Rose Dawn Baker

University of Salford · Salford Business School

Spline curves, originally developed by numerical analysts for interpolation, are widely used in statistical work, mainly as regression splines and smoothing splines. Barycentric rational interpolants have recently been developed by numerical analysts, but have yet seen very few statistical applications. We give the necesssary information to enable...

Tests of space-time clustering such as the Knox test are used by epidemiologists in the preliminary analysis of datasets where an infectious aetiology is suspected. The Knox test statistic is the number of cases close in both space and time to another case. The test statistic proposed here is the excess number of such cases over that expected under...

We present a methodology for fitting time-varying paired comparisons models in which the parameters are allowed to vary deterministically, as opposed to stochastically, with time. Our dynamic paired comparisons model is based on a new closed-form for Stern’s continuum of paired comparisons models which include the Bradley–Terry model and the Thurst...

In the author's concept of risk-averse maintenance, introduced in a previous paper, we seek to minimize the disutility of cost per unit time rather than to minimize cost per unit time itself. This gives a maintenance policy that is optimal under risk aversion. This paper extends the earlier work by providing a solution to the problem of combining r...

We first present a model for the outcome of snooker matches in which player strengths are allowed to vary deterministically with time. The results allow us to identify the greatest players of all time, and to examine the relationship between age and performance. Second, we present a random effects model which uses the estimated strengths from our f...

We present a new mixed linear model for the relationship between age and performance. The model allows for random effects at the nodes of a barycentric interpolation, such that performance evolves with age in a non-prescriptive way. We use the model to investigate the effects of age on performance in golf and find that performance peaks in the 30s...

Using differential equations to try to understand yo-yo dieting.

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 l...

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 bi...

We present a unified theory that posits three fundamental models as necessary and sufficient for modelling the bivariate scores in possessive ball-sports. These models provide the basis for perhaps more complicated models that can be used for prediction, experimentation, and explanation. First is the Poisson-match, for when goals are rare, or when...

Confirmation bias is a cognitive bias that adversely affects management decisions, and mathematical modelling is an aid to its detailed understanding. Bias in opinion update about the value of a parameter is modelled here assuming that observations are discounted depending on their distance from prior opinion. The models allow belief persistence, a...

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...

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...

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...

The magnetic technique, consisting of a magnetic tracer and a handheld magnetometer, is a promising alternative technique for sentinel lymph node dissection (SLND) and was shown to be non-inferior to the standard technique in terms of identification rates. In this study, injection characteristics (iron dose, dilution, time course and massaging) wer...

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 iden...

The efferent control chain for an upper-limb myoelectric prosthesis can be separated into 3 key areas: signal generation, signal acquisition, and device response. Data were collected from twenty trans-radial myoelectric prosthesis users using their own clinically prescribed devices, to establish the relative impact of these potential control factor...

Models derived from distributions of order-statistics are useful for modelling ranked data. The well-known Bradley–Terry (BT) and Plackett–Luce (PL) models can be derived from the order statistics of the exponential distribution but cannot handle ties. However, ties often occur in sports, and the ability to accommodate them leads to more useful ran...

We apply seven alternative t-distributions to estimate the market risk measures Value at Risk (VaR) and its extension Expected Shortfall (ES). Of these seven, the twin t-distribution (TT) of Baker and Jackson (in Twin t distribution, University of Salford Manchester. https://arxiv.org/abs/1408.3237, 2014) and generalized asymmetric distribution (GA...

Sweetcorn plants are wind pollinated, and can be arranged for maximum pollination. The article presents a simple mathematical model for this, and then waxes philosophical about inequality in society---some plants are better placed than others.

A model of reactive social distancing in epidemics is proposed, in which the infection rate changes with the number infected. The final-size equation for the total number that the epidemic will infect can be derived analytically, as can the peak infection proportion. This model could assist planners during for example the COVID-19 pandemic.

Background: Walking aids are issued to older adults to prevent falls, however, paradoxically their use has been identified as a risk factor for falling. To prevent falls, walking aids must be used in a stable manner, but it remains unknown to what extent associated clinical guidance is adhered to at home, and whether following guidance facilitates...

A new alternative to the standard Poisson regression model for count data is suggested. This new family of models is based on discrete distributions derived from renewal processes, i.e., distributions of the number of events by some time t. Unlike the Poisson model, these models have, in general, time-dependent hazard functions. Any survival distri...

The adaptive asymmetric trimmed mean is a known way of estimating central location, usually in conjunction with the bootstrap. It is here modified and applied to meta-analysis, as a way of dealing with outlying results by down-weighting the corresponding studies. This requires a modified bootstrap and a method of down-weighting studies, as opposed...

Purpose The steady move towards axillary conservatism in breast cancer is based on studies demonstrating that axillary node clearance affords no survival benefit in a subset of patients with a positive pre-operative axillary ultrasound (AUS). However, less attention has been paid to AUS-negative patients who receive sentinel node biopsy as standard...

Modelling lottery sales as a function of the mean, standard deviation and skewness of the probability distribution of returns potentially gives insights into how the design of a game could be modified to maximise net revenue. But use of OLS is problematic because the level of sales itself affects values of the moments (and insufficient instruments...

Methods for generating new distributions from old can be thought of as techniques for simplifying integrals used in reverse. Hence integrating a probability density function (pdf) by parts provides a new way of modifying distributions; the resulting pdfs are integrals that sometimes require computation as special functions. Summation by parts can b...

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 usefu...

Walking aids are widely used by older adults, however, alarmingly, their use has been linked to increased falls-risk, yet clinicians have no objective way of assessing user stability. This work aims to demonstrate the application of a novel methodology to investigate how the type of walking task, the amount of body weight supported by the device (i...

Validation of the instrumented rollator. (DOCX)

Participants’ descriptive parameters. (DOCX)

A general method for deriving new survival distributions from old is presented. This yields a class of useful mixture distributions. Fitting such distributions to failure-time data allows estimation of the improvement in reliability that could be gained from eliminating `frail' components. One model parameter is the proportional increase of expect...

Studies of the effectiveness of prosthetic hands involve assessing user performance on functional tasks, typically collected in the lab, sometimes combined with self-report of real-world use. In this paper we compare real-world upper limb activity between a group of 20 myoelectric prosthesis users and 20 anatomically intact adults. Activity was mea...

Comparative binary outcome data are of fundamental interest in statistics and are often pooled in meta-analyses. Here we examine the simplest case where for each study there are two patient groups and a binary event of interest, giving rise to a series of $2 \times 2$ tables. A variety of measures of treatment effect are then available and are conv...

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 fo...

Aims The magnetic technique using a magnetic tracer and handheld magnetometer was successfully evaluated in breast surgery. Residual tracer at the injection site can cause susceptibility artefacts on breast magnetic resonance imaging (MRI), therefore for lesion localization a solid marker would be preferable. Four magnetic markers were developed fo...

We present a model for rating international football teams. Using data from 1944 to 2016, we ask 'which was the greatest team?'. To answer the question requires some sophisticated methodology. Specifically, we have used k-fold cross-validation, which allows us to optimally down-weight the results of friendly matches in explaining World Cup results....

Background: Management of the axilla in breast cancer is becoming increasingly conservative. Patients identified with a low axillary nodal burden (two or fewer involved nodes) at sentinel node biopsy (SNB) can avoid completion axillary node clearance (cANC). 'Fast track' to ANC in patients with involved nodes on pre-operative ultrasound may be ove...

A new model with a variable size of random effect is introduced for the meta-analysis of 2 × 2 tables. The random-effects parameter has a simple interpretation in terms of sample size and offers a new measure of heterogeneity.

Background: High intensity focused ultrasound (HIFU) is a non-invasive ablative technique utilising the application of high frequency ultrasound (US) pressure waves to cause tissue necrosis. This emerging technology is currently limited by prolonged treatment times. The aim of the HIFU-F trial was to perform circumferential HIFU treatment as a mean...

Discrete distributions derived from renewal processes, i.e. distributions of the number of events by some time t, are beginning to be used in management science, econometrics and health sciences. A new fast method is presented for computation of the probabilities for these distributions. This will enable practitioners in management science to explo...

Network meta-analysis is used to simultaneously compare multiple treatments in a single analysis. However, network meta-analyses may exhibit inconsistency, where direct and different forms of indirect evidence are not in agreement with each other, even after allowing for between-study heterogeneity. Models for network meta-analysis with random inco...

A simple method is proposed for ‘blunting’ cusped distributions, i.e. removing the cusp. No additional parameters are required. The method is applied to the asymmetric Laplace distribution, to the van Dorp and Kotz double-sided power distribution, and to the double-sided asymmetric Pareto distribution, and some properties of the blunted distributio...

The beta distribution is the best-known distribution for modelling doubly-bounded data, \eg percentage data or probabilities. A new generalization of the beta distribution is proposed, which uses a cubic transformation of the beta random variable. The new distribution is label-invariant like the beta distribution and has rational expressions for th...

Background In early breast cancer, the optimal technique for sentinel lymph node biopsy (SLNB) is the combined technique (radioisotope and Patent Blue V) which achieves high identification rates. Despite this, many centres have decided to stop using blue dye due to blue-dye-related complications (tattoo, anaphylaxis). We evaluated the SLNB identifi...

Background: The standard for sentinel lymph node biopsy (SLNB), the dual technique (radiolabelled tracer and blue dye), has several drawbacks. A novel magnetic technique without these drawbacks has been evaluated in a number of clinical trials. It uses a magnetic tracer and a handheld magnetometer to identify and excise sentinel lymph nodes. A sys...

Background: Sentinel node biopsy (SNB) in recurrent breast cancer offers targeted axillary staging compared with axillary lymph node dissection (ALND) or no treatment. The evidence for lymphatic mapping in recurrent breast cancer is reviewed, focusing on aberrant drainage and its implications for patient management. Methods: A meta-analysis of s...

The combined technique (radioisotope and blue dye) is the gold standard for sentinel lymph node biopsy (SLNB) and there is wide variation in techniques and blue dyes used. We performed a systematic review and meta-analysis to assess the need for radioisotope and the optimal blue dye for SLNB. A total of 21 studies were included. The SLNB identifica...

Purpose: Breast conserving surgery is effective for breast cancer treatment but is associated with morbidity in particular high re-excision rates. We performed a systematic review to assess the current evidence for clinical outcomes with minimally invasive ablative techniques in the non-surgical treatment of breast cancer. Methods: A systematic...

Objectives: Breast fibroadenomata (FAD) are the most common breast lumps in women. High intensity focused ultrasound (HIFU) is a non-invasive ablative technique that can be used to treat FAD but is associated with prolonged treatment times. In the HIFU-F trial, we evaluated the change in volume over time with circumferential HIFU treatment of FAD a...

We present a methodology for fitting a time-varying paired comparisons model using an empirical Bayes approach. The model simultaneously avoids two problems that typically arise with paired comparisons data: first, that extreme values of estimated strengths can occur for competitors appearing in and winning a small number of games, producing absurd...

A 6-parameter fat-tailed distribution is proposed that generalises the t-distribution and allows asymmetry of scale and also of tail power, whilst avoiding the discontinuity of the second derivative of the split-t (AST) distribution. With the sixth parameter set to unity and no asymmetry, the distribution reduces to a t-distribution, but with the s...

Discrete distributions derived from renewal processes, i.e. distributions of the number of events by some time t are beginning to be used in econometrics and health sciences. A new fast method is presented for computation of the probabilities for these distributions. We calculate the count probabilities by repeatedly convolving the discretized dist...

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 th...

The preoccupation with modelling credit scoring systems including their relevance to predicting and decision making in the financial sector has been with developed countries, whilst developing countries have been largely neglected. The focus of our investigation is on the Cameroonian banking sector with implications for fellow members of the Banque...

Sales are modelled for 50 Spanish provinces over 522 draws of a high prize lotto game. A crossed random effects model allows for random shocks specific to particular draws and to particular provinces. The paper explores how demographic and socio-economic factors influence sales volumes, with particular focus on the relationship between sales and re...

Euromillions is a lotto game played across nine countries. We examine more than 8 years of sales data for individual states to assess whether a jackpot win in a country increases subsequent sales in that country. We propose a novel test for the presence of such a ‘compatriot win effect’ that has as its only assumption that the lottery draw is rando...

Unlabelled: The magnetic technique for sentinel node biopsy provides a radioisotope-free alternative for staging breast cancer. It requires refinement to reduce "residual iron content" at injection sites by maximising lymphatic uptake to prevent "void artefacts" on magnetic resonance imaging (MRI), which could adversely affect clinical use. The si...

An unobserved random effect is often used to describe the between-study variation that is apparent in meta-analysis datasets. A normally distributed random effect is conventionally used for this purpose. When outliers or other unusual estimates are included in the analysis, the use of alternative random effect distributions has previously been prop...

Moment-based estimators of the between-study variance are very popular when performing random effects meta-analyses. This type of estimation has many advantages including computational and conceptual simplicity. Furthermore, by using these estimators in large samples, valid meta-analyses can be performed without the assumption that the treatment ef...

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, diffe...

Thirty-five percent of people above age 65 fall each year, and half of their falls are associated with tripping: tripping, an apparently 'mundane' everyday problem, therefore, significantly impacts on older people's health and associated medical costs. To avoid tripping and subsequent falling, sufficient toe clearance during the swing phase is cruc...

Some new survival distributions are introduced based on a generalised exponential function. This class of distributions includes heavy-tailed generalisations of exponential, Weibull and gamma distributions. Properties of the distributions are described, and R code is available for computation of pdf, quantiles, inverse quantiles, random numbers, et...

A new class of copulas based on order statistics was introduced by Baker (2008). Here, further properties of the bivariate and multivariate copulas are described, such as that of likelihood ratio dominance (LRD), and further bivariate copulas are introduced that generalize the earlier work. One of the new copulas is an integral of a product of Bess...

We used a validated questionnaire to explore the views of patients regarding receiving intensive care and life-sustaining technology. Data was obtained from 38 patients. A score was obtained for ‘general attitude towards use of life-sustaining/prolonging technology’ that varied from 18.9 to 48.5 out of 52, the higher score reflecting a more positiv...

We describe the development and laboratory assessment of a refined prototype tactile feedback device for the safe and accurate application of cricoid pressure. We recruited 20 operating department practitioners and compared their performance of cricoid pressure on a training simulator using both the device and a manual unaided technique. The device...

Frullani's integral dates from 1821, but a probabilistic interpretation of it has never been made. In this paper, Frullani's integral formula is shown to result from mixing a lifetime distribution by allowing the logarithm of the scale factor to be uniformly distributed over a finite range. This gives a class of long-tailed distributions related to...

A new distribution is introduced, which we call the twin-t distribution. This distribution is heavy-tailed like the t distribution, but closer to normality in the central part of the curve. Its properties are described, e.g. the pdf, the distribution function, moments, and random number generation. This distribution could have many applications, bu...

Introduction: Laser Doppler imaging (LDI) provides early accurate determination of wound healing potential. LDI can scan large areas of up to 2500 cm2 within 2 min. This duration may require additional sedation in a mobile, uncooperative child. In five burn centres a faster Laser Doppler Line Scanner (LDLS) was assessed. This new imager scans 300...

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...

We present a statistical methodology for fitting time-varying rankings, by estimating the strength parameters of the Plackett–Luce multiple comparisons model at regularly spaced times for each ranked item. We use the little-known method of barycentric rational interpolation to interpolate between the strength parameters so that a competitor's stren...

We present a new methodology to estimate time varying team strengths of football teams. Our dynamic model allows for deterministic, rather than stochastic, evolution of team strengths. We use the model to identify the best team in England since the English Football Association was formed and match results were recorded in 1888. Our results suggest...

Several researchers have established a link between the presence of house mouse (Mus domesticus) infestations and detrimental effects on human health. Controlling mouse infestations therefore requires methods that are quick, safe and effective. A tamper-resistant bait station with a wax block which is manufactured to fit within it so that it cannot...

Stricturing is a common complication of Crohn's disease. Endoscopic balloon dilatation (EBD) offers a valuable alternative to surgical intervention, but there are limited data on factors influencing its safety and efficacy. A multicenter retrospective audit across 4 U.K. teaching hospitals was performed on the use of EBD for Crohn's strictures betw...

The Kelly betting criterion ignores uncertainty in the probability of winning the bet and uses an estimated probability. In general, such replacement of population parameters by sample estimates gives poorer out-of-sample than in-sample performance. We show that to improve out-of-sample performance the size of the bet should be shrunk in the presen...

In this note, we explain how the method proposed by Hartung and Knapp provides a compromise between conventional meta-analysis methodology and 'unconstrained averaging', as used by the Particle Data Group. Copyright © 2013 John Wiley & Sons, Ltd. Copyright © 2013 John Wiley & Sons, Ltd.

The use of meta-analysis in medicine and epidemiology really took off in the 1970s. However, in high-energy physics, the Particle Data Group has been carrying out meta-analyses of measurements of particle masses and other properties since 1957. Curiously, there has been virtually no interaction between those working inside and outside particle phys...

Emotional intelligence (EI) in the UK radiographer workforce has been benchmarked using the trait emotional intelligence model and the profile of the profession in the UK has begun to emerge. There are cultural differences between countries that have been shown to have an effect on EI, therefore this paper aims to benchmark the Global and four fact...

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...

The process of undertaking a meta-analysis involves a sequence of decisions, one of which is deciding which measure of treatment effect to use. In particular, for comparative binary data from randomised controlled trials, a wide variety of measures are available such as the odds ratio and the risk difference. It is often of interest to know whether...

The aim of this study was to profile the Trait emotional intelligence (EI) of the radiography profession, explore any differences between subgroups, compare the profession with a normative group and investigate the relationship between EI and the leaders of the profession. An online UK-wide survey was conducted using the Trait Emotional Intelligenc...

The Institute of Mathematics and its Applications has been organising the IMA International Conference on Quantitative Modelling in the Management of Health Care since 1995. The aim of the conference is to bring together health care managers, clinicians, management consultants, and mathematicians, operational researchers, statisticians, economists...

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 technic...

Ian McHale dreams of winning the lottery. As a statistician, does he stand a better chance? With Rose D. Baker, he explains…

The Institute of Mathematics and its Applications has been organising the IMA International Conference on Quantitative Modelling in the Management of Health Care since 1995. The aim of the conference is to bring together health care managers, clinicians, management consultants, and mathematicians, operational researchers, statisticians, economists...