How good is Tiger Woods?

A major objective of professional sport is to find out which player or team is the best. Unfortunately the structure of some sports means that this is often a difficult question to answer. For example, there may be too many competitors to run a round-robin league, whilst knock-out tournaments do not compare every player with every other player. The problem gets worse when one has to compare players whose performance varies over time. Fortunately mathematical modelling can help and in this article, we use the Plackett-Luce model to estimate time-varying player strengths of golfers. We use the model to investigate how good golf's current biggest attraction, Tiger Woods, really is

New survival distributions that quantify the gain from eliminating flawed components

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 expected survival time that could be achieved. Some 2 and 3 parameter distributions in this class are described, which are extensions of the Weibull, exponential, gamma and lognormal distributions. The methodology is illustrated by fitting some well travelled datasets. Keywords: Weibull distribution, gamma distribution, mixture distribution, hazard function, partial integration, frailty mode

New order-statistics-based ranking models and faster computation of outcome probabilities

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 2 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 2 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, that exploits the fact that the integral to be evaluated is an iterated integral

Event count distributions from renewal processes : fast computation of probabilities

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 exploit this rich class of models. We calculate the count probabilities by repeatedly convolving the discretized distribution, and then correct them using Richardson extrapolation. When just one probability is required, a second algorithm is described, an adaptation of De Pril's method, in which the computation time does not depend on the ordinality, so that even high-order probabilities can be rapidly found. Any survival distribution can be used to model the inter-arrival times, which gives models with great flexibility for modelling both underdispersed and overdispersed data. This work could pave the way for the routine use of these distributions as an additional tool for modelling event count data. An empirical example using fertility data illustrates the use of the method and has been fully implemented using an R package Countr developed by the authors and available from the Comprehensive R Archive Network (CRAN)

Time-varying ratings for international football teams

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. In addition to the central aim of the paper, we also discuss, from a philosophical perspective, situations in which model over-fitting is perhaps desirable. Results suggest that Hungary in 1952, is a strong candidate for the all-time greatest international football team

Are older people putting themselves at risk when using their walking frames?

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 stable walking pattern. It was the aim of this study to investigate adherence to guidance on walking frame use, and to quantify user stability whilst using walking frames. Additionally, we explored the views of users and healthcare professionals on walking aid use, and regarding the instrumented walking frames (‘Smart Walkers’) utilized in this study. Methods This observational study used Smart Walkers and pressure-sensing insoles to investigate usage patterns of 17 older people in their home environment; corresponding video captured contextual information. Additionally, stability when following, or not, clinical guidance was quantified for a subset of users during walking in an Activities of Daily Living Flat and in a gait laboratory. Two focus groups (users, healthcare professionals) shared their experiences with walking aids and provided feedback on the Smart Walkers. Results Incorrect use was observed for 16% of single support periods and for 29% of dual support periods, and was associated with environmental constraints and a specific frame design feature. Incorrect use was associated with reduced stability. Participants and healthcare professionals perceived the Smart Walker technology positively. Conclusions Clinical guidance cannot easily be adhered to and self-selected strategies reduce stability, hence are placing the user at risk. Current guidance needs to be improved to address environmental constraints whilst facilitating stable walking. The research is highly relevant considering the rising number of walking aid users, their increased falls-risk, and the costs of falls. Trial Registration Not applicable

Safety aspects of infliximab in inflammatory bowel disease patients - A retrospective cohort study in 100 patients of a German University Hospital

Background: Infliximab, a chimeric anti-tumour necrosis factor monoclonal antibody with potent anti-inflammatory effects, represents an effective treatment option in patients with severe inflammatory bowel disease (IBD). Serious side-effects of such an immunomodulating therapy are speculated and therefore we reviewed our clinical experience in a retrospective safety study looking upon a single cohort of 100 IBD patients from a large German University Hospital. Methods: 100 patients with severe Crohn's disease (n = 92), ulcerative colitis (n = 7) or indeterminate colitis (n = 1) treated with infliximab (5 mg/kg) from January 2000 to December 2003 were retrospectively analysed for acute and subacute adverse events by chart review. Results: Overall, infliximab therapy was generally well tolerated. No fatal complications, malignancies, autoimmune diseases, neurologic or cardiovascular complications were observed in the cohort during the study period. Overall, adverse events were observed in 10 patients: 2 patients showed an acute infusion reaction, 1 patient a serum sickness-like reaction, in 4 patients a bacterial or viral infection occurred, in 1 patient pancytopenia and 2 patients developed surgical complications. Only 6 patients with adverse events required admission to hospital. A case of tuberculosis after infliximab was not found. The lack of adverse side-effects was associated with young median age and infrequent comorbidities of the cohort. Conclusion: Regarding its strong immunomodulating capacity, infliximab appears to be an efficient and relatively safe therapeutic option for patients with severe IBD. However, the use of infliximab requires careful screening and close patient monitoring to identify patients at risk and the infrequent, but sometimes serious complications of infliximab. Copyright (C) 2004 S. Karger AG, Basel

Objective measures of rollator user stability and device loading during different walking scenarios

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.e., device loading), and task performance strategy affect stability of rollator users. In this context, ten users performed six walking tasks with an instrumented rollator. The combined stability margin “SM” was calculated, which considers user and rollator as a combined system. A Friedman Test was used to investigate the effects of task on SM and a least-squares regression model was applied to investigate the relationship between device loading and SM. In addition, the effects of task performance strategy on SM were explored. As a result, it was found that: the minimum SM for straight line walking was higher than for more complex tasks (p<0.05); an increase in device loading was associated with an increase in SM (p<0.05); stepping up a kerb with at least 1 rollator wheel in ground contact at all times resulted in higher SM than lifting all four wheels simultaneously. Hence, we conclude that training should not be limited to straight line walking but should include various everyday tasks. Within person, SM informs on which tasks need practicing, and which strategy facilitates stability, thereby enabling person-specific guidance/training. The relevance of this work lies in an increase in walking aid users, and the costs arising from fall-related injuries. Supplementary data is available in Figshare

Selecting patients for randomized trials: a systematic approach based on risk group

BACKGROUND: A key aspect of randomized trial design is the choice of risk group. Some trials include patients from the entire at-risk population, others accrue only patients deemed to be at increased risk. We present a simple statistical approach for choosing between these approaches. The method is easily adapted to determine which of several competing definitions of high risk is optimal. METHOD: We treat eligibility criteria for a trial, such as a smoking history, as a prediction rule associated with a certain sensitivity (the number of patients who have the event and who are classified as high risk divided by the total number patients who have an event) and specificity (the number of patients who do not have an event and who do not meet criteria for high risk divided by the total number of patients who do not have an event). We then derive simple formulae to determine the proportion of patients receiving intervention, and the proportion who experience an event, where either all patients or only those at high risk are treated. We assume that the relative risk associated with intervention is the same over all choices of risk group. The proportion of events and interventions are combined using a net benefit approach and net benefit compared between strategies. RESULTS: We applied our method to design a trial of adjuvant therapy after prostatectomy. We were able to demonstrate that treating a high risk group was superior to treating all patients; choose the optimal definition of high risk; test the robustness of our results by sensitivity analysis. Our results had a ready clinical interpretation that could immediately aid trial design. CONCLUSION: The choice of risk group in randomized trials is usually based on rather informal methods. Our simple method demonstrates that this decision can be informed by simple statistical analyses