Data analysis methods in optometry Part 8: Principal components analysis (PCA) and factor analysis (FA)

PCA/FA is a method of analyzing complex data sets in which there are no clearly defined X or Y variables. It has multiple uses including the study of the pattern of variation between individual entities such as patients with particular disorders and the detailed study of descriptive variables. In most applications, variables are related to a smaller number of ‘factors’ or PCs that account for the maximum variance in the data and hence, may explain important trends among the variables. An increasingly important application of the method is in the ‘validation’ of questionnaires that attempt to relate subjective aspects of a patients experience with more objective measures of vision.

Quantitative methods in neuropathology

The last decade has seen a considerable increase in the application of quantitative methods in the study of histological sections of brain tissue and especially in the study of neurodegenerative disease. These disorders are characterised by the deposition and aggregation of abnormal or misfolded proteins in the form of extracellular protein deposits such as senile plaques (SP) and intracellular inclusions such as neurofibrillary tangles (NFT). Quantification of brain lesions and studying the relationships between lesions and normal anatomical features of the brain, including neurons, glial cells, and blood vessels, has become an important method of elucidating disease pathogenesis. This review describes methods for quantifying the abundance of a histological feature such as density, frequency, and 'load' and the sampling methods by which quantitative measures can be obtained including plot/quadrat sampling, transect sampling, and the point-quarter method. In addition, methods for determining the spatial pattern of a histological feature, i.e., whether the feature is distributed at random, regularly, or is aggregated into clusters, are described. These methods include the use of the Poisson and binomial distributions, pattern analysis by regression, Fourier analysis, and methods based on mapped point patterns. Finally, the statistical methods available for studying the degree of spatial correlation between pathological lesions and neurons, glial cells, and blood vessels are described.

Quantitative neuropathology:data collection and statistical analysis

The use of quantitative methods has become increasingly important in the study of neuropathology and especially in neurodegenerative disease. Disorders such as Alzheimer's disease (AD) and the frontotemporal dementias (FTD) are characterized by the formation of discrete, microscopic, pathological lesions which play an important role in pathological diagnosis. This chapter reviews the advantages and limitations of the different methods of quantifying pathological lesions in histological sections including estimates of density, frequency, coverage, and the use of semi-quantitative scores. The sampling strategies by which these quantitative measures can be obtained from histological sections, including plot or quadrat sampling, transect sampling, and point-quarter sampling, are described. In addition, data analysis methods commonly used to analysis quantitative data in neuropathology, including analysis of variance (ANOVA), polynomial curve fitting, multiple regression, classification trees, and principal components analysis (PCA), are discussed. These methods are illustrated with reference to quantitative studies of a variety of neurodegenerative disorders.

The classification of HLA supertypes by GRID/CPCA and hierarchical clustering methods

Biological experiments often produce enormous amount of data, which are usually analyzed by data clustering. Cluster analysis refers to statistical methods that are used to assign data with similar properties into several smaller, more meaningful groups. Two commonly used clustering techniques are introduced in the following section: principal component analysis (PCA) and hierarchical clustering. PCA calculates the variance between variables and groups them into a few uncorrelated groups or principal components (PCs) that are orthogonal to each other. Hierarchical clustering is carried out by separating data into many clusters and merging similar clusters together. Here, we use an example of human leukocyte antigen (HLA) supertype classification to demonstrate the usage of the two methods. Two programs, Generating Optimal Linear Partial Least Square Estimations (GOLPE) and Sybyl, are used for PCA and hierarchical clustering, respectively. However, the reader should bear in mind that the methods have been incorporated into other software as well, such as SIMCA, statistiXL, and R.

A comparison of denoising methods for X-ray fluoroscopic images

Fluoroscopic images exhibit severe signal-dependent quantum noise, due to the reduced X-ray dose involved in image formation, that is generally modelled as Poisson-distributed. However, image gray-level transformations, commonly applied by fluoroscopic device to enhance contrast, modify the noise statistics and the relationship between image noise variance and expected pixel intensity. Image denoising is essential to improve quality of fluoroscopic images and their clinical information content. Simple average filters are commonly employed in real-time processing, but they tend to blur edges and details. An extensive comparison of advanced denoising algorithms specifically designed for both signal-dependent noise (AAS, BM3Dc, HHM, TLS) and independent additive noise (AV, BM3D, K-SVD) was presented. Simulated test images degraded by various levels of Poisson quantum noise and real clinical fluoroscopic images were considered. Typical gray-level transformations (e.g. white compression) were also applied in order to evaluate their effect on the denoising algorithms. Performances of the algorithms were evaluated in terms of peak-signal-to-noise ratio (PSNR), signal-to-noise ratio (SNR), mean square error (MSE), structural similarity index (SSIM) and computational time. On average, the filters designed for signal-dependent noise provided better image restorations than those assuming additive white Gaussian noise (AWGN). Collaborative denoising strategy was found to be the most effective in denoising of both simulated and real data, also in the presence of image gray-level transformations. White compression, by inherently reducing the greater noise variance of brighter pixels, appeared to support denoising algorithms in performing more effectively. © 2012 Elsevier Ltd. All rights reserved.

On Probabilistic Rationing Methods

Rationing occurs if the demand for a certain good exceeds its supply. In such situations a rationing method has to be specified in order to determine the allocation of the scarce good to the agents. Moulin (1999) introduced the notion of probabilistic rationing methods for the discrete framework. In this paper we establish a link between classical and probabilistic rationing methods. In particular, we assign to any given classical rationing method a probabilistic rationing method with minimal variance among those probabilistic rationing methods, which result in the same expected distributions as the given classical rationing method.

A Minor Change?: A Case Study of Carleton Place's Integration of Minor Variance Procedures into Ontario's Development Permit System

The Development Permit System has been introduce with minimal directives for establishing a decision making process. This is in opposition to the long established process for minor variances and suggests that the Development Permit System does not necessarily incorporate all of Ontario’s fundamental planning principles. From this concept, the study aimed to identify how minor variances are incorporated into the Development Permit System. In order to examine this topic, the research was based around the following research questions: • How are ‘minor variance’ applications processed within the DPS? • To what extent do the four tests of a minor variance influence the outcomes of lower level applications in the DPS approval process? A case study approach was used for this research. The single-case design employed both qualitative and quantitative research methods including a review of academic literature, court cases, and official documents, as well as a content analysis of Class 1, 1A, and 2 Development Permit application files from the Town of Carleton Place that were decided between 2011 and 2015. Upon the completion of the content analysis, it was found that minor variance issues were most commonly assigned to Class 1 applications. Planning staff generally met approval timelines and embraced their delegated approval authority, readily attaching conditions to applications in order to mitigate off-site impacts. While staff met the regulatory requirements of the DPS, ‘minor variance’ applications were largely decided on impact alone, demonstrating that the principles established by the four tests, the defining quality of the minor variance approval process, had not transferred to the Development Permit System. Alternatively, there was some evidence that the development community has not fully adjusted to the requirements of the new approvals process, as some applications were supported using a rationale containing the four tests. Subsequently, a set of four recommendations were offered which reflect the main themes established by the findings. The first two recommendations are directed towards the Province, the third to municipalities and the fourth to developers and planning consultants: 1) Amend Ontario Regulation 608/06 so that provisions under Section 4(3)(e) fall under Section 4(2). 2) Change the rhetoric from “combining elements of minor variances” to “replacing minor variances”. 3) Establish clear evaluation criteria. 4) Understand the evaluative criteria of the municipality in which you are working.

Comparison of five popular normalization methods using a spike-in proteomics data set

Mass spectrometry (MS)-based proteomics has seen significant technical advances during the past two decades and mass spectrometry has become a central tool in many biosciences. Despite the popularity of MS-based methods, the handling of the systematic non-biological variation in the data remains a common problem. This biasing variation can result from several sources ranging from sample handling to differences caused by the instrumentation. Normalization is the procedure which aims to account for this biasing variation and make samples comparable. Many normalization methods commonly used in proteomics have been adapted from the DNA-microarray world. Studies comparing normalization methods with proteomics data sets using some variability measures exist. However, a more thorough comparison looking at the quantitative and qualitative differences of the performance of the different normalization methods and at their ability in preserving the true differential expression signal of proteins, is lacking. In this thesis, several popular and widely used normalization methods (the Linear regression normalization, Local regression normalization, Variance stabilizing normalization, Quantile-normalization, Median central tendency normalization and also variants of some of the forementioned methods), representing different strategies in normalization are being compared and evaluated with a benchmark spike-in proteomics data set. The normalization methods are evaluated in several ways. The performance of the normalization methods is evaluated qualitatively and quantitatively on a global scale and in pairwise comparisons of sample groups. In addition, it is investigated, whether performing the normalization globally on the whole data or pairwise for the comparison pairs examined, affects the performance of the normalization method in normalizing the data and preserving the true differential expression signal. In this thesis, both major and minor differences in the performance of the different normalization methods were found. Also, the way in which the normalization was performed (global normalization of the whole data or pairwise normalization of the comparison pair) affected the performance of some of the methods in pairwise comparisons. Differences among variants of the same methods were also observed.

Comparison of two field methods for estimating body fat in different Spanish Dance disciplines

The purpose of the present study was to investigate percentage body fat (%BF) differences in three Spanish dance disciplines and to compare skinfold and bioelectrical impedance predictions of body fat percentage in the same sample. Seventy-six female dancers, divided into three groups, Classical (n=23), Spanish (n=29) and Flamenco (n=24), were measured using skinfold measurements at four sites: triceps, subscapular, biceps and iliac crest, and whole body multi-frequency bioelectrical impedance (BIA). The skin-fold measures were used to predict body fat percentage via Durnin and Womersley's and Segal, Sun and Yannakoulia equations by BIA. Differences in percent fat mass between groups (Classical, Spanish and Flamenco) were tested by using repeated measures analysis (ANOVA). Also, Pearson's product-moment correlations were performed on the body fat percentage values obtained using both methods. In addition, Bland-Altman plots were used to assess agreement, between anthropometric and BIA methods. Repeated measures analysis of variance did not found differences in %BF between modalities (p<0.05). Fat percentage correlations ranged from r= 0.57 to r=0.97 (all, p<0.001). Bland-Altman analysis revealed differences between BIA Yannakoulia as a reference method with BIA Segal (-0.35 ± 2.32%, 95%CI: -0.89to 0.18, p=0.38), with BIA Sun (-0.73 ± 2.3%, 95%CI: -1.27 to -0.20, p=0.014) and Durnin-Womersley (-2.65 ± 2,48%, 95%CI: -3.22 to -2.07, p<0.0001). It was concluded that body fat percentage estimates by BIA compared with skinfold method were systematically different in young adult female ballet dancers, having a tendency to produce underestimations as %BF increased with Segal and Durnin-Womersley equations compared to Yannakoulia, concluding that these methods are not interchangeable.

Quality evaluation of cortex berberidis from different geographical origins by simultaneous high performance liquid chromatography combined with statistical methods

Purpose: To develop an effective method for evaluating the quality of Cortex berberidis from different geographical origins. Methods: A simple, precise and accurate high performance liquid chromatography (HPLC) method was first developed for simultaneous quantification of four active alkaloids (magnoflorine, jatrorrhizine, palmatine, and berberine) in Cortex berberidis obtained from Qinghai, Tibet and Sichuan Provinces of China. Method validation was performed in terms of precision, repeatability, stability, accuracy, and linearity. Besides, partial least squares discriminant analysis (PLS-DA) and one-way analysis of variance (ANOVA) were applied to study the quality variations of Cortex berberidis from various geographical origins. Results: The proposed HPLC method showed good linearity, precision, repeatability, and accuracy. The four alkaloids were detected in all samples of Cortex berberidis. Among them, magnoflorine (36.46 - 87.30 mg/g) consistently showed the highest amounts in all the samples, followed by berberine (16.00 - 37.50 mg/g). The content varied in the range of 0.66 - 4.57 mg/g for palmatine and 1.53 - 16.26 mg/g for jatrorrhizine, respectively. The total content of the four alkaloids ranged from 67.62 to 114.79 mg/g. Moreover, the results obtained by the PLS-DA and ANOVA showed that magnoflorine level and the total content of these four alkaloids in Qinghai and Tibet samples were significantly higher (p < 0.01) than those in Sichuan samples. Conclusion: Quantification of multi-ingredients by HPLC combined with statistical methods provide an effective approach for achieving origin discrimination and quality evaluation of Cortex berberidis. The quality of Cortex berberidis closely correlates to the geographical origin of the samples, with Cortex berberidis samples from Qinghai and Tibet exhibiting superior qualities to those from Sichuan.

Evaluation Of Different Treatment Methods Against Denture Stomatitis: A Randomized Clinical Study.

The aim of this clinical study was to determine the efficacy of Uncaria tomentosa (cat's claw) against denture stomatitis (DS). Fifty patients with DS were randomly assigned into 3 groups to receive 2% miconazole, placebo, or 2% U tomentosa gel. DS level was recorded immediately, after 1 week of treatment, and 1 week after treatment. The clinical effectiveness of each treatment was measured using Newton's criteria. Mycologic samples from palatal mucosa and prosthesis were obtained to determinate colony forming units per milliliter (CFU/mL) and fungal identification at each evaluation period. Candida species were identified with HiCrome Candida and API 20C AUX biochemical test. DS severity decreased in all groups (P < .05). A significant reduction in number of CFU/mL after 1 week (P < .05) was observed for all groups and remained after 14 days (P > .05). C albicans was the most prevalent microorganism before treatment, followed by C tropicalis, C glabrata, and C krusei, regardless of the group and time evaluated. U tomentosa gel had the same effect as 2% miconazole gel. U tomentosa gel is an effective topical adjuvant treatment for denture stomatitis.

Petroleomics By Electrospray Ionization Ft-icr Mass Spectrometry Coupled To Partial Least Squares With Variable Selection Methods: Prediction Of The Total Acid Number Of Crude Oils.

Negative-ion mode electrospray ionization, ESI(-), with Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR MS) was coupled to a Partial Least Squares (PLS) regression and variable selection methods to estimate the total acid number (TAN) of Brazilian crude oil samples. Generally, ESI(-)-FT-ICR mass spectra present a power of resolution of ca. 500,000 and a mass accuracy less than 1 ppm, producing a data matrix containing over 5700 variables per sample. These variables correspond to heteroatom-containing species detected as deprotonated molecules, [M - H](-) ions, which are identified primarily as naphthenic acids, phenols and carbazole analog species. The TAN values for all samples ranged from 0.06 to 3.61 mg of KOH g(-1). To facilitate the spectral interpretation, three methods of variable selection were studied: variable importance in the projection (VIP), interval partial least squares (iPLS) and elimination of uninformative variables (UVE). The UVE method seems to be more appropriate for selecting important variables, reducing the dimension of the variables to 183 and producing a root mean square error of prediction of 0.32 mg of KOH g(-1). By reducing the size of the data, it was possible to relate the selected variables with their corresponding molecular formulas, thus identifying the main chemical species responsible for the TAN values.

Estimated Disability-adjusted Life Years Averted By Long-term Provision Of Long Acting Contraceptive Methods In A Brazilian Clinic.

What is the contribution of the provision, at no cost for users, of long acting reversible contraceptive methods (LARC; copper intrauterine device [IUD], the levonorgestrel-releasing intrauterine system [LNG-IUS], contraceptive implants and depot-medroxyprogesterone [DMPA] injection) towards the disability-adjusted life years (DALY) averted through a Brazilian university-based clinic established over 30 years ago. Over the last 10 years of evaluation, provision of LARC methods and DMPA by the clinic are estimated to have contributed to DALY averted by between 37 and 60 maternal deaths, 315-424 child mortalities, 634-853 combined maternal morbidity and mortality and child mortality, and 1056-1412 unsafe abortions averted. LARC methods are associated with a high contraceptive effectiveness when compared with contraceptive methods which need frequent attention; perhaps because LARC methods are independent of individual or couple compliance. However, in general previous studies have evaluated contraceptive methods during clinical studies over a short period of time, or not more than 10 years. Furthermore, information regarding the estimation of the DALY averted is scarce. We reviewed 50 004 medical charts from women who consulted for the first time looking for a contraceptive method over the period from 2 January 1980 through 31 December 2012. Women who consulted at the Department of Obstetrics and Gynaecology, University of Campinas, Brazil were new users and users switching contraceptive, including the copper IUD (n = 13 826), the LNG-IUS (n = 1525), implants (n = 277) and DMPA (n = 9387). Estimation of the DALY averted included maternal morbidity and mortality, child mortality and unsafe abortions averted. We obtained 29 416 contraceptive segments of use including 25 009 contraceptive segments of use from 20 821 new users or switchers to any LARC method or DMPA with at least 1 year of follow-up. The mean (± SD) age of the women at first consultation ranged from 25.3 ± 5.7 (range 12-47) years in the 1980s, to 31.9 ± 7.4 (range 16-50) years in 2010-2011. The most common contraceptive chosen at the first consultation was copper IUD (48.3, 74.5 and 64.7% in the 1980s, 1990s and 2000s, respectively). For an evaluation over 20 years, the cumulative pregnancy rates (SEM) were 0.4 (0.2), 2.8 (2.1), 4.0 (0.4) and 1.3 (0.4) for the LNG-IUS, the implants, copper IUD and DMPA, respectively and cumulative continuation rates (SEM) were 15.1 (3.7), 3.9 (1.4), 14.1 (0.6) and 7.3 (1.7) for the LNG-IUS, implants, copper IUD and DMPA, respectively (P < 0.001). Over the last 10 years of evaluation, the estimation of the contribution of the clinic through the provision of LARC methods and DMPA to DALY averted was 37-60 maternal deaths; between 315 and 424 child mortalities; combined maternal morbidity and mortality and child mortality of between 634 and 853, and 1056-1412 unsafe abortions averted. The main limitations are the number of women who never returned to the clinic (overall 14% among the four methods under evaluation); consequently the pregnancy rate could be different. Other limitations include the analysis of two kinds of copper IUD and two kinds of contraceptive implants as the same IUD or implant, and the low number of users of implants. In addition, the DALY calculation relies on a number of estimates, which may vary in different parts of the world. LARC methods and DMPA are highly effective and women who were well-counselled used these methods for a long time. The benefit of averting maternal morbidity and mortality, child mortality, and unsafe abortions is an example to health policy makers to implement more family planning programmes and to offer contraceptive methods, mainly LARC and DMPA, at no cost or at affordable cost for the underprivileged population. This study received partial financial support from the Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP), grant # 2012/12810-4 and from the National Research Council (CNPq), grant #573747/2008-3. B.F.B., M.P.G., and V.M.C. were fellows from the scientific initiation programme from FAPESP. Since the year 2001, all the TCu380A IUD were donated by Injeflex, São Paulo, Brazil, and from the year 2006 all the LNG-IUS were donated by the International Contraceptive Access Foundation (ICA), Turku, Finland. Both donations are as unrestricted grants. The authors declare that there are no conflicts of interest associated with this study.

Evaluation Of The Effect Of Different Methods Of Microabrasion And Polishing On Surface Roughness Of Dental Enamel.

The microabrasion technique of enamel consists of selectively abrading the discolored areas or causing superficial structural changes in a selective way. In microabrasion technique, abrasive products associated with acids are used, and the evaluation of enamel roughness after this treatment, as well as surface polishing, is necessary. This in-vitro study evaluated the enamel roughness after microabrasion, followed by different polishing techniques. Roughness analyses were performed before microabrasion (L1), after microabrasion (L2), and after polishing (L3).Thus, 60 bovine incisive teeth divided into two groups were selected (n=30): G1- 37% phosphoric acid (37%) (Dentsply) and pumice; G2- hydrochloric acid (6.6%) associated with silicon carbide (Opalustre - Ultradent). Thereafter, the groups were divided into three sub-groups (n=10), according to the system of polishing: A - Fine and superfine granulation aluminum oxide discs (SofLex 3M); B - Diamond Paste (FGM) associated with felt discs (FGM); C - Silicone tips (Enhance - Dentsply). A PROC MIXED procedure was applied after data exploratory analysis, as well as the Tukey-Kramer test (5%). No statistical differences were found between G1 and G2 groups. L2 differed statistically from L1 and showed superior amounts of roughness. Differences in the amounts of post-polishing roughness for specific groups (1A, 2B, and 1C) arose, which demonstrated less roughness in L3 and differed statistically from L2 in the polishing system. All products increased enamel roughness, and the effectiveness of the polishing systems was dependent upon the abrasive used.