Nonparametric Estimation of Data Dimensionality Prior to Data Compression: the case of the Human Development Index

In many applications in applied statistics researchers reduce the complexity of a data set by combining a group of variables into a single measure using factor analysis or an index number. We argue that such compression loses information if the data actually has high dimensionality. We advocate the use of a non-parametric estimator, commonly used in physics (the Takens estimator), to estimate the correlation dimension of the data prior to compression. The advantage of this approach over traditional linear data compression approaches is that the data does not have to be linearized. Applying our ideas to the United Nations Human Development Index we find that the four variables that are used in its construction have dimension three and the index loses information.

Effect of cataract extraction on the Glaucoma Progression Index (GPI) in glaucoma patients

PURPOSE: To determine the effect of cataract extraction on the glaucoma progression index (GPI) in glaucoma patients with coexisting cataract.

PATIENTS AND METHODS: This is a retrospective noncomparative study. Consecutive eligible patients with glaucoma who underwent phacoemulsification alone or in combination with augmented trabeculectomy were included. All patients had Swedish Interactive Threshold Algorithm-standard 24-2 visual fields within 10 months of surgery. Exclusion criteria included other ocular morbidity, intraoperative complications, and perimetric reliability indices greater than 33%. Comparison was made between the immediate visual fields before and after surgery. The main outcome measure was the change in GPI. Changes in the pattern standard deviation (PSD) and mean deviation (MD) were also assessed. Comparison of means was performed with the paired t test.

RESULTS: Thirty-three eyes of 33 patients (all Whites) were analyzed. The mean age at surgery was 77.0+/-8.7 years. Visual field tests were performed 3.3+/-3.0 months SD before surgery and 5.4+/-2.6 months after surgery. There was a statistically significant increase in the GPI after cataract surgery (from 71.5+/-18.5% to 74.6+/-17.1%; P=0.02). The improvement in MD was also statistically significant (from -11.8+/-5.3 to -10.2+/-5.3 dB; P <0.01), but the change in PSD did not reach statistical significance.

CONCLUSIONS: Uncomplicated cataract extraction resulted in a statistically significant improvement in the 24-2 Swedish Interactive Threshold Algorithm-standard GPI and MD, but not in PSD. Both the MD and the GPI may be influenced by lens opacities, which could make detection of glaucoma visual field progression more difficult for clinicians in glaucoma patients with concurrent cataract.

Perimetric progression in open angle glaucoma and the Visual Field Index (VFI)

PURPOSE: To evaluate the changes in the Visual Field Index (VFI) in eyes with perimetric glaucomatous progression, and to compare these against stable glaucoma patients.

PATIENTS AND METHODS: Consecutive patients with open angle glaucoma with a minimum of 6 reliable visual fields and 2 years of follow-up were identified. Perimetric progression was assessed by 4 masked glaucoma experts from different units, and classified into 3 categories: "definite progression," "suspected progression," or "no progression." This was compared with the Glaucoma Progression Analysis (GPA) II and VFI linear regression analysis, where progression was defined as a negative slope with significance of <5%.

RESULTS: Three hundred ninety-seven visual fields from 51 eyes of 39 patients were assessed. The mean number of visual fields was 7.8 (SD 1.1) per eye, and the mean follow-up duration was 63.7 (SD 13.4) months. The mean VFI linear regression slope showed an overall statistically significant difference (P<0.001, analysis of variance) for each category of progression. Using expert consensus opinion as the reference standard, both VFI analysis and GPA II had high specificity (0.93 and 0.90, respectively), but relatively low sensitivity (0.45 and 0.41, respectively).

CONCLUSIONS: The mean VFI regression slope in our cohort of eyes without perimetric progression showed a statistically significant difference compared with those with suspected and definite progression. VFI analysis and GPA II both had similarly high specificity but low sensitivity when compared with expert consensus opinion.

Liquid densities, heat capacities, refractive index and excess quantities for {protic ionic liquids plus water} binary system

Densities, rho, of aqueous solutions of the room temperature protic ionic liquid (PIL), pyrrolidinium nitrate are determined at the atmospheric pressure over the temperature range from (283.15 to 323.15) K and within the whole composition range. The molar isobaric heat capacities, C(p), and refractive index, n(D), of {PIL + water} binary system are measured at 298.15 K. The excess molar volumes V(E), excess molar isobaric heat capacities C(p)(E), and deviation from ideality of refractive index Delta(phi)n, of pyrrolidinium nitrate aqueous solutions were deduced from the experimental results as well as apparent molar volumes V(phi), partial molar volumes (V) over bar (m,i), and thermal expansion coefficients alpha(p). The V(E) values were found to be positive over the entire composition range at all temperatures studied therein, whereas deviations from ideality were negative for refractive index Delta(phi)n. The volumetric properties of binary mixtures containing water and four other protic ionic liquids, such as pyrrolidinium hydrogen sulfate, pyrrolidinium formiate, collidinium formate, and diisopropyl-ethylammonium formate were also determined at 298.15 K. Results have been then discussed in terms of molecular interactions and molecular structures in these binary mixtures. (C) 2009 Elsevier Ltd. All rights reserved.

Dietary Carbohydrate Intake, Glycemic Index, and Glycemic Load and Endometrial Cancer Risk: A Prospective Cohort Study

Endometrial cancer risk has been directly associated with glycemic load. However, few studies have investigated this link, and the etiological role of specific dietary carbohydrate components remains unclear. Our aim was to investigate associations of carbohydrate intake, glycemic index, and glycemic load with endometrial cancer risk in the US Prostate, Lung, Colorectal and Ovarian Cancer Screening Trial. Recruitment took place in 1993-2001. Over a median of 9.0 years of follow-up through 2009, 386 women developed endometrial cancer among 36,115 considered in the analysis. Dietary intakes were assessed using a 124-item diet history questionnaire. Cox proportional hazards models were applied to calculate hazard ratios and 95% confidence intervals. Significant inverse associations were detected between endometrial cancer risk and total available carbohydrate intake (hazard ratio (HR) = 0.66, 95% confidence interval (CI): 0.49, 0.90), total sugars intake (HR = 0.71, 95% CI: 0.52, 0.96), and glycemic load (HR = 0.63, 95% CI: 0.46, 0.84) when women in the highest quartile of intake were compared with those in the lowest. These inverse associations were strongest among overweight and obese women. No associations with endometrial cancer risk were observed for glycemic index or dietary fiber. Our findings contrast with previous evidence and suggest that high carbohydrate intakes and glycemic loads are protective against endometrial cancer development. Further clarification of these associations is warranted.

Prospective investigation of body mass index, colorectal adenoma, and colorectal cancer in the prostate, lung, colorectal, and ovarian cancer screening trial

Obesity has consistently been linked to an increased risk of colorectal cancer, particularly among men. Whether body mass index (BMI) differentially influences the risk across the stages of colorectal cancer development remains unclear. We evaluated the associations of BMI with colorectal adenoma incidence, adenoma recurrence, and cancer in the context of a large screening trial, in which cases and controls had an equal chance for disease detection.

Fetal Umbilical Artery Doppler Pulsatility Index as a Predictor of Cardiovascular Risk Factors in Children - A Long-Term Follow Up Study

Abstract Objective To determine if high umbilical artery Doppler (UAD) pulsatility index (PI) is associated with cardio-vascular (CV) risk-factors in children at age 12 years. Methods We studied 195 children at age 12 years who had had in-utero UAD studies performed at 28 weeks gestation. The children were grouped according to whether their umbilical Doppler PI was high (indicating poor feto-placental circulation) or normal. At age 12 years we assessed CV risk factors, including anthropometric measures, blood pressure, pulse wave velocity (a measure of arterial compliance), cardio-respiratory fitness and homocysteine and cholesterol serum levels. Results Compared with children with a normal UAD PI (N=88), the children (N=107) with high UAD PI had higher resting pulse rate (p=0.04), higher pulse wave velocity (p=0.046), higher serum homocysteine levels (p=0.032) and reduced arterial compliance (7.58 v 8.50 m/sec, p=0.029) using univariate analysis. These differences were not present when adjusting for cofounders was modelled. Conclusion High PI on UAD testing in-utero may be associated with increased likelihood of some cardio-vascular risk factors at age 12-years but confounding variables may be as important. Our study raises possible long-term benefits of in-utero UAD measurements.