- I started off as a theoretical physicist, and did a PhD in bubble-chamber physics. Subsequently I spent a year in Ind... moreI started off as a theoretical physicist, and did a PhD in bubble-chamber physics. Subsequently I spent a year in India, at I.I.T. Powai, before moving to Rutherford High Energy Laboratory in 1974. When funds began drying up in
big physics, I moved to Salford University, where I have been
a computing officer, senior computing officer, lecturer,
reader and Professor of Statistics. I'm now retired, a Prof. Emeritus, doing a lot of research, now that I no longer have to inflict Statistics lectures on students.edit - the cat next door has listened patiently to my thoughts.edit
Research Interests: Breast Cancer, Medicine, Biopsy, Humans, Female, and 15 moreMeta Analysis, Clinical Sciences, Aged, Middle Aged, Concordance, Adult, Analysis of Variance, Lymph Node, Minimally Invasive, Axilla, Axillary Lymph Node Dissection, False Negative, Lymph nodes, Breast Neoplasms, and Medical and Health Sciences
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Research Interests: Mathematics, Computer Science, Algorithms, Research Design, Treatment Outcome, and 12 moreMedicine, Humans, Computer Simulation, Regression Analysis, Meta Analysis, Methods for Research Synthesis, Statistical models, Estimator, Alzheimer Disease, Network Meta Analysis, Likelihood Functions, and Univariate Analysis
There is sometimes a clear evidence of a strong secular trend in the treatment effect of studies included in a meta-analysis. In such cases, estimating the present-day treatment effect by meta-regression is both reasonable and... more
There is sometimes a clear evidence of a strong secular trend in the treatment effect of studies included in a meta-analysis. In such cases, estimating the present-day treatment effect by meta-regression is both reasonable and straightforward. We however consider the more common situation where a secular trend is suspected, but is not strongly statistically significant. Typically, this lack of significance is due to the small number of studies included in the analysis, so that a meta-regression could give wild point estimates. We introduce an empirical Bayes meta-analysis methodology, which shrinks the secular trend toward zero. This has the effect that treatment effects are adjusted for trend, but where the evidence from data is weak, wild results are not obtained. We explore several frequentist approaches and a fully Bayesian method is also implemented. A measure of trend analogous to I(2) is described, and exact significance tests for trend are given. Our preferred method is one based on penalized or h-likelihood, which is computationally simple, and allows invariance of predictions to the (arbitrary) choice of time origin. We suggest that a trendless standard random effects meta-analysis should routinely be supplemented with an h-likelihood analysis as a sensitivity analysis.
Research Interests: Mathematics, Econometrics, Statistics, Schizophrenia, Nonlinear dynamics, and 15 moreSuicide, Inference, Medicine, Humans, Regression Analysis, Exercise, Health and Wellbeing, Meta Analysis, Random Effects Model, Time Factors, Bayes Theorem, Hemorrhage, Bayesian Probability, Likelihood Functions, and Clozapine
The synthesis of evidence from trials and medical studies using meta-analysis is essential for Evidence Based Medicine. However, problematical outlying results often occur even under the random-effects model. We propose a model that... more
The synthesis of evidence from trials and medical studies using meta-analysis is essential for Evidence Based Medicine. However, problematical outlying results often occur even under the random-effects model. We propose a model that allows a long-tailed distribution for the random effect, which removes the necessity for an arbitrary decision to include or exclude outliers. In this approach, they are included, but with a reduced weight. We also introduce a modification of the forest plot to show the downweighting of outliers. We illustrate the methodology and its usefulness by carrying out both frequentist and Bayesian meta-analyses using data sets from the Cochrane Collaboration.
Research Interests: Computer Science, Evidence Based Medicine, Medicine, Humans, Confidence intervals, and 13 moreHealth and Wellbeing, Long Tail, Meta Analysis, Importance Sampling, Random Effects Model, Public health systems and services research, Random-Effects Models, Statistical models, Bias (Epidemiology), Bayesian Probability, Outlier, Clinical Trials as Topic, and Random effects
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Purpose Axillary staging is an important prognostic factor in breast cancer. Sentinel lymph node biopsy (SNB) is currently used to stage patients who are clinically and radiologically node-negative. Since the establishment that axillary... more
Purpose Axillary staging is an important prognostic factor in breast cancer. Sentinel lymph node biopsy (SNB) is currently used to stage patients who are clinically and radiologically node-negative. Since the establishment that axillary node clearance (ANC) does not improve overall survival in breast-conserving surgery for patients with low-risk biological cancers, axillary management has become increasingly conservative. This study aims to identify and assess the clinical predictive value of variables that could play a role in the quantification of axillary burden, including the accuracy of quantifying abnormal axillary nodes on ultrasound. Methods A retrospective analysis was conducted of hospital data for female breast cancer patients receiving an ANC at our centre between January 2018 and January 2020. The reference standard for axillary burden was surgical histology following SNB and ANC, allowing categorisation of the patients under ‘low axillary burden’ (2 or fewer pathologic...
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The existence (or not) of the hot hand in sport continues to attract the attention of economists and psychologists. The paper presents analysis to test the belief prevalent in golfing circles that golfers go in and out of form quickly,... more
The existence (or not) of the hot hand in sport continues to attract the attention of economists and psychologists. The paper presents analysis to test the belief prevalent in golfing circles that golfers go in and out of form quickly, while ‘class’ remains relatively constant. By going in and out of form, the golfer is effectively experiencing a longer-run hot hand: one can speculate that periods of confidence breed good performance. To test for the existence of ‘form’, we present a new application of the Ornstein–Uhlenbeck model and use it to identify both a golfer’s class and form when modelling golf scores. The findings suggest that short-term form does exist in golf and that this hot hand lasts for about four weeks.
In this comprehensive Handbook, John Goddard and Peter Sloane present a collection of analytical contributions by internationally regarded scholars in the field, which extensively examine the many economic challenges facing the... more
In this comprehensive Handbook, John Goddard and Peter Sloane present a collection of analytical contributions by internationally regarded scholars in the field, which extensively examine the many economic challenges facing the world's most popular team sport.
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The paper presents a point process model for predicting exact end-of-match scores in the premier league of American football, the National Football League. The hazards of scoring are allowed to vary with team statistics from previous... more
The paper presents a point process model for predicting exact end-of-match scores in the premier league of American football, the National Football League. The hazards of scoring are allowed to vary with team statistics from previous games and/or the bookmaker point spread and over-under. The model is used to generate out-of-sample forecasts, which are evaluated using several criteria, including a Kelly betting strategy. In predicting the results of games, the model is marginally outperformed by the betting market. However, when it is used to forecast exact scores, the model proves to do at least as well as the market.
Research Interests: Marketing, Economics, Econometrics, Forecasting, Football, and 5 moreSports, Other, Point processes, Predictions, and League
Laser Doppler imaging (LDI) has been investigated and used since 1993 for the assessment of burn wounds. Here we describe tests that validate use of the dedicated colour palette, derived in Part 1, for a standardised interpretation of LDI... more
Laser Doppler imaging (LDI) has been investigated and used since 1993 for the assessment of burn wounds. Here we describe tests that validate use of the dedicated colour palette, derived in Part 1, for a standardised interpretation of LDI images for prediction of healing time (<14 days, 14-21 days or >21 days). We also describe clinical and technical factors to be taken into account during LDI imaging and during image interpretation. (1) A cohort of images, selected at random, were assessed, according to strict rules of interpretation, by 6 clinicians against photographs of healing, for accuracy of healing time prediction and clinical usefulness using five-point scales. (2) All images were assessed technically in a similar way for accuracy and the accuracy was further studied by analysing the data by ordinal logistic regression to predict the dependence of burn healing time on demographic variables (age, sex, race, %TBSA, burn cause and site). (3) Where average LDI blood flow could be determined, regression analysis was used to assess the potential accuracy of the technique. (1) Clinical accuracy was found to be 93% and usefulness was 89%; (2) technical accuracy was found to be 96%; (3) regression analysis found that a potential accuracy of 90.9% could be achieved using LDI results alone, increasing to 92% if gender was also considered; no other parameters had an influence on healing time prediction. LDI can be used in a standardised way as a valid tool for improving on clinical assessment of burn wounds. This can enable earlier appropriate management.
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ABSTRACT We describe a model to obtain strengths and rankings of players appearing in golf's Ryder Cup. Obtaining rankings is complicated because of two reasons. First, competitors do not compete on an equal number of occasions,... more
ABSTRACT We describe a model to obtain strengths and rankings of players appearing in golf's Ryder Cup. Obtaining rankings is complicated because of two reasons. First, competitors do not compete on an equal number of occasions, with some competitors appearing too infrequently for their ranking to be estimated with any degree of certainty, and second, different competitors experience different levels of volatility in results. Our approach is to assume the competitor strengths are drawn from some common distribution. For small numbers of competitors, as is the case here, we fit the model using Monte-Carlo integration. Results suggest there is very little difference between the top performing players, though Scotland's Colin Montgomerie is estimated as the strongest Ryder Cup player.
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Disturbed upper limb skin blood flow has been described in insulin-dependent (Type 1) diabetes mellitus, but the pathophysiological mechanism remains unclear. Hand skin blood flow was therefore measured at room temperature and following... more
Disturbed upper limb skin blood flow has been described in insulin-dependent (Type 1) diabetes mellitus, but the pathophysiological mechanism remains unclear. Hand skin blood flow was therefore measured at room temperature and following immersion of hands in cold and warm water in 13 healthy control subjects, in 10 patients with Type 1 diabetes mellitus and cardiovascular autonomic neuropathy, and a further 10 Type 1 diabetic patients with normal cardiovascular autonomic tone. Following cold challenge there was failure of digital artery clampdown in all diabetic patients in comparison with healthy control subjects (p less than 0.005), and the index finger temperature fell less (p less than 0.05). Laser Doppler flow was reduced at the palms at room temperature or following the warm challenge (p less than 0.008), as well as on the dorsum at room temperature (p less than 0.05), in all diabetic patients. In addition laser Doppler flow in the diabetic patients was reduced at the palms and dorsum immediately following cold water challenge (p less than 0.004) and this reduction persisted 15 min (p less than 0.05) and 30 min (p less than 0.01) into the recovery phase. In comparison to those diabetic patients with normal cardiovascular tone, those with cardiovascular autonomic neuropathy had reduced laser Doppler flow at the pulp 15 min after cold water immersion (p less than 0.05), at the nailbed immediately after cold water immersion (p less than 0.01), and at the palms immediately after warm water challenge (p less than 0.01).
Research Interests: Medicine, Autonomic Nervous System, Humans, Internal Medicine, Insulin, and 15 moreDiabetes mellitus, Blood Pressure, Female, Male, Ultrasonics, Heart rate, Skin, Clinical Sciences, Middle Aged, Adult, Blood Flow, Hand, Skin blood flow, Laser Doppler Velocimetry, and Insulin dependent diabetes mellitus
Research Interests: Mathematics, Approximation Theory, Econometrics, Game Design, Experimental Design, and 15 moreCopulas, Probability, Multivariate Analysis, Lottery, Correlation, Other, Application, Copula, Overdispersion, Moments, Multivariate Normal Distribution, Empirical Model, Probability Distribution, Distribution Function, and Model fitting
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Laser Doppler imaging (LDI) has been investigated and used since 1993 for the assessment of burn wounds. Here we describe tests that validate use of the dedicated colour palette, derived in Part 1, for a standardised interpretation of LDI... more
Laser Doppler imaging (LDI) has been investigated and used since 1993 for the assessment of burn wounds. Here we describe tests that validate use of the dedicated colour palette, derived in Part 1, for a standardised interpretation of LDI images for prediction of healing time (<14 days, 14-21 days or >21 days). We also describe clinical and technical factors to be taken into account during LDI imaging and during image interpretation. (1) A cohort of images, selected at random, were assessed, according to strict rules of interpretation, by 6 clinicians against photographs of healing, for accuracy of healing time prediction and clinical usefulness using five-point scales. (2) All images were assessed technically in a similar way for accuracy and the accuracy was further studied by analysing the data by ordinal logistic regression to predict the dependence of burn healing time on demographic variables (age, sex, race, %TBSA, burn cause and site). (3) Where average LDI blood flow could be determined, regression analysis was used to assess the potential accuracy of the technique. (1) Clinical accuracy was found to be 93% and usefulness was 89%; (2) technical accuracy was found to be 96%; (3) regression analysis found that a potential accuracy of 90.9% could be achieved using LDI results alone, increasing to 92% if gender was also considered; no other parameters had an influence on healing time prediction. LDI can be used in a standardised way as a valid tool for improving on clinical assessment of burn wounds. This can enable earlier appropriate management.
Research Interests: Adolescent, Medicine, Logistic Regression, Image Interpretation, Humans, and 15 moreChild, Female, Male, Regression Analysis, Infant, Health and Wellbeing, Clinical Sciences, Aged, Middle Aged, Burns, Adult, Sensitivity and Specificity, Predictive value of tests, Laser Doppler Flowmetry, and Child preschool
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The concept of shrinking bet size in Kelly betting to minimize estimated frequentist risk has recently been mooted. This rescaling appears to conflict with Bayesian decision theory through the likelihood principle and the complete class... more
The concept of shrinking bet size in Kelly betting to minimize estimated frequentist risk has recently been mooted. This rescaling appears to conflict with Bayesian decision theory through the likelihood principle and the complete class theorem; the Bayesian solution should already be optimal. We show theoretically and through examples that when the modeldetermining the likelihood function is correct, the prior distribution (if not dominated by data) is `correct' in a frequentist sense, and the posterior distribution is proper, then no further rescaling is required. However, if the model or the prior distribution is incorrect, or the posterior distribution improper, frequentist risk minimization can be a useful technique. We discuss how it might best be exploited. Another example, from maintenance, is used to show the wider applicability of the methodology; these conclusionsapply generally to decision-making.
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Research Interests: Statistical Analysis, Medicine, Logistic Regression, Humans, Female, and 15 moreMale, Skin, Health and Wellbeing, Decision support tool, Burns, Public health systems and services research, Sex Factors, Time Factors, Blood Flow, Permutation Test, Logistic Models, Predictive value of tests, Laser Doppler Flowmetry, Statistical Method, and Random effects
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Mathematical reflections on doing jury duty, emphasizing the probability of being called up for duty, and how improvements could be made. An improved selection method that would avoid some people being called up more than once is discussed.
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BACKGROUND Patients with early breast cancer undergoing primary surgery who have low axillary nodal burden can safely forego axillary node clearance (ANC). However, routine use of axillary ultrasound (AUS) leads to 43% of patients in this... more
BACKGROUND Patients with early breast cancer undergoing primary surgery who have low axillary nodal burden can safely forego axillary node clearance (ANC). However, routine use of axillary ultrasound (AUS) leads to 43% of patients in this group having ANC unnecessarily following a positive AUS. The intersection of machine learning with medicine can provide innovative ways to understand specific risk within large patient data sets, but this has not yet been trialled in the arena of axillary node management in breast cancer. OBJECTIVE To assess if machine learning techniques could be used to improve pre-operative identification of patients with low and high axillary metastatic burden. METHODS A single-centre retrospective analysis was performed on patients with breast cancer who had a preoperative axillary ultrasound, and the specificity and sensitivity of AUS were calculated. Machine learning and standard statistical methods were applied to the data to see if, when used preoperativel...
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In sport, order-statistics-based models such as Henery’s gamma model and the Thurstone–Mosteller type V model are useful in estimating competitor strengths from observed performance of players in competitions between two or more players.... more
In sport, order-statistics-based models such as Henery’s gamma model and the Thurstone–Mosteller type V model are useful in estimating competitor strengths from observed performance of players in competitions between two or more players. They can also be applied in many other areas, such as analysis of consumer preference data, which would be useful to marketing management. Two new families of such models derived from the exponentiated exponential, and Pareto distributions are introduced. Use of order-statistics-based models when there are more than two competitors has been hampered by lack of an efficient method of computation of outcome probabilities as a function of competitor strengths, and a fast method of computation of outcome probabilities is presented, which exploits the fact that the integral to be evaluated is an iterated integral.
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Abstract The problem of comparing the deviation from a target of two or more treatments or procedures arises now and again in medicine. Practitioners usually carry out a t-test on a loss function such as absolute error. We have adapted... more
Abstract The problem of comparing the deviation from a target of two or more treatments or procedures arises now and again in medicine. Practitioners usually carry out a t-test on a loss function such as absolute error. We have adapted and developed statistical methods to give a normative methodology for deviation-from-target problems and exemplify them by evaluating the performance of a tactile feedback device. Parametric and nonparametric analyses are compared and contrasted. We recommend nonparametric methods for inference about loss functions such as absolute error, with a permutation test for testing the hypothesis that the two methods perform identically, and the nonparametric bootstrap for deriving standard errors and confidence intervals on loss function ratios. We develop a new permutation test that can be used when the practitioner is unwilling to decide which loss function should be used. We recommend parametric analysis when more insight into how one method is superior is desired, or there are covariates, and discuss the complications. The results for our example are that the tactile sensing device reduces an upwards bias in applied force, and more importantly reduces the spread (variance) of the applied force. It performs significantly better than manual force application.
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It is argued that there is a need for fat-tailed distributions that become thin in the extreme tail. A 3-parameter distribution is introduced that visually resembles the t-distribution and interpolates between the normal distribution and... more
It is argued that there is a need for fat-tailed distributions that become thin in the extreme tail. A 3-parameter distribution is introduced that visually resembles the t-distribution and interpolates between the normal distribution and the Cauchy distribution. It is fat-tailed, but has all moments finite, and the moment-generating function exists. It would be useful as an alternative to the t-distribution for a sensitivity analysis to check the robustness of results or for computations where finite moments are needed, such as in option-pricing. It can be motivated probabilistically in at least two ways, either as the random thinning of a long-tailed distribution, or as random variation of the variance of a normal distribution. Its properties are described, algorithms for random-number generation are provided, and examples of its use in data-fitting given. Some related distributions are also discussed, including asymmetric and multivariate distributions.
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A class of discrete distributions can be derived from stationary renewal processes. They have the useful property that the mean is a simple function of the model parameters. Thus regressions of the distribution mean on covariates can be... more
A class of discrete distributions can be derived from stationary renewal processes. They have the useful property that the mean is a simple function of the model parameters. Thus regressions of the distribution mean on covariates can be carried out and marginal effects of covariates calculated. Probabilities can be easily computed in closed form for only two such distributions, when the event interarrival times in the renewal process follow either a gamma or an inverse Gaussian distribution. The gamma-based distribution has more attractive properties and is described and fitted to data. The inverse-Gaussian based distribution is also briefly discussed.
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Purpose 1. To systematically analyse studies comparing survival outcomes between axillary lymph-node dissection (ALND) and axilla observation (Obs), in women with low-risk, clinically node-negative breast cancer. 2. To consider results in... more
Purpose 1. To systematically analyse studies comparing survival outcomes between axillary lymph-node dissection (ALND) and axilla observation (Obs), in women with low-risk, clinically node-negative breast cancer. 2. To consider results in the context of current axillary surgery de-escalation trials and studies. Methods 9 eligible studies were identified, 6 RCTs and 3 non-randomized studies (4236 women in total). Outcomes assessed: overall survival (OS) and disease-free survival (DFS). The logged (ln) hazard ratio (HR) was calculated and used as the statistic of interest. Data was grouped by follow-up. Results Meta-analyses found no significant difference in OS at 5, 10 and 25-years follow-up (5-year ln HR = 0.08, 95% CI − 0.09, 0.25, 10-year ln HR = 0.33, 95% CI − 0.07, 0.72, 25-year ln HR = 0.00, 95% CI − 0.18, 0.19). ALND caused improvement in DFS at 5-years follow-up (ln HR = 0.16, 95% CI 0.03, 0.29), this was not demonstrated at 10 and 25-years follow-up (10-year ln HR = 0.07, ...
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In February, 2005 the Spanish National Lottery Agency (LAE) made several modifications to the design of one of its lotto games. The entry fee was not changed but the familiar 6/49 format was replaced by 5/54 + 1/10. This considerably... more
In February, 2005 the Spanish National Lottery Agency (LAE) made several modifications to the design of one of its lotto games. The entry fee was not changed but the familiar 6/49 format was replaced by 5/54 + 1/10. This considerably lengthened the odds against winning a share of the grand prize. However, extra lower tiers of prizes were added and