefficient


A large number of patients do not have cauda equina syndrome (CES) on MRI to account for their clinical findings; consequently, the majority of urgent scans requested are normal. We aimed to determine whether any clinical manifestation of CES, as stated in Royal College of Radiology guidelines, could predict the presence of established CES on MRI. We also aimed to support a larger study to develop a more universal assessment tool for acute lower back pain.A retrospective analysis of consecutive patients who warranted urgent MRI was conducted. Seventy-nine patients were eligible for study. The Kendall’s tau test was used for statistical analysis of all data. A p value of less than 0.05 was considered to be significant. MRI was performed in 62 patients out of 79.A total of 32.9% of patients had scans within 24 hours of admission. Nine of these patients were referred to neurosurgery for urgent neurosurgical review. Of these, 6.3% of patients had an established CES on MRI scan. One patient who had an out-patient MRI spine (15 days from hospital presentation) was found to have an established CES, was urgently referred to spinal surgery and underwent primary fenestration excision of the lumbar vertebra. No clinical features that were able to predict the presence of an established CES on MRI were elucidated. Findings included decreased anal tone 7.6% (p = 0.282), faecal incontinence 3.8% (p = 0.648), urinary retention 7.6% (p = 0.510), bladder incontinence 8.9% (p = 0.474), constipation 2.5% (p = 0.011) and saddle anaesthesia 8.9% (p = 0.368). Patients who had an abnormal MRI spine for back pain prior to this presentation showed a correlation with a newly diagnosed CES on MRI (p = 0.016) with a correlation coefficient of 0.272.

Concepts: Spearman's rank correlation coefficient, Surgery, Urinary incontinence, Vertebral column, Urinary bladder, Cauda equina, Cauda equina syndrome, Kendall tau rank correlation coefficient


This article considers nonparametric methods for studying recurrent disease and death with competing risks. We first point out that comparisons based on the well-known cumulative incidence function can be confounded by different prevalence rates of the competing events, and that comparisons of the conditional distribution of the survival time given the failure event type are more relevant for investigating the prognosis of different patterns of recurrence disease. We then propose nonparametric estimators for the conditional cumulative incidence function as well as the conditional bivariate cumulative incidence function for the bivariate gap times, that is, the time to disease recurrence and the residual lifetime after recurrence. To quantify the association between the two gap times in the competing risks setting, a modified Kendall’s tau statistic is proposed. The proposed estimators for the conditional bivariate cumulative incidence distribution and the association measure account for the induced dependent censoring for the second gap time. Uniform consistency and weak convergence of the proposed estimators are established. Hypothesis testing procedures for two-sample comparisons are discussed. Numerical simulation studies with practical sample sizes are conducted to evaluate the performance of the proposed nonparametric estimators and tests. An application to data from a pancreatic cancer study is presented to illustrate the methods developed in this article.

Concepts: Cancer, Sample size, Spearman's rank correlation coefficient, Non-parametric statistics, Probability theory, Prevalence, Statistical inference, Kendall tau rank correlation coefficient


BACKGROUND: Lymphedema is a feared complication of breast cancer surgery. We evaluated the trends in lymphedema development, patient worry, and risk reduction behaviors. STUDY DESIGN: We prospectively enrolled 120 women undergoing sentinel node biopsy (SLNB) or axillary node dissection (ALND) for breast cancer and assessed lymphedema by upper extremity volume preoperatively and at 6 and 12 months postoperatively. We defined lymphedema as a >10% volume change from baseline relative to the contralateral upper extremity. Patients completed a validated instrument evaluating lymphedema worry and risk reducing behaviors. Associations were determined by Fisher’s exact and signed rank tests. RESULTS: At 6 months, lymphedema was similar between ALND and SLNB patients (p = 0.22), but was higher in ALND women at 12 months (19% vs 3%, p = 0.005). A clear relationship exists between relative change in upper extremity volume at 6 and 12 months (Kendall tau coefficient 0.504, p < 0.001). Among the women with 0 to 9% volume change at 6 months, 22% had progressive swelling, and 18% resolved their volume changes at 12 months. Overall, 75% of ALND and 50% of SLNB patients had persistent worry about lymphedema at follow-up, and no difference existed in the number of risk reducing behaviors practiced among the 2 groups (p > 0.34). CONCLUSIONS: Upper extremity volumes fluctuate, and there is a period of latency before development of lymphedema. Despite the low risk of lymphedema after SLNB, most women worry about lymphedema and practice risk reducing behaviors. Additional study into early upper extremity volume changes is warranted to allay the fears of most women and better predict which women will progress to lymphedema.

Concepts: Cancer, Breast cancer, Metastasis, Oncology, Estrogen, Non-parametric statistics, Sentinel lymph node, Kendall tau rank correlation coefficient


The dataset for this article contains geostatistical analysis of heavy metals contamination from limestone samples collected from Ewekoro Formation in the eastern Dahomey basin, Ogun State Nigeria. The samples were manually collected and analysed using Microwave Plasma Atomic Absorption Spectrometer (MPAS). Analysis of the twenty different samples showed different levels of heavy metals concentration. The analysed nine elements are Arsenic, Mercury, Cadmium, Cobalt, Chromium, Nickel, Lead, Vanadium and Zinc. Descriptive statistics was used to explore the heavy metal concentrations individually. Pearson, Kendall tau and Spearman rho correlation coefficients was used to establish the relationships among the elements and the analysis of variance showed that there is a significant difference in the mean distribution of the heavy metals concentration within and between the groups of the 20 samples analysed. The dataset can provide insights into the health implications of the contaminants especially when the mean concentration levels of the heavy metals are compared with recommended regulatory limit concentration.

Concepts: Statistics, Spearman's rank correlation coefficient, Metal, Pearson product-moment correlation coefficient, Lead, Heavy metal music, Nickel, Kendall tau rank correlation coefficient


We present the performance of HADDOCK, our information-driven docking software, in the second edition of the D3R Grand Challenge. In this blind experiment, participants were requested to predict the structures and binding affinities of complexes between the Farnesoid X nuclear receptor and 102 different ligands. The models obtained in Stage1 with HADDOCK and ligand-specific protocol show an average ligand RMSD of 5.1 Å from the crystal structure. Only 6/35 targets were within 2.5 Å RMSD from the reference, which prompted us to investigate the limiting factors and revise our protocol for Stage2. The choice of the receptor conformation appeared to have the strongest influence on the results. Our Stage2 models were of higher quality (13 out of 35 were within 2.5 Å), with an average RMSD of 4.1 Å. The docking protocol was applied to all 102 ligands to generate poses for binding affinity prediction. We developed a modified version of our contact-based binding affinity predictor PRODIGY, using the number of interatomic contacts classified by their type and the intermolecular electrostatic energy. This simple structure-based binding affinity predictor shows a Kendall’s Tau correlation of 0.37 in ranking the ligands (7th best out of 77 methods, 5th/25 groups). Those results were obtained from the average prediction over the top10 poses, irrespective of their similarity/correctness, underscoring the robustness of our simple predictor. This results in an enrichment factor of 2.5 compared to a random predictor for ranking ligands within the top 25%, making it a promising approach to identify lead compounds in virtual screening.

Concepts: Scientific method, Spearman's rank correlation coefficient, Receptor, Ligand, Non-parametric statistics, Drug discovery, Affinity, Kendall tau rank correlation coefficient


OBJECTIVE After endoscopic third ventriculostomy (ETV), some patients develop recurrent symptoms of hydrocephalus. The optimal treatment for these patients is not clear: repeat ETV (re-ETV) or CSF shunting. The goals of the study were to assess the effectiveness of re-ETV relative to initial ETV in pediatric patients and validate the ETV success score (ETVSS) for re-ETV. METHODS Retrospective data of 624 ETV and 93 re-ETV procedures were collected from 6 neurosurgical centers in the Netherlands (1998-2015). Multivariable Cox proportional hazards modeling was used to provide an adjusted estimate of the hazard ratio for re-ETV failure relative to ETV failure. The correlation coefficient between ETVSS and the chance of re-ETV success was calculated using Kendall’s tau coefficient. Model discrimination was quantified using the c-statistic. The effects of intraoperative findings and management on re-ETV success were also analyzed. RESULTS The hazard ratio for re-ETV failure relative to ETV failure was 1.23 (95% CI 0.90-1.69; p = 0.20). At 6 months, the success rates for both ETV and re-ETV were 68%. ETVSS was significantly related to the chances of re-ETV success (τ = 0.37; 95% bias corrected and accelerated CI 0.21-0.52; p < 0.001). The c-statistic was 0.74 (95% CI 0.64-0.85). The presence of prepontine arachnoid membranes and use of an external ventricular drain (EVD) were negatively associated with treatment success, with ORs of 4.0 (95% CI 1.5-10.5) and 9.7 (95% CI 3.4-27.8), respectively. CONCLUSIONS Re-ETV seems to be as safe and effective as initial ETV. ETVSS adequately predicts the chance of successful re-ETV. The presence of prepontine arachnoid membranes and the use of EVD negatively influence the chance of success.

Concepts: Proportional hazards models, Survival analysis, Spearman's rank correlation coefficient, Effectiveness, Cerebrospinal fluid, Hazard ratio, Success, Kendall tau rank correlation coefficient


Pearson’s chi-square test has been widely used in testing for association between two categorical responses. Spearman rank correlation and Kendall’s tau are often used for measuring and testing association between two continuous or ordered categorical responses. However, the established statistical properties of these tests are only valid when each pair of responses are independent, where each sampling unit has only one pair of responses. When each sampling unit consists of a cluster of paired responses, the assumption of independent pairs is violated. In this article, we apply the within-cluster resampling technique to U-statistics to form new tests and rank-based correlation estimators for possibly tied clustered data. We develop large sample properties of the new proposed tests and estimators and evaluate their performance by simulations. The proposed methods are applied to a data set collected from a PET/CT imaging study for illustration.

Concepts: Statistical tests, Statistics, Spearman's rank correlation coefficient, Non-parametric statistics, Covariance and correlation, Statistical dependence, Pearson's chi-square test, Kendall tau rank correlation coefficient


Endpoints related to tumor progression are commonly used in clinical trials of novel therapeutic agents for neuroendocrine tumors (NETs). Whether improved tumor control translates into improved overall survival (OS), however, is uncertain. We assessed associations between tumor progression endpoints and OS in observational cohorts of patients with advanced neuroendocrine tumors treated with somatostatin analogs or with everolimus. We identified 440 patients with advanced NET who had received treatment with single-agent somatostatin analogs and 109 patients treated with everolimus, all of whom were treated at our institution and were evaluable for both tumor progression and survival. We assessed associations between progression-free survival (PFS) and OS by using the Kendall tau test, and we assessed associations between tumor progression and OS by using a landmark analysis. In the 440 patients treated with somatostatin analogs, we observed a significant correlation between PFS and OS by using the Kendall tau test (0.31; p < .0001). Additionally, the development of progressive disease was associated with OS in a landmark analysis, at landmark times of 6, 12, 18, and 24 months. In the 109 patients treated with everolimus, we similarly observed a significant correlation between PFS and OS by using the Kendall tau test (0.44; p < .0001) and associations between progressive disease and OS by using a landmark analysis at 3, 6, and 12 months. In these observational cohorts of patients with metastatic NET treated with single-agent somatostatin analogs or everolimus, longer times to disease progression and longer PFS were both associated with improved OS. Our findings support the continued use of disease progression endpoints in NET clinical trials. The Oncologist 2017;22:000-000Implications for Practice: Clinical trials in patients with advanced neuroendocrine tumors have used progression-free survival as a primary endpoint. While there is a general assumption that slowing or halting tumor growth is beneficial, little direct evidence links improvements in progression endpoints to improvements in overall survival. This study assessed associations between tumor progression endpoints and overall survival in observational cohorts of patients with advanced neuroendocrine tumor treated with somatostatin analogs or everolimus. Longer times to disease progression and improved progression-free survival were both associated with improved overall survival. The findings support the continued use of tumor progression endpoints in clinical trials for neuroendocrine tumors.

Concepts: Cancer, Oncology, Spearman's rank correlation coefficient, Kendall tau rank correlation coefficient


The purpose of this paper is to highlight the importance of a population model in guiding the design and interpretation of simulation studies used to investigate the Spearman rank correlation. The Spearman rank correlation has been known for over a hundred years to applied researchers and methodologists alike and is one of the most widely used non-parametric statistics. Still, certain misconceptions can be found, either explicitly or implicitly, in the published literature because a population definition for this statistic is rarely discussed within the social and behavioural sciences. By relying on copula distribution theory, a population model is presented for the Spearman rank correlation, and its properties are explored both theoretically and in a simulation study. Through the use of the Iman-Conover algorithm (which allows the user to specify the rank correlation as a population parameter), simulation studies from previously published articles are explored, and it is found that many of the conclusions purported in them regarding the nature of the Spearman correlation would change if the data-generation mechanism better matched the simulation design. More specifically, issues such as small sample bias and lack of power of the t-test and r-to-z Fisher transformation disappear when the rank correlation is calculated from data sampled where the rank correlation is the population parameter. A proof for the consistency of the sample estimate of the rank correlation is shown as well as the flexibility of the copula model to encompass results previously published in the mathematical literature.

Concepts: Statistics, Spearman's rank correlation coefficient, Non-parametric statistics, Pearson product-moment correlation coefficient, Covariance and correlation, Statistical dependence, Kendall tau rank correlation coefficient


The objectives of this study were to demonstrate that the length of the tracheoesophageal voice prosthesis changes over time and to determine whether the prosthesis length over time increased, decreased, or showed no predictable change in size. A retrospective chart review was performed at a tertiary care referral center. Patients who underwent either primary or secondary tracheoesophageal puncture between January 2006 and August 2014 were evaluated. Patients were excluded if the tracheoesophageal prosthesis size was not consistently recorded or if they required re-puncturing for an extruded prosthesis. Data analyzed included patient demographics and the length of the tracheoesophageal voice prosthesis at each change. A total of 37 patients were identified. The mean age was 64 years. Seventy-six percent were male. 24 % underwent primary tracheoesophageal puncture and 76 % underwent secondary tracheoesophageal puncture. The length of the prosthesis decreased over time (median Kendall correlation coefficient = -0.60; mean = -0.44) and this correlation between length and time was significant (p = 0.00085). Therefore, in conclusion, tracheoesophageal prosthesis length is not constant over time. The tracheoesophageal wall thins, necessitating placement of shorter prostheses over time. Patients with a tracheoesophageal voice prosthesis will require long-term follow-up and repeat sizing of their prosthesis. Successful tracheoesophageal voicing will require periodic reevaluation of these devices, and insurers must, therefore, understand that long-term professional care will be required to manage these patients and their prostheses.

Concepts: Retrospective, Arithmetic mean, Fistula, Prosthesis, Palatal obturator, Kendall tau rank correlation coefficient