Statnote 25: Stepwise multiple regression

An investigator may also wish to select a small subset of the X variables which give the best prediction of the Y variable. In this case, the question is how many variables should the regression equation include? One method would be to calculate the regression of Y on every subset of the X variables and choose the subset that gives the smallest mean square deviation from the regression. Most investigators, however, prefer to use a ‘stepwise multiple regression’ procedure. There are two forms of this analysis called the ‘step-up’ (or ‘forward’) method and the ‘step-down’ (or ‘backward’) method. This Statnote illustrates the use of stepwise multiple regression with reference to the scenario introduced in Statnote 24, viz., the influence of climatic variables on the growth of the crustose lichen Rhizocarpon geographicum (L.)DC.

A stepwise fuzzy linear programming model with possibility and necessity relations

Linear programming (LP) is the most widely used optimization technique for solving real-life problems because of its simplicity and efficiency. Although conventional LP models require precise data, managers and decision makers dealing with real-world optimization problems often do not have access to exact values. Fuzzy sets have been used in the fuzzy LP (FLP) problems to deal with the imprecise data in the decision variables, objective function and/or the constraints. The imprecisions in the FLP problems could be related to (1) the decision variables; (2) the coefficients of the decision variables in the objective function; (3) the coefficients of the decision variables in the constraints; (4) the right-hand-side of the constraints; or (5) all of these parameters. In this paper, we develop a new stepwise FLP model where fuzzy numbers are considered for the coefficients of the decision variables in the objective function, the coefficients of the decision variables in the constraints and the right-hand-side of the constraints. In the first step, we use the possibility and necessity relations for fuzzy constraints without considering the fuzzy objective function. In the subsequent step, we extend our method to the fuzzy objective function. We use two numerical examples from the FLP literature for comparison purposes and to demonstrate the applicability of the proposed method and the computational efficiency of the procedures and algorithms. © 2013-IOS Press and the authors. All rights reserved.

Investigation of assessment methods for final year optometry undergraduates

This retrospective study was designed to investigate the factors that influence performance in examinations comprised of multiple-choice questions (MCQs), short-answer questions (SAQs), and essay questions in an undergraduate population. Final year optometry degree examination marks were analyzed for two separate cohorts. Direct comparison found that students performed better in MCQs than essays. However, forward stepwise regression analysis of module marks compared with the overall score showed that MCQs were the least influential, and the essay or SAQ mark was a more reliable predictor of overall grade. This has implications for examination design.

Knowledge management applied to enterprise risk management

Risk and knowledge are two concepts and components of business management which have so far been studied almost independently. This is especially true where risk management (RM) is conceived mainly in financial terms, as for example, in the financial institutions sector. Financial institutions are affected by internal and external changes with the consequent accommodation to new business models, new regulations and new global competition that includes new big players. These changes induce financial institutions to develop different methodologies for managing risk, such as the enterprise risk management (ERM) approach, in order to adopt a holistic view of risk management and, consequently, to deal with different types of risk, levels of risk appetite, and policies in risk management. However, the methodologies for analysing risk do not explicitly include knowledge management (KM). This research examines the potential relationships between KM and two RM concepts: perceived quality of risk control and perceived value of ERM. To fulfill the objective of identifying how KM concepts can have a positive influence on some RM concepts, a literature review of KM and its processes and RM and its processes was performed. From this literature review eight hypotheses were analysed using a classification into people, process and technology variables. The data for this research was gathered from a survey applied to risk management employees in financial institutions and 121 answers were analysed. The analysis of the data was based on multivariate techniques, more specifically stepwise regression analysis. The results showed that the perceived quality of risk control is significantly associated with the variables: perceived quality of risk knowledge sharing, perceived quality of communication among people, web channel functionality, and risk management information system functionality. However, the relationships of the KM variables to the perceived value of ERM are not identified because of the low performance of the models describing these relationships. The analysis reveals important insights into the potential KM support to RM such as: the better adoption of KM people and technology actions, the better the perceived quality of risk control. Equally, the results suggest that the quality of risk control and the benefits of ERM follow different patterns given that there is no correlation between both concepts and the distinct influence of the KM variables in each concept. The ERM scenario is different from that of risk control because ERM, as an answer to RM failures and adaptation to new regulation in financial institutions, has led organizations to adopt new processes, technologies, and governance models. Thus, the search for factors influencing the perceived value of ERM implementation needs additional analysis because what is improved in RM processes individually is not having the same effect on the perceived value of ERM. Based on these model results and the literature review the basis of the ERKMAS (Enterprise Risk Knowledge Management System) is presented.

Developing a scalable model of recombinant protein yield from Pichia pastoris:the influence of culture conditions, biomass and induction regime

Background The optimisation and scale-up of process conditions leading to high yields of recombinant proteins is an enduring bottleneck in the post-genomic sciences. Typical experiments rely on varying selected parameters through repeated rounds of trial-and-error optimisation. To rationalise this, several groups have recently adopted the 'design of experiments' (DoE) approach frequently used in industry. Studies have focused on parameters such as medium composition, nutrient feed rates and induction of expression in shake flasks or bioreactors, as well as oxygen transfer rates in micro-well plates. In this study we wanted to generate a predictive model that described small-scale screens and to test its scalability to bioreactors. Results Here we demonstrate how the use of a DoE approach in a multi-well mini-bioreactor permitted the rapid establishment of high yielding production phase conditions that could be transferred to a 7 L bioreactor. Using green fluorescent protein secreted from Pichia pastoris, we derived a predictive model of protein yield as a function of the three most commonly-varied process parameters: temperature, pH and the percentage of dissolved oxygen in the culture medium. Importantly, when yield was normalised to culture volume and density, the model was scalable from mL to L working volumes. By increasing pre-induction biomass accumulation, model-predicted yields were further improved. Yield improvement was most significant, however, on varying the fed-batch induction regime to minimise methanol accumulation so that the productivity of the culture increased throughout the whole induction period. These findings suggest the importance of matching the rate of protein production with the host metabolism. Conclusion We demonstrate how a rational, stepwise approach to recombinant protein production screens can reduce process development time.

The impact of performance measurement in strategic planning

Purpose – To investigate the impact of performance measurement in strategic planning process. Design/methodology/approach – A large scale survey was conducted online with Warwick Business School alumni. The questionnaire was based on the Strategic Development Process model by Dyson. The questionnaire was designed to map the current practice of strategic planning and to determine its most influential factors on the effectiveness of the process. All questions were close ended and a seven-point Likert scale used. The independent variables were grouped into four meaningful factors by factor analysis (Varimax, coefficient of rotation 0.4). The factors produced were used to build regression models (stepwise) for the five assessments of strategic planning process. Regression models were developed for the totality of the responses, comparing SMEs and large organizations and comparing organizations operating in slowly and rapidly changing environments. Findings – The results indicate that performance measurement stands as one of the four main factors characterising the current practice of strategic planning. This research has determined that complexity coming from organizational size and rate of change in the sector creates variation in the impact of performance measurement in strategic planning. Large organizations and organizations operating in rapidly changing environments make greater use of performance measurement. Research limitations/implications – This research is based on subjective data, therefore the conclusions do not concern the impact of strategic planning process' elements on the organizational performance achievements, but on the success/effectiveness of the strategic planning process itself. Practical implications – This research raises a series of questions about the use and potential impact of performance measurement, especially in the categories of organizations that are not significantly influenced by its utilisation. It contributes to the field of performance measurement impact. Originality/value – This research fills in the gap literature concerning the lack of large scale surveys on strategic development processes and performance measurement. It also contributes in the literature of this field by providing empirical evidences on the impact of performance measurement upon the strategic planning process.

Measuring the degree of spatial correlation between histological features in thin sections of brain tissue

Histological features visible in thin sections of brain tissue, such as neuronal perikarya, blood vessels, or pathological lesions may exhibit a degree of spatial association or correlation. In neurodegenerative disorders such as AD, Pick's disease, and CJD, information on whether different types of pathological lesion are spatially correlated may be useful in elucidating disease pathogenesis. In the present article the statistical methods available for studying spatial association in histological sections are reviewed. These include tests of interspecific association between two or more histological features using χ2 contingency tables, measurement of 'complete' and 'absolute' association, and more complex methods that use grids of contiguous samples. In addition, the use of correlation matrices and stepwise multiple regression methods are described. The advantages and limitations of each method are reviewed and possible future developments discussed.

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.

Effect of β-adrenoceptor antagonists on autonomic control of ciliary smooth muscle

Purpose: Pharmacological intervention with peripheral sympathetic transmission at ciliary smooth muscle neuro-receptor junctions has been used against a background of controlled parasympathetic activity to investigate the characteristics of autonomic control of ocular accommodation. Methods: A continuously recording infrared optometer was used to measure accommodation on a group of five visually normal emmetropic subjects under open- and closed-loop conditions. A double-blind protocol between saline, timolol and betaxolol was used to differentiate between the localised action on ciliary smooth muscle and effects induced by changes in stimulus conditions. Data were collected before and 45 min following the instillation of saline, timolol or betaxolol. Open-loop post-task decay was investigated following 3 min sustained near fixation of a stimulus placed 3 D above the subject's pre-task tonic accommodation level. Closed-loop dynamic responses were recorded for each treatment condition while subjects viewed sinusoidally (0.05-0.6 Hz) or stepwise vergence-modulated targets over a 2 D range (2-4 D). Results: Open-loop data demonstrate a rapid post-task regression to pre-task tonic accommodation levels for saline and betaxolol control conditions. A slow positive post-task shift was induced by timolol indicating that sympathetic inhibition contributes to accommodative adaptation during sustained near vision. Closed-loop accommodation responses to temporally modulated sinusoidal stimuli showed characteristic features for both saline and betaxolol control conditions. Timolol induced a reduced gain for low- and mid-temporal frequencies (< 0.3 Hz) but did not affect the response at higher temporal frequencies. Response times to stepwise stimuli increased following the instillation of timolol for the near-to-far fixation condition compared with the controls and was related to the period of sustained prior fixation. Conclusions: Modulation of accommodation under open- and closed-loop conditions by a non-selective β-blocker is consistent with the temporal and inhibitory features of sympathetic innervation to ciliary smooth muscle. Although parasympathetic innervation predominates there is evidence to support a role for sympathetic innervation in the control of ocular accommodation. © 2002 The College of Optometrists.

People, technology, processes and risk knowledge sharing

The present global economic crisis creates doubts about the good use of accumulated experience and knowledge in managing risk in financial services. Typically, risk management practice does not use knowledge management (KM) to improve and to develop new answers to the threats. A key reason is that it is not clear how to break down the “organizational silos” view of risk management (RM) that is commonly taken. As a result, there has been relatively little work on finding the relationships between RM and KM. We have been doing research for the last couple of years on the identification of relationships between these two disciplines. At ECKM 2007 we presented a general review of the literature(s) and some hypotheses for starting research on KM and its relationship to the perceived value of enterprise risk management. This article presents findings based on our preliminary analyses, concentrating on those factors affecting the perceived quality of risk knowledge sharing. These come from a questionnaire survey of RM employees in organisations in the financial services sector, which yielded 121 responses. We have included five explanatory variables for the perceived quality of risk knowledge sharing. These comprised two variables relating to people (organizational capacity for work coordination and perceived quality of communication among groups), one relating to process (perceived quality of risk control) and two related to technology (web channel functionality and RM information system functionality). Our findings so far are that four of these five variables have a significant positive association with the perceived quality of risk knowledge sharing: contrary to expectations, web channel functionality did not have a significant association. Indeed, in some of our exploratory regression studies its coefficient (although not significant) was negative. In stepwise regression, the variable organizational capacity for work coordination accounted for by far the largest part of the variation in the dependent variable perceived quality of risk knowledge sharing. The “people” variables thus appear to have the greatest influence on the perceived quality of risk knowledge sharing, even in a sector that relies heavily on technology and on quantitative approaches to decision making. We have also found similar results with the dependent variable perceived value of Enterprise Risk Management (ERM) implementation.

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.

Relationships between beta-amyloid (A beta) deposits and blood vessels in patients with sporadic and familial Alzheimer's disease

The density of diffuse, primitive and classic beta-amyloid (A beta) deposits was studied in relation to the incidence of blood vessels in the superior frontal gyrus of nine cases of sporadic Alzheimer's disease (SAD), two cases of familial Alzheimer's disease (FAD) with amyloid precursor protein (APP) mutations (APP717, Val --> Ile), and eight cases of FAD not linked to chromosomes 21, 14 or 1. Stepwise multiple regression was used to determine for each patient whether variations in the density of A beta deposits along the cortex were significantly correlated with the incidence of blood vessels. In the majority of FAD and SAD cases, the density of the diffuse and primitive type A beta deposits was not related to blood vessels. However, the incidence of the larger diameter (> 10 microns) blood vessels was positively correlated with the density of the classic A beta deposits in eight (89%) SAD and two (20%) FAD cases. The data suggest that the densities of vessels and deposits were not significantly correlated between cases but only within cases, suggesting a strictly local effect. In addition, the spatial association between classic A beta deposits and blood vessels may be more apparent in SAD compared with FAD cases.

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.

Measuring the degree of spatial correlation between pathological lesions in Alzheimer's disease

The pathological lesions characteristic of Alzheimer's disease (AD), viz., senile plaques (SP) and neurofibrillary tangles (NFT) may not be randomly distributed with reference to each other but exhibit a degree of sptial association or correlation, information on the degree of association between SP and NFT or between the lesions and normal histological features, such as neuronal perikarya and blood vessels, may be valuable in elucidating the pathogenesis of AD. This article reviews the statistical methods available for studying the degree of spatial association in histological sections of AD tissue. These include tests of interspecific association between two or more histological features using chi-square contingency tables, measurement of 'complete' and 'absolute' association, and more complex methods that use grids of contiguous samples. In addition, analyses of association using correlation matrices and stepwise multiple regression methods are described. The advantages and limitations of each method are reviewed and possible future developments discussed.