The Newcomb-Benford Law in Its Relation to Some Common Distributions

An often reported, but nevertheless persistently striking observation, formalized as the Newcomb-Benford law (NBL), is that the frequencies with which the leading digits of numbers occur in a large variety of data are far away from being uniform. Most spectacular seems to be the fact that in many data the leading digit 1 occurs in nearly one third of all cases. Explanations for this uneven distribution of the leading digits were, among others, scale- and base-invariance. Little attention, however, found the interrelation between the distribution of the significant digits and the distribution of the observed variable. It is shown here by simulation that long right-tailed distributions of a random variable are compatible with the NBL, and that for distributions of the ratio of two random variables the fit generally improves. Distributions not putting most mass on small values of the random variable (e.g. symmetric distributions) fail to fit. Hence, the validity of the NBL needs the predominance of small values and, when thinking of real-world data, a majority of small entities. Analyses of data on stock prices, the areas and numbers of inhabitants of countries, and the starting page numbers of papers from a bibliography sustain this conclusion. In all, these findings may help to understand the mechanisms behind the NBL and the conditions needed for its validity. That this law is not only of scientific interest per se, but that, in addition, it has also substantial implications can be seen from those fields where it was suggested to be put into practice. These fields reach from the detection of irregularities in data (e.g. economic fraud) to optimizing the architecture of computers regarding number representation, storage, and round-off errors

We are all one together : peer educators\u27 views about falls prevention education for community-dwelling older adults - a qualitative study

Background: Falls are common in older people. Despite strong evidence for effective falls prevention strategies, there appears to be limited translation of these strategies from research to clinical practice. Use of peers in delivering falls prevention education messages has been proposed to improve uptake of falls prevention strategies and facilitate translation to practice. Volunteer peer educators often deliver educational presentations on falls prevention to community-dwelling older adults. However, research evaluating the effectiveness of peer-led education approaches in falls prevention has been limited and no known study has evaluated such a program from the perspective of peer educators involved in delivering the message. The purpose of this study was to explore peer educators’ perspective about their role in delivering peer-led falls prevention education for community-dwelling older adults. Methods: A two-stage qualitative inductive constant comparative design was used.In stage one (core component) focus group interviews involving a total of eleven participants were conducted. During stage two (supplementary component) semi-structured interviews with two participants were conducted. Data were analysed thematically by two researchers independently. Key themes were identified and findings were displayed in a conceptual framework. Results: Peer educators were motivated to deliver educational presentations and importantly, to reach an optimal peer connection with their audience. Key themes identified included both personal and organisational factors that impact on educators’ capacity to facilitate their peers’ engagement with the message. Personal factors that facilitated message delivery and engagement included peer-to-peer connection and perceived credibility, while barriers included a reluctance to accept the message that they were at risk of falling by some members in the audience. Organisational factors, including ongoing training for peer educators and formative feedback following presentations, were perceived as essential because they affect successful message delivery. Conclusions: Peer educators have the potential to effectively deliver falls prevention education to older adults and influence acceptance of the message as they possess the peer-to-peer connection that facilitates optimal engagement. There is a need to consider incorporating learnings from this research into a formal large scale evaluation of the effectiveness of the peer education approach in reducing falls in older adults

Don't lose sight of the importance of the individual in effective falls prevention interventions

Falls remain a major public health problem, despite strong growth in the research evidence of effective single and multifactorial interventions, particularly in the community setting. A number of aspects of falls prevention require individual tailoring, despite limitations being reported regarding some of these, including questions being raised regarding the role of falls risk screening and falls risk assessment. Being able to personalise an individual's specific risk and risk factors, increase their understanding of what interventions are likely to be effective, and exploring options of choice and preference, can all impact upon whether or not an individual undertakes and sustains participation in one or more recommendations, which will ultimately influence outcomes. On all of these fronts, the individual patient receiving appropriate and targeted interventions that are meaningful, feasible and that they are motivated to implement, remains central to effective translation of falls prevention research evidence into practice

The leading digit distribution of the worldwide Illicit Financial Flows

Benford's law states that in data sets from different phenomena leading digits tend to be distributed logarithmically such that the numbers beginning with smaller digits occur more often than those with larger ones. Particularly, the law is known to hold for different types of financial data. The Illicit Financial Flows (IFFs) exiting the developing countries are frequently discussed as hidden resources which could have been otherwise properly utilized for their development. We investigate here the distribution of the leading digits in the recent data on estimates of IFFs to look for the existence of a pattern as predicted by Benford's law and establish that the frequency of occurrence of the leading digits in these estimates does closely follow the law.Comment: 13 pages, 10 figures, 6 tables, additional data analyi

Evaluation of the effect of patient education on rates of falls in older hospital patients: Description of a randomised controlled trial

Background. Accidental falls by older patients in hospital are one of the most commonly reported adverse events. Falls after discharge are also common. These falls have enormous physical, psychological and social consequences for older patients, including serious physical injury and reduced quality of life, and are also a source of substantial cost to health systems worldwide. There have been a limited number of randomised controlled trials, mainly using multifactorial interventions, aiming to prevent older people falling whilst inpatients. Trials to date have produced conflicting results and recent meta-analyses highlight that there is still insufficient evidence to clearly identify which interventions may reduce the rate of falls, and falls related injuries, in this population. Methods and design. A prospective randomised controlled trial (n = 1206) is being conducted at two hospitals in Australia. Patients are eligible to be included in the trial if they are over 60 years of age and they, or their family or guardian, give written consent. Participants are randomised into three groups. The control group continues to receive usual care. Both intervention groups receive a specifically designed patient education intervention on minimising falls in addition to usual care. The education is delivered by Digital Video Disc (DVD) and written workbook and aims to promote falls prevention activities by participants. One of the intervention groups also receives follow up education training visits by a health professional. Blinded assessors conduct baseline and discharge assessments and follow up participants for 6 months after discharge. The primary outcome measure is falls by participants in hospital. Secondary outcome measures include falls at home after discharge, knowledge of falls prevention strategies and motivation to engage in falls prevention activities after discharge. All analyses will be based on intention to treat principle. Discussion. This trial will examine the effect of a single intervention (specifically designed patient education) on rates of falls in older patients in hospital and after discharge. The results will provide robust recommendations for clinicians and researchers about the role of patient education in this population. The study has the potential to identify a new intervention that may reduce rates of falls in older hospital patients and could be readily duplicated and applied in a wide range of clinical settings. Trial Registration. ACTRN12608000015347

Foot pain and foot health in an educated population of adults: results from the Glasgow Caledonian University Alumni Foot Health Survey

Abstract Background Foot pain is common amongst the general population and impacts negatively on physical function and quality of life. Associations between personal health characteristics, lifestyle/behaviour factors and foot pain have been studied; however, the role of wider determinants of health on foot pain have received relatively little attention. Objectives of this study are i) to describe foot pain and foot health characteristics in an educated population of adults; ii) to explore associations between moderate-to-severe foot pain and a variety of factors including gender, age, medical conditions/co-morbidity/multi-morbidity, key indicators of general health, foot pathologies, and social determinants of health; and iii) to evaluate associations between moderate-to-severe foot pain and foot function, foot health and health-related quality-of-life. Methods Between February and March 2018, Glasgow Caledonian University Alumni with a working email address were invited to participate in the cross-sectional electronic survey (anonymously) by email via the Glasgow Caledonian University Alumni Office. The survey was constructed using the REDCap secure web online survey application and sought information on presence/absence of moderate-to-severe foot pain, patient characteristics (age, body mass index, socioeconomic status, occupation class, comorbidities, and foot pathologies). Prevalence data were expressed as absolute frequencies and percentages. Multivariate logistic and linear regressions were undertaken to identify associations 1) between independent variables and moderate-to-severe foot pain, and 2) between moderate-to-severe foot pain and foot function, foot health and health-related quality of life. Results Of 50,228 invitations distributed, there were 7707 unique views and 593 valid completions (median age [inter-quartile range] 42 [31–52], 67.3% female) of the survey (7.7% response rate). The sample was comprised predominantly of white Scottish/British (89.4%) working age adults (95%), the majority of whom were overweight or obese (57.9%), and in either full-time or part-time employment (82.5%) as professionals (72.5%). Over two-thirds (68.5%) of the sample were classified in the highest 6 deciles (most affluent) of social deprivation. Moderate-to-severe foot pain affected 236/593 respondents (39.8%). High body mass index, presence of bunions, back pain, rheumatoid arthritis, hip pain and lower occupation class were included in the final multivariate model and all were significantly and independently associated with moderate-to-severe foot pain (p < 0.05), except for rheumatoid arthritis (p = 0.057). Moderate-to-severe foot pain was significantly and independently associated lower foot function, foot health and health-related quality of life scores following adjustment for age, gender and body mass index (p < 0.05). Conclusions Moderate-to-severe foot pain was highly prevalent in a university-educated population and was independently associated with female gender, high body mass index, bunions, back pain, hip pain and lower occupational class. Presence of moderate-to-severe foot pain was associated with worse scores for foot function, foot health and health-related quality-of-life. Education attainment does not appear to be protective against moderate-to-severe foot pain

Can peer education improve beliefs, knowledge, motivation and intention to engage in falls prevention amongst community-dwelling older adults?

The aim of the study was to evaluate the effectiveness of delivering a contemporary peer-led falls prevention education presentation on community-dwelling older adults’ beliefs, knowledge, motivation and intention to engage in falls prevention strategies. A two-group quasi-experimental pre-test–post-test study using a convenience sample was conducted. A new falls prevention training package for peer educators was developed, drawing on contemporary adult learning and behaviour change principles. A 1-h presentation was delivered to community-dwelling older adults by peer educators trained with the new package (intervention group). Control group participants received an existing, 1-h falls prevention presentation by trained peer educators who had not received the adult learning and behaviour change training. Participants in both groups completed a purpose-developed questionnaire at pre-presentation, immediately post-presentation and at one-month follow-up. Participants’ levels of beliefs, knowledge, motivation and intention were compared across these three points of time. Generalised estimating equations models examined associations in the quantitative data, while deductive content analysis was used for qualitative data. Participants (control n = 99; intervention n = 133) in both groups showed significantly increased levels of beliefs and knowledge about falls prevention, and intention to engage in falls prevention strategies over time compared to baseline. The intervention group was significantly more likely to report a clear action plan to undertake falls prevention strategies compared to the control group. Peer-led falls prevention education is an effective approach for raising older adults’ beliefs, knowledge and intention to engage in falls prevention strategies

Tailored education for older patients to facilitate engagement in falls prevention strategies after hospital discharge—A pilot randomized controlled trial

Background The aims of the study were to evaluate the effect of providing tailored falls prevention education in hospital on: i) engagement in targeted falls prevention behaviors in the month after discharge: ii) patients’ self-perceived risk and knowledge about falls and falls prevention strategies after receiving the education. Methods A pilot randomized controlled trial (n = 50): baseline and outcome assessments conducted by blinded researchers. Participants: hospital inpatients 60 years or older, discharged to the community. Participants were randomized into two groups. The intervention was a tailored education package consisting of multimedia falls prevention information with trained health professional follow-up, delivered in addition to usual care. Outcome measures were engagement in falls prevention behaviors in the month after discharge measured at one month after discharge with a structured survey, and participants’ knowledge, confidence and motivation levels before and after receiving the education. The feasibility of providing the intervention was examined and falls outcomes (falls, fall-related injuries) were also collected. Results Forty-eight patients (98%) provided follow-up data. The complete package was provided to 21 (84%) intervention group participants. Participants in the intervention group were significantly more likely to plan how to safely restart functional activities [Adjusted odds ratio 3.80, 95% CI (1.07, 13.52), p = 0.04] and more likely to complete other targeted behaviors such as completing their own home exercise program [Adjusted odds ratio 2.76, 95% CI (0.72, 10.50), p = 0.14] than the control group. The intervention group was significantly more knowledgeable, confident and motivated to engage in falls prevention strategies after receiving the education than the control group. There were 23 falls (n = 5 intervention; n = 18 control) and falls rates were 5.4/1000 patient days (intervention); 18.7/1000 patient days (control). Conclusion This tailored education was received positively by older people, resulted in increased engagement in falls prevention strategies after discharge and is feasible to deliver to older hospital patients. Trial registration The study was registered with the Australian New Zealand Clinical Trials Registry; ACTRN12611000963921 on 8th November 2011

What Can We Conclude from Death Registration? Improved Methods for Evaluating Completeness

Julie Rajaratnam and colleagues evaluate the performance of a suite of demographic methods that estimate the fraction of deaths registered and counted by civil registration systems, and identify three variants that generally perform the best