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.

Laser-induced breakdown spectroscopy quantitative analysis method via adaptive analytical line selection and relevance vector machine regression model

Abstract A new LIBS quantitative analysis method based on analytical line adaptive selection and Relevance Vector Machine (RVM) regression model is proposed. First, a scheme of adaptively selecting analytical line is put forward in order to overcome the drawback of high dependency on a priori knowledge. The candidate analytical lines are automatically selected based on the built-in characteristics of spectral lines, such as spectral intensity, wavelength and width at half height. The analytical lines which will be used as input variables of regression model are determined adaptively according to the samples for both training and testing. Second, an LIBS quantitative analysis method based on RVM is presented. The intensities of analytical lines and the elemental concentrations of certified standard samples are used to train the RVM regression model. The predicted elemental concentration analysis results will be given with a form of confidence interval of probabilistic distribution, which is helpful for evaluating the uncertainness contained in the measured spectra. Chromium concentration analysis experiments of 23 certified standard high-alloy steel samples have been carried out. The multiple correlation coefficient of the prediction was up to 98.85%, and the average relative error of the prediction was 4.01%. The experiment results showed that the proposed LIBS quantitative analysis method achieved better prediction accuracy and better modeling robustness compared with the methods based on partial least squares regression, artificial neural network and standard support vector machine.

A laser induced breakdown spectroscopy quantitative analysis method based on the robust least squares support vector machine regression model

Data fluctuation in multiple measurements of Laser Induced Breakdown Spectroscopy (LIBS) greatly affects the accuracy of quantitative analysis. A new LIBS quantitative analysis method based on the Robust Least Squares Support Vector Machine (RLS-SVM) regression model is proposed. The usual way to enhance the analysis accuracy is to improve the quality and consistency of the emission signal, such as by averaging the spectral signals or spectrum standardization over a number of laser shots. The proposed method focuses more on how to enhance the robustness of the quantitative analysis regression model. The proposed RLS-SVM regression model originates from the Weighted Least Squares Support Vector Machine (WLS-SVM) but has an improved segmented weighting function and residual error calculation according to the statistical distribution of measured spectral data. Through the improved segmented weighting function, the information on the spectral data in the normal distribution will be retained in the regression model while the information on the outliers will be restrained or removed. Copper elemental concentration analysis experiments of 16 certified standard brass samples were carried out. The average value of relative standard deviation obtained from the RLS-SVM model was 3.06% and the root mean square error was 1.537%. The experimental results showed that the proposed method achieved better prediction accuracy and better modeling robustness compared with the quantitative analysis methods based on Partial Least Squares (PLS) regression, standard Support Vector Machine (SVM) and WLS-SVM. It was also demonstrated that the improved weighting function had better comprehensive performance in model robustness and convergence speed, compared with the four known weighting functions.

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.

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.

Statnote 24: Multiple regression

In previous statnotes, the application of correlation and regression methods to the analysis of two variables (X,Y) was described. These methods can be used to determine whether there is a linear relationship between the two variables, whether the relationship is positive or negative, to test the degree of significance of the linear relationship, and to obtain an equation relating Y to X. This Statnote extends the methods of linear correlation and regression to situations where there are two or more X variables, i.e., 'multiple linear regression’.

The normal optic nerve variations in an optometric population:Possible ocular and systemic influences

Early detection of glaucoma relies on a detailed knowledge of how the normal optic nerve (ONH) varies within the population. The purpose of this study focused on two main areas; 1. To explore the optic nerve head appearance in the normal optometric population and compare the south Asian (principally Pakistani) with the European white population, correcting for possible ocular and non-ocular influences in a multiple regression model. The main findings were: • The optic discs of the South Asian (SA) and White European (WE) populations were not statistically different in size. The SA group possessed discs with increased cupping and thinner neuro-retinal rims (NRR) compared with the WE group. The SA group also demonstrated a more vertically oval shape than the WE population. These differences were significant at the p<0.01 level. • The upper limits of inter-eye asymmetry were: ≤0.2 for cup to disc area ratio, and 3mmHg for intra-ocular pressure (IOP) for both ethnic groups and this did not increase with age. IOP asymmetry did not vary with gender, ethnicity or a family history of glaucoma and was independent of ONH asymmetry. ONH and IOP asymmetry are therefore independent risk factors when screening for glaucoma for both ethnic groups. 2. To investigate the validity of the ISNT rule: inferior> superior> nasal> temporal NRR thickness in the optometric population. The main findings were: • As disc size increased the disc become rounder and less vertically oval in shape. Vertically oval discs had thicker superior and inferior NRRs and thinner nasal and temporal NRRs compared with rounder disc shapes due to cup shape being independent of disc shape. Vertically oval discs were therefore more likely to obey the ISNT rule than larger rounder discs. • The ISNT rule has a low adherence in our sample of normal eyes (5.7%). However, by removing the nasal sector to become the IST rule, 74.5% of normal eyes obeyed. SA eyes and female gender were more likely to obey the ISNT rule due to increased disc ovality. The IST rule is independent of disc shape and therefore more suitable for assessing discs from both ethnic backgrounds. Obeying the ISNT rule or IST rule was not related to disc or cup size.

Visual field severity indices demonstrate dose-dependent visual loss from Vigabatrin therapy

Purpose: The aims of this study were to develop an algorithm to accurately quantify Vigabatrin (VGB)-induced central visual field loss and to investigate the relationship between visual field loss and maximum daily dose, cumulative dose and duration of dose. Methods: The sample comprised 31 patients (mean age 37.9 years; SD 14.4 years) diagnosed with epilepsy and exposed to VGB. Each participant underwent standard automated static visual field examination of the central visual field. Central visual field loss was determined using continuous scales quantifying severity in terms of area and depth of defect and additionally by symmetry of defect between the two eyes. A simultaneous multiple regression model was used to explore the relationship between these visual field parameters and the drug predictor variables. Results: The regression model indicated that maximum VGB dose was the only factor to be significantly correlated with individual eye severity (right eye: p = 0.020; left eye: p = 0.012) and symmetry of visual field defect (p = 0.024). Conclusions: Maximum daily dose was the single most reliable indicator of those patients likely to exhibit visual field defects due to VGB. These findings suggest that high maximum dose is more likely to result in visual field defects than high cumulative doses or those of long duration.

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.

Guiding local regression using visualisation

Solving many scientific problems requires effective regression and/or classification models for large high-dimensional datasets. Experts from these problem domains (e.g. biologists, chemists, financial analysts) have insights into the domain which can be helpful in developing powerful models but they need a modelling framework that helps them to use these insights. Data visualisation is an effective technique for presenting data and requiring feedback from the experts. A single global regression model can rarely capture the full behavioural variability of a huge multi-dimensional dataset. Instead, local regression models, each focused on a separate area of input space, often work better since the behaviour of different areas may vary. Classical local models such as Mixture of Experts segment the input space automatically, which is not always effective and it also lacks involvement of the domain experts to guide a meaningful segmentation of the input space. In this paper we addresses this issue by allowing domain experts to interactively segment the input space using data visualisation. The segmentation output obtained is then further used to develop effective local regression models.

Interaction of liquid copper with sintered iron compacts

Interaction of liquid copper with sintered iron is important in brazing, liquid phase sintering and infiltration. In brazing, the penetration of liquid copper into the pores is to be `avoided', whereas in infiltration processes it is `encouraged', and in liquid phase sintering it should be `controlled' so that optimum mechanical properties are achieved. The main objective of the research is to model the interaction by studying the effect of the process variables on the mechanisms of copper interaction in Fe-Cu and Fe-Cu-C systems. This involves both theoretical and experimental considerations. Dilatometric investigations at 950, 1125 and 1200oC, together with metallographic analyses were carried out to clarify the copper growth phenomenon. It is shown that penetration of liquid copper into the iron grain boundaries is the major cause of dimensional changes. Infiltration profiles revealed that copper penetration between the iron interparticle contact points and along iron grain boundaries is a rapid process. The extent of copper penetration depends on the dihedral angle. Large dihedral angles hinder, and small angles promote copper penetration into the grain boundaries. Dihedral angle analysis shows that the addition of 0.6wt.% graphite reduces the number of zero dihedral angle from 27 to 3o and increases the mean dihedral angle from 9.8 to 41.5o. The dihedral angle was lowest at 1125oC and then increased to higher values as the system approached its equilibrium condition. Elementally mixed (E.M.) Fe-Cu compacts showed a rapid expansion at the copper melting point. However, graphite additions reduced compact growth by increasing the mean dihedral angle. In order to reduce the copper growth phenomenon, iron powder was coated with a thin layer of copper by an immersion coating (I.C.) technique. The dilatometric curves revealed an overall shrinkage in the I.C. compacts compared to their corresponding E.M. compacts. Multiple regression models showed that temperature had the most effect on dimensional changes and density had the most contributing effect upon the copper penetration area in the infiltrated powder metallurgy compacts.

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.

Antecedents and consequences of new product development and international new product rollout timeliness:an examination of mediating and moderating influences

The study examined the relationships between antecedents, timeliness in NPD and INPR, and consequences. A conceptual framework was tested using 232 new products from South Korean firms. The hypothesized relationships among the constructs in the model were evaluated by multiple regression and hierarchal regression analyses using SPSS 12 as well as by structural equation modelling (SEM) using SIMPLIS LISREL. In addition, confirmatory factor analysis (CFA) was carried out using SIMPLIS LISREL. In the direct relationships, cross-functional linkages and marketing synergy exhibited a statistically significant effect on NPD timeliness. The results also supported the influences of the HQ-subsidiary/agent relationship and NPD timeliness on INPR timeliness as well as INPR timeliness on performance. In the mediating effect tests, marketing proficiency significantly accounts for the relationships between cross-functional linkages and NPD timeliness, between marketing synergy and NPD timeliness, and between the HQ-subsidiary/agent relationship and INPR timeliness. Technical proficiency also mediates the effect of the HQ-subsidiary/agent relationship on INPR timeliness. The influence of NPD timeliness on new product performance in target markets is attributed to INPR timeliness. As for the results of the external environmentals and standardization influences, competitive intensity moderates the relationship between NPD timeliness and new product performance. Technology change also moderates the relationship between cross-functional linkages and NPD timeliness and between timeliness in NPD and INPR and performance. Standardization has a moderating role on the relationship between NPD timeliness and INPR timeliness. This study presents the answers to research questions which concern what factors are predictors of criterion variables, how antecedents influence timeliness in NPD and INPR and when the direct relationships in the INPR process are strengthened.

An investigation of the retail marketing mix and its effectiveness in small shops

The recent history of small shop and independent retailing has been one of decline. The most desirable form of assistance is the provision of information which will increase the efficiency model of marketing mix effeciveness which may be applied in small scale retailing. A further aim is to enhance theoretical development in the marketing field. Recent changes in retailing have affected location, product range, pricing and promotion practices. Although a large number of variables representing aspects of the marketing mix may be identified, it is not possible, on the basis of currently available information, to quantify or rank them according to their effect on sales performance. In designing a suitable study a major issue is that of access to a suitable representative sample of small retailers. The publish nature of the retail activities involved facilitates the use of a novel observation approach to data collection. A cross-sectional survey research design was used focussing on a clustered random sample of greengrocers and gent's fashion outfitters in the West Midlands. Linear multiple regression was the main analytical technique. Powerful regression models were evolved for both types of retailing. For greengrocers the major influences on trade are pedestrian traffic and shelf display space. For gent's outfitters they are centrality-to-other shopping, advertising and shelf display space. The models may be utilised by retailers to determine the relative strength of marketing mix variables. The level of precision is not sufficient to permit cost benefit analysis. Comparison of the findings for the two distinct kinds of business studied suggests an overall model of marketing mix effectiveness might be based on frequency of purchase, homogeneity of the shopping environment, elasticity of demand and bulk characteristics of the good sold by a shop.