An introduction to analysis of variance (ANOVA) with special reference to data from clinical experiments in optometry

This article is aimed primarily at eye care practitioners who are undertaking advanced clinical research, and who wish to apply analysis of variance (ANOVA) to their data. ANOVA is a data analysis method of great utility and flexibility. This article describes why and how ANOVA was developed, the basic logic which underlies the method and the assumptions that the method makes for it to be validly applied to data from clinical experiments in optometry. The application of the method to the analysis of a simple data set is then described. In addition, the methods available for making planned comparisons between treatment means and for making post hoc tests are evaluated. The problem of determining the number of replicates or patients required in a given experimental situation is also discussed. Copyright (C) 2000 The College of Optometrists.

Introduction to the theory and application of data envelopment analysis:a foundation text with integrated software

The book aims to introduce the reader to DEA in the most accessible manner possible. It is specifically aimed at those who have had no prior exposure to DEA and wish to learn its essentials, how it works, its key uses, and the mechanics of using it. The latter will include using DEA software. Students on degree or training courses will find the book especially helpful. The same is true of practitioners engaging in comparative efficiency assessments and performance management within their organisation. Examples are used throughout the book to help the reader consolidate the concepts covered. Table of content: List of Tables. List of Figures. Preface. Abbreviations. 1. Introduction to Performance Measurement. 2. Definitions of Efficiency and Related Measures. 3. Data Envelopment Analysis Under Constant Returns to Scale: Basic Principles. 4. Data Envelopment Analysis under Constant Returns to Scale: General Models. 5. Using Data Envelopment Analysis in Practice. 6. Data Envelopment Analysis under Variable Returns to Scale. 7. Assessing Policy Effectiveness and Productivity Change Using DEA. 8. Incorporating Value Judgements in DEA Assessments. 9. Extensions to Basic DEA Models. 10. A Limited User Guide for Warwick DEA Software. Author Index. Topic Index. References.

Principal components analysis of Alzheimer’s disease based on neuropathological data: A study of 79 patients

A Principal Components Analysis of neuropathological data from 79 Alzheimer’s disease (AD) cases was performed to determine whether there was evidence for subtypes of the disease. Two principal components were extracted from the data which accounted for 72% and 12% of the total variance respectively. The results suggested that 1) AD was heterogeneous but subtypes could not be clearly defined; 2) the heterogeneity, in part, reflected disease onset; 3) familial cases did not constitute a distinct subtype of AD and 4) there were two forms of late onset AD, one of which was associated with less senile plaque and neurofibrillary tangle development but with a greater degree of brain atherosclerosis.

Spatial aspects of MRSA epidemiology:A case study using stochastic simulation, kernel estimation and SaTScan

The identification of disease clusters in space or space-time is of vital importance for public health policy and action. In the case of methicillin-resistant Staphylococcus aureus (MRSA), it is particularly important to distinguish between community and health care-associated infections, and to identify reservoirs of infection. 832 cases of MRSA in the West Midlands (UK) were tested for clustering and evidence of community transmission, after being geo-located to the centroids of UK unit postcodes (postal areas roughly equivalent to Zip+4 zip code areas). An age-stratified analysis was also carried out at the coarser spatial resolution of UK Census Output Areas. Stochastic simulation and kernel density estimation were combined to identify significant local clusters of MRSA (p<0.025), which were supported by SaTScan spatial and spatio-temporal scan. In order to investigate local sampling effort, a spatial 'random labelling' approach was used, with MRSA as cases and MSSA (methicillin-sensitive S. aureus) as controls. Heavy sampling in general was a response to MRSA outbreaks, which in turn appeared to be associated with medical care environments. The significance of clusters identified by kernel estimation was independently supported by information on the locations and client groups of nursing homes, and by preliminary molecular typing of isolates. In the absence of occupational/ lifestyle data on patients, the assumption was made that an individual's location and consequent risk is adequately represented by their residential postcode. The problems of this assumption are discussed, with recommendations for future data collection.

Spatial pattern analysis of beta-amyloid (A beta) deposits in Alzheimer disease by linear regression

The spatial patterns of discrete beta-amyloid (Abeta) deposits in brain tissue from patients with Alzheimer disease (AD) were studied using a statistical method based on linear regression, the results being compared with the more conventional variance/mean (V/M) method. Both methods suggested that Abeta deposits occurred in clusters (400 to <12,800 mu m in diameter) in all but 1 of the 42 tissues examined. In many tissues, a regular periodicity of the Abeta deposit clusters parallel to the tissue boundary was observed. In 23 of 42 (55%) tissues, the two methods revealed essentially the same spatial patterns of Abeta deposits; in 15 of 42 (36%), the regression method indicated the presence of clusters at a scale not revealed by the V/M method; and in 4 of 42 (9%), there was no agreement between the two methods. Perceived advantages of the regression method are that there is a greater probability of detecting clustering at multiple scales, the dimension of larger Abeta clusters can be estimated more accurately, and the spacing between the clusters may be estimated. However, both methods may be useful, with the regression method providing greater resolution and the V/M method providing greater simplicity and ease of interpretation. Estimates of the distance between regularly spaced Abeta clusters were in the range 2,200-11,800 mu m, depending on tissue and cluster size. The regular periodicity of Abeta deposit clusters in many tissues would be consistent with their development in relation to clusters of neurons that give rise to specific neuronal projections.

The use of data analysis methods: basic concepts for optometrists

This article explains first, the reasons why a knowledge of statistics is necessary and describes the role that statistics plays in an experimental investigation. Second, the normal distribution is introduced which describes the natural variability shown by many measurements in optometry and vision sciences. Third, the application of the normal distribution to some common statistical problems including how to determine whether an individual observation is a typical member of a population and how to determine the confidence interval for a sample mean is described.

Data analysis methods in optometry Part 3: the analysis of frequencies and proportions

In some studies, the data are not measurements but comprise counts or frequencies of particular events. In such cases, an investigator may be interested in whether one specific event happens more frequently than another or whether an event occurs with a frequency predicted by a scientific model.

Data analysis methods in optometry Part 4: an introduction to analysis of variance (ANOVA)

In any investigation in optometry involving more that two treatment or patient groups, an investigator should be using ANOVA to analyse the results assuming that the data conform reasonably well to the assumptions of the analysis. Ideally, specific null hypotheses should be built into the experiment from the start so that the treatments variation can be partitioned to test these effects directly. If 'post-hoc' tests are used, then an experimenter should examine the degree of protection offered by the test against the possibilities of making either a type 1 or a type 2 error. All experimenters should be aware of the complexity of ANOVA. The present article describes only one common form of the analysis, viz., that which applies to a single classification of the treatments in a randomised design. There are many different forms of the analysis each of which is appropriate to the analysis of a specific experimental design. The uses of some of the most common forms of ANOVA in optometry have been described in a further article. If in any doubt, an investigator should consult a statistician with experience of the analysis of experiments in optometry since once embarked upon an experiment with an unsuitable design, there may be little that a statistician can do to help.

Data methods in optometry Part 9: experimental design and analysis of variance

The key to the correct application of ANOVA is careful experimental design and matching the correct analysis to that design. The following points should therefore, be considered before designing any experiment: 1. In a single factor design, ensure that the factor is identified as a 'fixed' or 'random effect' factor. 2. In more complex designs, with more than one factor, there may be a mixture of fixed and random effect factors present, so ensure that each factor is clearly identified. 3. Where replicates can be grouped or blocked, the advantages of a randomised blocks design should be considered. There should be evidence, however, that blocking can sufficiently reduce the error variation to counter the loss of DF compared with a randomised design. 4. Where different treatments are applied sequentially to a patient, the advantages of a three-way design in which the different orders of the treatments are included as an 'effect' should be considered. 5. Combining different factors to make a more efficient experiment and to measure possible factor interactions should always be considered. 6. The effect of 'internal replication' should be taken into account in a factorial design in deciding the number of replications to be used. Where possible, each error term of the ANOVA should have at least 15 DF. 7. Consider carefully whether a particular factorial design can be considered to be a split-plot or a repeated measures design. If such a design is appropriate, consider how to continue the analysis bearing in mind the problem of using post hoc tests in this situation.

Principal components analysis of Alzheimer's disease based on neuropathological data: a study of 79 patients

A principal components analysis was carried out on neuropathological data collected from 79 cases of Alzheimer's disease (AD) diagnosed in a single centre. The purpose of the study was to determine whether on neuropathological criteria there was evidence for clearly defined subtypes of the disease. Two principal components (PC1 and PC2) were extracted from the data. PC1 was considerable more important than PC2 accounting for 72% of the total variance. When plotted in relation to the first two principal components the majority of cases (65/79) were distributed in a single cluster within which subgroupings were not clearly evident. In addition, there were a number of individual, mainly early-onset cases, which were neither related to each other nor to the main cluster. The distribution of each neuropathological feature was examined in relation to PC1 and 2, Disease onset, rhe degree of gross brain atrophy, neuronal loss and the devlopment of senile plaques (SP) and neurofibrillary tangles (NFT) were negatively correlated with PC1. The devlopment of SP and NFT and the degree of brain athersclerosis were positively correlated with PC2. These results suggested: 1) that there were different forms of AD but no clear division of the cases into subclasses could be made based on the neuropathological criteria used; the cases showing a more continuous distribution from one form to another, 2) that disease onset was an important variable and was associated with a greater development of pathological changes, 3) familial cases were not a distinct subclass of AD; the cases being widely distributed in relation to PC1 and PC2 and 4) that there may be two forms of late-onset AD whic grade into each other, one of which was associated with less SP and NFT development but with a greater degree of brain atherosclerosis.