The use of correlation and regression methods in optometry

Correlation and regression are two of the statistical procedures most widely used by optometrists. However, these tests are often misused or interpreted incorrectly, leading to erroneous conclusions from clinical experiments. This review examines the major statistical tests concerned with correlation and regression that are most likely to arise in clinical investigations in optometry. First, the use, interpretation and limitations of Pearson's product moment correlation coefficient are described. Second, the least squares method of fitting a linear regression to data and for testing how well a regression line fits the data are described. Third, the problems of using linear regression methods in observational studies, if there are errors associated in measuring the independent variable and for predicting a new value of Y for a given X, are discussed. Finally, methods for testing whether a non-linear relationship provides a better fit to the data and for comparing two or more regression lines are considered.

Apparatus and test methods for measuring the impact of golf balls on turf and their application in the field

An apparatus was developed to project spinning golf balls directly onto golf greens. This employed a modified baseball/practice machine with two counter-rotating pneumatic wheels. The speed of the wheels could be varied independently allowing backspin to be given to the ball. The ball was projected into a darkened enclosure where the motion of the ball before and after impacting with the turf was recorded using a still camera and a stroboscope. The resulting photographs contained successive images of the ball on a single frame of film. The apparatus was tested on eighteen golf courses resulting in 721 photographs of impacts. Statistical analysis was carried out on the results of the photographs and from this, two types of green emerged. On the first, the ball tended to rebound with topspin, while on the second, the ball retained backspin after impact if the initial backspin was greater than about 350 rads-1. Eleven tests were devised to determine the characteristics of greens and statistical techniques were used to analyse the relationships between these tests. These showed the effects of the green characteristics on ball/turf impacts. It was found that the ball retained backspin on greens that were freely drained and had less than 60% of Poa annua (annual meadow grass) in their swards. Visco-elastic models were used to simulate the impact of the ball with the turf. Impacts were simulated by considering the ball to be rigid and the turf to be a two layered system consisting of springs and dampers. The model showed good agreement with experiment and was used to simulate impacts from two different shots onto two contrasting types of green.

Numerical and statistical analysis of long-haul undersea optical communication systems

Firstly, we numerically model a practical 20 Gb/s undersea configuration employing the Return-to-Zero Differential Phase Shift Keying data format. The modelling is completed using the Split-Step Fourier Method to solve the Generalised Nonlinear Schrdinger Equation. We optimise the dispersion map and per-channel launch power of these channels and investigate how the choice of pre/post compensation can influence the performance. After obtaining these optimal configurations, we investigate the Bit Error Rate estimation of these systems and we see that estimation based on Gaussian electrical current systems is appropriate for systems of this type, indicating quasi-linear behaviour. The introduction of narrower pulses due to the deployment of quasi-linear transmission decreases the tolerance to chromatic dispersion and intra-channel nonlinearity. We used tools from Mathematical Statistics to study the behaviour of these channels in order to develop new methods to estimate Bit Error Rate. In the final section, we consider the estimation of Eye Closure Penalty, a popular measure of signal distortion. Using a numerical example and assuming the symmetry of eye closure, we see that we can simply estimate Eye Closure Penalty using Gaussian statistics. We also see that the statistics of the logical ones dominates the statistics of the logical ones dominates the statistics of signal distortion in the case of Return-to-Zero On-Off Keying configurations.

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.

Sampling and measurement methods for a study of childhood refractive error in a UK population

Background There is a paucity of data describing the prevalence of childhood refractive error in the United Kingdom. The Northern Ireland Childhood Errors of Refraction study, along with its sister study the Aston Eye Study, are the first population-based surveys of children using both random cluster sampling and cycloplegic autorefraction to quantify levels of refractive error in the United Kingdom. Methods Children aged 6–7 years and 12–13 years were recruited from a stratified random sample of primary and post-primary schools, representative of the population of Northern Ireland as a whole. Measurements included assessment of visual acuity, oculomotor balance, ocular biometry and cycloplegic binocular open-field autorefraction. Questionnaires were used to identify putative risk factors for refractive error. Results 399 (57%) of 6–7 years and 669 (60%) of 12–13 years participated. School participation rates did not vary statistically significantly with the size of the school, whether the school is urban or rural, or whether it is in a deprived/non-deprived area. The gender balance, ethnicity and type of schooling of participants are reflective of the Northern Ireland population. Conclusions The study design, sample size and methodology will ensure accurate measures of the prevalence of refractive errors in the target population and will facilitate comparisons with other population-based refractive data.

CDMA multiuser detection, neural networks, and statistical mechanics

A novel approach, based on statistical mechanics, to analyze typical performance of optimum code-division multiple-access (CDMA) multiuser detectors is reviewed. A `black-box' view ot the basic CDMA channel is introduced, based on which the CDMA multiuser detection problem is regarded as a `learning-from-examples' problem of the `binary linear perceptron' in the neural network literature. Adopting Bayes framework, analysis of the performance of the optimum CDMA multiuser detectors is reduced to evaluation of the average of the cumulant generating function of a relevant posterior distribution. The evaluation of the average cumulant generating function is done, based on formal analogy with a similar calculation appearing in the spin glass theory in statistical mechanics, by making use of the replica method, a method developed in the spin glass theory.

Accommodating intraocular lenses:a review of design concepts, usage and assessment methods

The correction of presbyopia and restoration of true accommodative function to the ageing eye is the focus of much ongoing research and clinical work. A range of accommodating intraocular lenses (AIOLs) implanted during cataract surgery has been developed and they are designed to change either their position or shape in response to ciliary muscle contraction to generate an increase in dioptric power. Two main design concepts exist. First, axial shift concepts rely on anterior axial movement of one or two optics creating accommodative ability. Second, curvature change designs are designed to provide significant amplitudes of accommodation with little physical displacement. Single-optic devices have been used most widely, although the true accommodative ability provided by forward shift of the optic appears limited and recent findings indicate that alternative factors such as flexing of the optic to alter ocular aberrations may be responsible for the enhanced near vision reported in published studies. Techniques for analysing the performance of AIOLs have not been standardised and clinical studies have reported findings using a wide range of both subjective and objective methods, making it difficult to gauge the success of these implants. There is a need for longitudinal studies using objective methods to assess long-term performance of AIOLs and to determine if true accommodation is restored by the designs available. While dual-optic and curvature change IOLs are designed to provide greater amplitudes of accommodation than is possible with single-optic devices, several of these implants are in the early stages of development and require significant further work before human use is possible. A number of challenges remain and must be addressed before the ultimate goal of restoring youthful levels of accommodation to the presbyopic eye can be achieved.

Writing and characterisation methods for UV-photosensitivity based devices and their applications

The underlying work to this thesis focused on the exploitation and investigation of photosensitivity mechanisms in optical fibres and planar waveguides for the fabrication of advanced integrated optical devices for telecoms and sensing applications. One major scope is the improvement of grating fabrication specifications by introducing new writing techniques and the use of advanced characterisation methods for grating testing. For the first time the polarisation control method for advanced grating fabrication has successfully been converted to apodised planar waveguide fabrication and the development of a holographic method for the inscription of chirped gratings at arbitrary wavelength is presented. The latter resulted in the fabrication of gratings for pulse-width suppression and wavelength selection in diode lasers. In co-operation with research partners a number of samples were tested using optical frequency domain and optical low coherence reflectometry for a better insight into the limitations of grating writing techniques. Using a variety of different fabrication methods, custom apodised and chirped fibre Bragg gratings were written for the use as filter elements for multiplexer-demultiplexer devices, as well as for short pulse generation and wavelength selection in telecommunication transmission systems. Long period grating based devices in standard, speciality and tapered fibres are presented, showing great potential for multi-parameter sensing. One particular scope is the development of vectorial curvature and refractive index sensors with potential for medical, chemical and biological sensing. In addition the design of an optically tunable Mach-Zehnder based multiwavelength filter is introduced. The discovery of a Type IA grating type through overexposure of hydrogen loaded standard and Boron-Germanium co-doped fibres strengthened the assumption of UV-photosensitivity being a highly non-linear process. Gratings of this type show a significantly lower thermal sensitivity compared to standard gratings, which makes them useful for sensing applications. An Oxford Lasers copper-vapour laser operating at 255 nm in pulsed mode was used for their inscription, in contrast to previous work using CW-Argon-Ion lasers and contributing to differences in the processes of the photorefractive index change

A comparison of histological and immunohistochemical methods for quantifying the pathological lesions of Pick's disease

Counts of Pick bodies (PB), Pick cells (PC), senile plaques (SP) and neurofibrillary tangles (NFT) were made in the frontal and temporal cortex from patients with Pick's disease (PD). Lesions were stained histologically with hematoxylin and eosin (HE) and the Bielschowsky silver impregnation method and labeled immunohistochemically with antibodies raised to ubiquitin and tau. The greatest numbers of PB were revealed by immunohistochemistry. Counts of PB revealed by ubiquitin and tau were highly positively correlated which suggested that the two antibodies recognized virtually identical populations of PB. The greatest numbers of PC were revealed by HE followed by the anti-ubiquitin antibody. However, the correlation between counts was poor, suggesting that HE and ubiquitin revealed different populations of PC. The greatest numbers of SP and NFT were revealed by the Bielschowsky method indicating the presence of Alzheimer-type lesions not revealed by the immunohistochemistry. In addition, more NFT were revealed by the anti-ubiquitin compared with the anti-tau antibody. The data suggested that in PD: (i) the anti-ubiquitin and anti-tau antibodies were equally effective at labeling PB; (ii) both HE and anti-ubiquitin should be used to quantitate PC; and (iii) the Bielschowsky method should be used to quantitate SP and NFT.

Sample size estimation and statistical power analyses

The concept of sample size and statistical power estimation is now something that Optometrists that want to perform research, whether it be in practice or in an academic institution, cannot simply hide away from. Ethics committees, journal editors and grant awarding bodies are now increasingly requesting that all research be backed up with sample size and statistical power estimation in order to justify any study and its findings. This article presents a step-by-step guide of the process for determining sample sizeand statistical power. It builds on statistical concepts presented in earlier articles in Optometry Today by Richard Armstrong and Frank Eperjesi.

An empirical investigation of the effect of rights issue announcements on share returns and the determinants of abnormal returns on the Kuala Lumpur Stock Exchange

This thesis examines the effect of rights issue announcements on stock prices by companies listed on the Kuala Lumpur Stock Exchange (KLSE) between 1987 to 1996. The emphasis is to report whether the KLSE is semi strongly efficient with respect to the announcement of rights issues and to check whether the implications of corporate finance theories on the effect of an event can be supported in the context of an emerging market. Once the effect is established, potential determinants of abnormal returns identified by previous empirical work and corporate financial theory are analysed. By examining 70 companies making clean rights issue announcements, this thesis will hopefully shed light on some important issues in long term corporate financing. Event study analysis is used to check on the efficiency of the Malaysian stock market; while cross-sectional regression analysis is executed to identify possible explanators of the rights issue announcements' effect. To ensure the results presented are not contaminated, econometric and statistical issues raised in both analyses have been taken into account. Given the small amount of empirical research conducted in this part of the world, the results of this study will hopefully be of use to investors, security analysts, corporate financial managements, regulators and policy makers as well as those who are interested in capital market based research of an emerging market. It is found that the Malaysian stock market is not semi strongly efficient since there exists a persistent non-zero abnormal return. This finding is not consistent with the hypothesis that security returns adjust rapidly to reflect new information. It may be possible that the result is influenced by the sample, consisting mainly of below average size companies which tend to be thinly traded. Nevertheless, these issues have been addressed. Another important issue which has emerged from the study is that there is some evidence to suggest that insider trading activity existed in this market. In addition to these findings, when the rights issue announcements' effect is compared to the implications of corporate finance theories in predicting the sign of abnormal returns, the signalling model, asymmetric information model, perfect substitution hypothesis and Scholes' information hypothesis cannot be supported.

Chemical and physical methods of enhancing the percutaneous absorption of antimicrobial agents

Contrary to previously held beliefs, it is now known that bacteria exist not only on the surface of the skin but they are also distributed at varying depths beneath the skin surface. Hence, in order to sterilise the skin, antimicrobial agents are required to penetrate across the skin and eliminate the bacteria residing at all depths. Chlorhexidine is an antimicrobial agent with the widest use for skin sterilisation. However, due to its poor permeation rate across the skin, sterilisation of the skin cannot be achieved and, therefore, the remaining bacteria can act as a source of infection during an operation or insertion of catheters. The underlying theme of this study is to enhance the permeation of this antimicrobial agent in the skin by employing chemical (enhancers and supersaturated systems) or physical (iontophoresis) techniques. The hydrochloride salt of chlorhexidine (CHX), a poorly soluble salt, was used throughout this study. The effect of ionisation on in vitro permeation rate across the excised human epidennis was investigated using Franz-type diffusion cells. Saturated solutions of CHX were used as donor and the variable studied was vehicle pH. Permeation rate was increased with increasing vehicle pH. The pH effect was not related to the level of ionisation of the drug. The effect of donor vehicle was also studied using saturated solutions of CHX in 10% and 20% ethanol as the donor solutions. Permeation of CHX was enhanced by increasing the concentration of ethanol which could be due to the higher concentration of CHX in the donor phase and the effect of ethanol itself on the membrane. The interplay between drug diffusion and enhancer pretreatment of the epidennis was studied. Pretreatment of the membrane with 10% Azone/PG demonstrated the highest diffusion rate followed by 10% olcic acid/PG pretreatment compared to other pretreatment regimens (ethanol, dimethyl sulfoxide (DMSO), propylene glycol (PG), sodium dodecyl sulphate (SDS) and dodecyl trimethyl ammonium bromide (DT AB). Differential Scanning Calorimetry (DSC) was also employed to study the mode of action of these enhancers. The potential of supersaturated solutions in enhancing percutaneous absorption of CHX was investigated. Various anti-nucleating polymers were screened in order to establish the most effective agent. Polyvinylpyrrolidone (PVP, K30) was found to be a better candidate than its lower molecular weight counterpart (K25) and hydroxypropyl methyleellulose (HPMC). The permeation studies showed an increase in diffusion rate by increasing the degree of saturation. Iontophoresis is a physical means of transdemal drug delivery enhancement that causes an increased penetration of molecules into or through the skin by the application of an electric field. This technique was employed in conjunction with chemical enhancers to assess the effect on CHX permeation across the human epidermis. An improved transport of CHX, which was pH dependant was observed upon application of the current. Combined use of iontophoresis and chemical enhancers further increased the CHX transport indicating a synergistic effect. Pretreatment of the membrane with 10% Azone/PG demonstrated the greatest effect.

Modeling of spectral and statistical properties of a random distributed feedback fiber laser

For the first time we report full numerical NLSE-based modeling of generation properties of random distributed feedback fiber laser based on Rayleigh scattering. The model which takes into account the random backscattering via its average strength only describes well power and spectral properties of random DFB fiber lasers. The influence of dispersion and nonlinearity on spectral and statistical properties is investigated. The evidence of non-gaussian intensity statistics is found. © 2013 Optical Society of America.