Statnote 29:discriminant analysis

Discriminant analysis (also known as discriminant function analysis or multiple discriminant analysis) is a multivariate statistical method of testing the degree to which two or more populations may overlap with each other. It was devised independently by several statisticians including Fisher, Mahalanobis, and Hotelling ). The technique has several possible applications in Microbiology. First, in a clinical microbiological setting, if two different infectious diseases were defined by a number of clinical and pathological variables, it may be useful to decide which measurements were the most effective at distinguishing between the two diseases. Second, in an environmental microbiological setting, the technique could be used to study the relationships between different populations, e.g., to what extent do the properties of soils in which the bacterium Azotobacter is found differ from those in which it is absent? Third, the method can be used as a multivariate ‘t’ test , i.e., given a number of related measurements on two groups, the analysis can provide a single test of the hypothesis that the two populations have the same means for all the variables studied. This statnote describes one of the most popular applications of discriminant analysis in identifying the descriptive variables that can distinguish between two populations.

Predicting class I major histocompatibility complex (MHC) binders using multivariate statistics:comparison of discriminant analysis and multiple linear regression

The accurate in silico identification of T-cell epitopes is a critical step in the development of peptide-based vaccines, reagents, and diagnostics. It has a direct impact on the success of subsequent experimental work. Epitopes arise as a consequence of complex proteolytic processing within the cell. Prior to being recognized by T cells, an epitope is presented on the cell surface as a complex with a major histocompatibility complex (MHC) protein. A prerequisite therefore for T-cell recognition is that an epitope is also a good MHC binder. Thus, T-cell epitope prediction overlaps strongly with the prediction of MHC binding. In the present study, we compare discriminant analysis and multiple linear regression as algorithmic engines for the definition of quantitative matrices for binding affinity prediction. We apply these methods to peptides which bind the well-studied human MHC allele HLA-A*0201. A matrix which results from combining results of the two methods proved powerfully predictive under cross-validation. The new matrix was also tested on an external set of 160 binders to HLA-A*0201; it was able to recognize 135 (84%) of them.

Mathematical modelling of patient risks in a hospital environment, using multiple regression analysis

The aim of this research work was primarily to examine the relevance of patient parameters, ward structures, procedures and practices, in respect of the potential hazards of wound cross-infection and nasal colonisation with multiple resistant strains of Staphylococcus aureus, which it is thought might provide a useful indication of a patient's general susceptibility to wound infection. Information from a large cross-sectional survey involving 12,000 patients from some 41 hospitals and 375 wards was collected over a five-year period from 1967-72, and its validity checked before any subsequent analysis was carried out. Many environmental factors and procedures which had previously been thought (but never conclusively proved) to have an influence on wound infection or nasal colonisation rates, were assessed, and subsequently dismissed as not being significant, provided that the standard of the current range of practices and procedures is maintained and not allowed to deteriorate. Retrospective analysis revealed that the probability of wound infection was influenced by the patient's age, duration of pre-operative hospitalisation, sex, type of wound, presence and type of drain, number of patients in ward, and other special risk factors, whilst nasal colonisation was found to be influenced by the patient's age, total duration of hospitalisation, sex, antibiotics, proportion of occupied beds in the ward, average distance between bed centres and special risk factors. A multi-variate regression analysis technique was used to develop statistical models, consisting of variable patient and environmental factors which were found to have a significant influence on the risks pertaining to wound infection and nasal colonisation. A relationship between wound infection and nasal colonisation was then established and this led to the development of a more advanced model for predicting wound infections, taking advantage of the additional knowledge of the patient's state of nasal colonisation prior to operation.

Incremental tensor biased discriminant analysis:a new color-based visual tracking method

Most existing color-based tracking algorithms utilize the statistical color information of the object as the tracking clues, without maintaining the spatial structure within a single chromatic image. Recently, the researches on the multilinear algebra provide the possibility to hold the spatial structural relationship in a representation of the image ensembles. In this paper, a third-order color tensor is constructed to represent the object to be tracked. Considering the influence of the environment changing on the tracking, the biased discriminant analysis (BDA) is extended to the tensor biased discriminant analysis (TBDA) for distinguishing the object from the background. At the same time, an incremental scheme for the TBDA is developed for the tensor biased discriminant subspace online learning, which can be used to adapt to the appearance variant of both the object and background. The experimental results show that the proposed method can track objects precisely undergoing large pose, scale and lighting changes, as well as partial occlusion. © 2009 Elsevier B.V.

Data analysis methods in optometry Part 7: multiple linear regression

Multiple regression analysis is a complex statistical method with many potential uses. It has also become one of the most abused of all statistical procedures since anyone with a data base and suitable software can carry it out. An investigator should always have a clear hypothesis in mind before carrying out such a procedure and knowledge of the limitations of each aspect of the analysis. In addition, multiple regression is probably best used in an exploratory context, identifying variables that might profitably be examined by more detailed studies. Where there are many variables potentially influencing Y, they are likely to be intercorrelated and to account for relatively small amounts of the variance. Any analysis in which R squared is less than 50% should be suspect as probably not indicating the presence of significant variables. A further problem relates to sample size. It is often stated that the number of subjects or patients must be at least 5-10 times the number of variables included in the study.5 This advice should be taken only as a rough guide but it does indicate that the variables included should be selected with great care as inclusion of an obviously unimportant variable may have a significant impact on the sample size required.

Probing three-way interactions in moderated multiple regression:Development and application of a slope difference test

Researchers often use 3-way interactions in moderated multiple regression analysis to test the joint effect of 3 independent variables on a dependent variable. However, further probing of significant interaction terms varies considerably and is sometimes error prone. The authors developed a significance test for slope differences in 3-way interactions and illustrate its importance for testing psychological hypotheses. Monte Carlo simulations revealed that sample size, magnitude of the slope difference, and data reliability affected test power. Application of the test to published data yielded detection of some slope differences that were undetected by alternative probing techniques and led to changes of results and conclusions. The authors conclude by discussing the test's applicability for psychological research. Copyright 2006 by the American Psychological Association.

Electronic commerce adoption:a study of business-to-business practice in Saudi Arabia

Electronic commerce (e-commerce) has become an increasingly important initiative among organisations. The factors affecting adoption decisions have been well-documented, but there is a paucity of empirical studies that examine the adoption of e-commerce in developing economies in the Arab world. The aim of this study is to provide insights into the salient e-commerce adoption issues by focusing on Saudi Arabian businesses. Based on the Technology-Organisational-Environmental framework, an integrated research model was developed that explains the relative influence of 19 known determinants. A measurement scale was developed from prior empirical studies and revised based on feedback from the pilot study. Non-interactive adoption, interactive adoption and stabilisation of e-commerce adoption were empirically investigated using survey data collected from Saudi manufacturing and service companies. Multiple discriminant function analysis (MDFA) was used to analyse the data and research hypotheses. The analysis demonstrates that (1) regarding the non-interactive adoption of e-commerce, IT readiness, management team support, learning orientation, strategic orientation, pressure from business partner, regulatory and legal environment, technology consultants‘ participation and economic downturn are the most important factors, (2) when e-commerce interactive adoption is investigated, IT readiness, management team support, regulatory environment and technology consultants‘ participation emerge as the strongest drivers, (3) pressure from customers may not have much effect on the non-interactive adoption of e-commerce by companies, but does significantly influence the stabilisation of e-commerce use by firms, and (4) Saudi Arabia has a strong ICT infrastructure for supporting e-commerce practices. Taken together, these findings on the multi-dimensionality of e-commerce adoption show that non-interactive adoption, interactive adoption and stabilisation of e-commerce are not only different measures of e-commerce adoption, but also have different determinants. Findings from this study may be valuable for both policy and practice as it can offer a substantial understanding of the factors that enhance the widespread use of B2B e-commerce. Also, the integrated model provides a more comprehensive explanation of e-commerce adoption in organisations and could serve as a foundation for future research on information systems.

Correlation between visual function and visual ability in patients with uveitis

Aim: To investigate the correlation between tests of visual function and perceived visual ability recorded with a quality of life questionnaire for patients with uveitis. Methods: 132 patients with various types of uveitis were studied. High (monocular and binocular) and low (binocular) contrast logMAR letter acuities were recorded using a Bailey-Lovie chart. Contrast sensitivity (binocular) was determined using a Pelli-Robson chart. Vision related quality of life was assessed using the Vision Specific Quality of Life (VQOL) questionnaire. Results: VQOL declined with reduced performance on the following tests: binocular high contrast visual acuity (p = 0.0011), high contrast visual acuity of the better eye (p = 0.0012), contrast sensitivity (p = 0.005), binocular low contrast visual acuity (p = 0.0065), and high contrast visual acuity of the worse eye (p = 0.015). Stepwise multiple regression analysis revealed binocular high contrast visual acuity (p <0.01) to be the only visual function adequate to predict VQOL. The age of the patient was also significantly associated with perceived visual ability (p <0.001). Conclusions: Binocular high contrast visual acuity is a good measure of how uveitis patients perform in real life situations. Vision quality of life is worst in younger patients with poor binocular visual acuity.

The effect of corneal thickness and corneal curvature on pneumatonometer measurements

Purpose. The purpose of this study was to investigate the influence of corneal topography and thickness on intraocular pressure (IOP) and pulse amplitude (PA) as measured using the Ocular Blood Flow Analyzer (OBFA) pneumatonometer (Paradigm Medical Industries, Utah, USA). Methods. 47 university students volunteered for this cross-sectional study: mean age 20.4 yrs, range 18 to 28 yrs; 23 male, 24 female. Only the measurements from the right eye of each participant were used. Central corneal thickness and mean corneal radius were measured using Scheimpflug biometry and corneal topographic imaging respectively. IOP and PA measurements were made with the OBFA pneumatonometer. Axial length was measured using A-scan ultrasound, due to its known correlation with these corneal parameters. Stepwise multiple regression analysis was used to identify those components that contributed significant variance to the independent variables of IOP and PA. Results. The mean IOP and PA measurements were 13.1 (SD 3.3) mmHg and 3.0 (SD 1.2) mmHg respectively. IOP measurements made with the OBFA pneumatonometer correlated significantly with central corneal thickness (r = +0.374, p = 0.010), such that a 10 mm change in CCT was equivalent to a 0.30 mmHg change in measured IOP. PA measurements correlated significantly with axial length (part correlate = -0.651, p < 0.001) and mean corneal radius (part correlate = +0.459, p < 0.001) but not corneal thickness. Conclusions. IOP measurements taken with the OBFA pneumatonometer are correlated with corneal thickness, but not axial length or corneal curvature. Conversely, PA measurements are unaffected by corneal thickness, but correlated with axial length and corneal radius. These parameters should be taken into consideration when interpreting IOP and PA measurements made with the OBFA pneumatonometer.

Macular pigment optical density is related to blood glutathione levels in healthy individuals

Purpose. To assess the relationship between macular pigment optical density (MPOD) and blood markers for antioxidant defense in otherwise healthy volunteers. Methods. Forty-seven healthy volunteers were subjected to blood analysis to detect the level of circulating glutathione in its reduced (GSH) and oxidized (GSSG) forms. The level of MPOD was measured using heterochromatic flicker photometry. Systemic blood pressure (BP) parameters, heart rate (HR), body mass index (BMI), and plasma levels of total, HDL, and LDL cholesterol and triglycerides (TGs) were also determined. Results. A simple correlation model revealed that the level of MPOD correlated significantly and positively with both GSH (P < 0.001) and t-GSH (P < 0.001) levels but not with those of GSSG (P > 0.05). Age, sex, systemic BP parameters, HR, BMI, and plasma levels of cholesterol and TGs did not have any influence on either MPOD or glutathione levels (all P > 0.05). In addition, a forward stepwise multiple regression analysis showed MPOD to have a significantly and independent correlation with GSH levels (ß = 0.63; P < 0.001). Conclusions. In otherwise healthy older individuals, there is a positive correlation between local and systemic antioxidant defense mechanisms.

Alzheimer's disease: the relationship between the density of senile plaques, neurofibrillary tangles and A4 protein in human patients

The numerical density of senile plaques (SP) and neurofibrillary tangles (NFT) as revealed by the Glees silver method was compared with SP and NFT revealed by the Gallyas method and with amyloid (A4) deposits in immunostained sections in 6 elderly cases of Alzheimer's disease. The density of NFT was generally greater and A4 lower in tissue from hippocampus compared with the neocortex suggesting that A4 deposition was less important than the degree of paired helical filament (PHF) related damage in the hippocampus. The density of Glees SP was positively correlated Gallyas SP weakly correlated with A4 deposit number. A stepwise multiple regression analysis which included A4 deposit and Gallyas SP density and accounted for 54% of the variation in Glees SP density. Hence, different populations of SP were revealed by the different staining methods. The results suggested that the Glees method may stain a population of SP in a region of cortex where both amyloid deposition and neurofibrillary changes have occurred.

Beta-amyloid (Abeta) deposits and blood vessels: laminar distribution in the frontal cortex of patients with Alzheimer’s disease

The laminar distribution of diffuse, primitive and classic beta-amyloid (Abeta) deposits and blood vessels was studied in the frontal cortex of patients with Alzheimer’s disease (AD). In most patients, the density of the diffuse and primitive Abeta deposits was greatest in the upper cortical layers and the classic deposits in the deeper cortical layers. The distribution of the larger blood vessels (>10 micron in diameter) was often bimodal with peaks in the upper and deeper cortical layers. The incidence of capillaries (<10 micron) was significantly higher in the deeper cortical layers in most patients. Multiple regression analysis selected vertical distance below the pia mater as the most significant factor correlated with the Abeta deposit density. With the exception of the classic deposits in two patients, there was no evidence that these vertical distributions were related to laminar variations in the incidence of large or small blood vessels.

Seasonal growth of foliose lichens in successive years in South Gwynedd, Wales

The aim of this study was to test the hypothesis that differences in the pattern of seasonal growth in foliose lichens from year to year were determined by yearly differences in the distribution of rainfall, shortwave radiation and temperature. Hence, the radial growth of Parmelia conspersa (Ehrh. Ex Ach.) Ach. , P. glabratula ssp. fuliginosa (Fr. ex Duby) Laund. and Physcia orbicularis (Neck) Poetsch. was studied on slate fragments over 34 successive months in an area of South Gwynedd, Wales. U.K. Similarities and differences were observed in the pattern of seasonal growth in the three species. Periods of maximum growth of a species occurred in different seasons in successive years. Correlation and multiple regression analysis suggested that total rainfall per month was the most important climatic variable positively correlated with monthly growth. Significant positive correlations were found in some growth periods with number of raindays per month, average wind speed and maximum and minimum temperature. Total number of sunshine hours per month and the frequency of ground frosts were negatively correlated with monthly growth in some growth periods. For each species, monthly radial growth was correlated with different climatic variables in each growth period. Hence, the results support the hypothesis in that periods of maximum growth can occur in any season in South Gwynedd and depend on (1) the distribution of periods of high total rainfall and (2) whether or not these periods coincide with periods of maximum sunlight.