The first international workshop on the role and impact of mathematics in medicine: a collective account

The First International Workshop on The Role and Impact of Mathematics in Medicine (RIMM) convened in Paris in June 2010. A broad range of researchers discussed the difficulties, challenges and opportunities faced by those wishing to see mathematical methods contribute to improved medical outcomes. Finding mechanisms for inter- disciplinary meetings, developing a common language, staying focused on the medical problem at hand, deriving realistic mathematical solutions, obtaining

A pharmacist-led information technology intervention for medication errors (PINCER): a multicentre, cluster randomised, controlled trial and cost-effectiveness analysis

Background: Medication errors are common in primary care and are associated with considerable risk of patient harm. We tested whether a pharmacist-led, information technology-based intervention was more effective than simple feedback in reducing the number of patients at risk of measures related to hazardous prescribing and inadequate blood-test monitoring of medicines 6 months after the intervention. Methods: In this pragmatic, cluster randomised trial general practices in the UK were stratified by research site and list size, and randomly assigned by a web-based randomisation service in block sizes of two or four to one of two groups. The practices were allocated to either computer-generated simple feedback for at-risk patients (control) or a pharmacist-led information technology intervention (PINCER), composed of feedback, educational outreach, and dedicated support. The allocation was masked to general practices, patients, pharmacists, researchers, and statisticians. Primary outcomes were the proportions of patients at 6 months after the intervention who had had any of three clinically important errors: non-selective non-steroidal anti-inflammatory drugs (NSAIDs) prescribed to those with a history of peptic ulcer without co-prescription of a proton-pump inhibitor; β blockers prescribed to those with a history of asthma; long-term prescription of angiotensin converting enzyme (ACE) inhibitor or loop diuretics to those 75 years or older without assessment of urea and electrolytes in the preceding 15 months. The cost per error avoided was estimated by incremental cost-eff ectiveness analysis. This study is registered with Controlled-Trials.com, number ISRCTN21785299. Findings: 72 general practices with a combined list size of 480 942 patients were randomised. At 6 months’ follow-up, patients in the PINCER group were significantly less likely to have been prescribed a non-selective NSAID if they had a history of peptic ulcer without gastroprotection (OR 0∙58, 95% CI 0∙38–0∙89); a β blocker if they had asthma (0∙73, 0∙58–0∙91); or an ACE inhibitor or loop diuretic without appropriate monitoring (0∙51, 0∙34–0∙78). PINCER has a 95% probability of being cost eff ective if the decision-maker’s ceiling willingness to pay reaches £75 per error avoided at 6 months. Interpretation: The PINCER intervention is an effective method for reducing a range of medication errors in general practices with computerised clinical records. Funding: Patient Safety Research Portfolio, Department of Health, England.

Limit operators, collective compactness, and the spectral theory of infinite matrices

In the first half of this memoir we explore the interrelationships between the abstract theory of limit operators (see e.g. the recent monographs of Rabinovich, Roch and Silbermann (2004) and Lindner (2006)) and the concepts and results of the generalised collectively compact operator theory introduced by Chandler-Wilde and Zhang (2002). We build up to results obtained by applying this generalised collectively compact operator theory to the set of limit operators of an operator (its operator spectrum). In the second half of this memoir we study bounded linear operators on the generalised sequence space , where and is some complex Banach space. We make what seems to be a more complete study than hitherto of the connections between Fredholmness, invertibility, invertibility at infinity, and invertibility or injectivity of the set of limit operators, with some emphasis on the case when the operator is a locally compact perturbation of the identity. Especially, we obtain stronger results than previously known for the subtle limiting cases of and . Our tools in this study are the results from the first half of the memoir and an exploitation of the partial duality between and and its implications for bounded linear operators which are also continuous with respect to the weaker topology (the strict topology) introduced in the first half of the memoir. Results in this second half of the memoir include a new proof that injectivity of all limit operators (the classic Favard condition) implies invertibility for a general class of almost periodic operators, and characterisations of invertibility at infinity and Fredholmness for operators in the so-called Wiener algebra. In two final chapters our results are illustrated by and applied to concrete examples. Firstly, we study the spectra and essential spectra of discrete Schrödinger operators (both self-adjoint and non-self-adjoint), including operators with almost periodic and random potentials. In the final chapter we apply our results to integral operators on .

Adaptation-induced collective dynamics of a single-cell protozoan

We investigate the behavior of a single-cell protozoan in a narrow tubular ring. This environment forces them to swim under a one-dimensional periodic boundary condition. Above a critical density, single-cell protozoa aggregate spontaneously without external stimulation. The high-density zone of swimming cells exhibits a characteristic collective dynamics including translation and boundary fluctuation. We analyzed the velocity distribution and turn rate of swimming cells and found that the regulation of the turing rate leads to a stable aggregation and that acceleration of velocity triggers instability of aggregation. These two opposing effects may help to explain the spontaneous dynamics of collective behavior. We also propose a stochastic model for the mechanism underlying the collective behavior of swimming cells.

Can valuation factors be prescribed? The case of collective enfranchisement and leasehold extension of flats in England and Wales

Recent concerns over the valuation process in collective leasehold enfranchisement and lease extension cases have culminated in new legislation. To underpin this, the Government (Department of Environment Transport and the Regions (DETR)) commissioned new research, which examined whether the valuation of the freehold in such cases could be simplified through the prescription of either yield or marriage value/relativity. This paper, which is based on that research, examines whether it is possible or desirable to prescribe such factors in the valuation process. Market, settlement and Local Valuation Tribunal (LVT) decisions are analysed, and the basis of 'relativity charts' used in practice is critically examined. Ultimately the imperfect nature of the market in freehold investment sales and leasehold vacant possession sales means that recommendations must rest on an analysis of LVT data. New relativity curves are developed from this data and used in conjunction with an alternative approach to valuation yields (based on other investment assets). However, the paper concludes that although the prescription of yields and relativity is possible, it is not fully defensible because of problems in determining risk premia; that the evidential basis for relativity consists of LVT decisions; and that a formula approach would tend to 'lead' the market as a whole.

Description and process evaluation of pharmacists’ interventions in a pharmacist-led information technology-enabled multicentre cluster randomised controlled trial for reducing medication errors in general practice (PINCER trial)

Objective To undertake a process evaluation of pharmacists' recommendations arising in the context of a complex IT-enabled pharmacist-delivered randomised controlled trial (PINCER trial) to reduce the risk of hazardous medicines management in general practices. Methods PINCER pharmacists manually recorded patients’ demographics, details of interventions recommended, actions undertaken by practice staff and time taken to manage individual cases of hazardous medicines management. Data were coded and double entered into SPSS v15, and then summarised using percentages for categorical data (with 95% CI) and, as appropriate, means (SD) or medians (IQR) for continuous data. Key findings Pharmacists spent a median of 20 minutes (IQR 10, 30) reviewing medical records, recommending interventions and completing actions in each case of hazardous medicines management. Pharmacists judged 72% (95%CI 70, 74) (1463/2026) of cases of hazardous medicines management to be clinically relevant. Pharmacists recommended 2105 interventions in 74% (95%CI 73, 76) (1516/2038) of cases and 1685 actions were taken in 61% (95%CI 59, 63) (1246/2038) of cases; 66% (95%CI 64, 68) (1383/2105) of interventions recommended by pharmacists were completed and 5% (95%CI 4, 6) (104/2105) of recommendations were accepted by general practitioners (GPs), but not completed at the end of the pharmacists’ placement; the remaining recommendations were rejected or considered not relevant by GPs. Conclusions The outcome measures were used to target pharmacist activity in general practice towards patients at risk from hazardous medicines management. Recommendations from trained PINCER pharmacists were found to be broadly acceptable to GPs and led to ameliorative action in the majority of cases. It seems likely that the approach used by the PINCER pharmacists could be employed by other practice pharmacists following appropriate training.

Whole-brain functional connectivity during emotional word classification in medication-free Major Depressive Disorder: abnormal salience circuitry and relations to positive emotionality

Major Depressive Disorder (MDD) has been associated with biased processing and abnormal regulation of negative and positive information, which may result from compromised coordinated activity of prefrontal and subcortical brain regions involved in evaluating emotional information. We tested whether patients with MDD show distributed changes in functional connectivity with a set of independently derived brain networks that have shown high correspondence with different task demands, including stimulus salience and emotional processing. We further explored if connectivity during emotional word processing related to the tendency to engage in positive or negative emotional states. In this study, 25 medication-free MDD patients without current or past comorbidity and matched controls (n=25) performed an emotional word-evaluation task during functional MRI. Using a dual regression approach, individual spatial connectivity maps representing each subject’s connectivity with each standard network were used to evaluate between-group differences and effects of positive and negative emotionality (extraversion and neuroticism, respectively, as measured with the NEO-FFI). Results showed decreased functional connectivity of the medial prefrontal cortex, ventrolateral prefrontal cortex, and ventral striatum with the fronto-opercular salience network in MDD patients compared to controls. In patients, abnormal connectivity was related to extraversion, but not neuroticism. These results confirm the hypothesis of a relative (para)limbic-cortical decoupling that may explain dysregulated affect in MDD. As connectivity of these regions with the salience network was related to extraversion, but not to general depression severity or negative emotionality, dysfunction of this network may be responsible for the failure to sustain engagement in rewarding behavior.

On collective intentions: collective action in economics and philosophy

Philosophers and economists write about collective action from distinct but related points of view. This paper aims to bridge these perspectives. Economists have been concerned with rationality in a strategic context. There, problems posed by “coordination games” seem to point to a form of rational action, “team thinking,” which is not individualistic. Philosophers’ analyses of collective intention, however, sometimes reduce collective action to a set of individually instrumental actions. They do not, therefore, capture the first person plural perspective characteristic of team thinking. Other analyses, problematically, depict intentions ranging over others’ actions. I offer an analysis of collective intention which avoids these problems. A collective intention aims only at causing an individual action, but its propositional content stipulates its mirroring in other minds.

Care homes’ use of medicines study: prevalence, causes and potential harm of medication errors in care homes for older people

Introduction: Care home residents are at particular risk from medication errors, and our objective was to determine the prevalence and potential harm of prescribing, monitoring, dispensing and administration errors in UK care homes, and to identify their causes. Methods: A prospective study of a random sample of residents within a purposive sample of homes in three areas. Errors were identified by patient interview, note review, observation of practice and examination of dispensed items. Causes were understood by observation and from theoretically framed interviews with home staff, doctors and pharmacists. Potential harm from errors was assessed by expert judgement. Results: The 256 residents recruited in 55 homes were taking a mean of 8.0 medicines. One hundred and seventy-eight (69.5%) of residents had one or more errors. The mean number per resident was 1.9 errors. The mean potential harm from prescribing, monitoring, administration and dispensing errors was 2.6, 3.7, 2.1 and 2.0 (0 = no harm, 10 = death), respectively. Contributing factors from the 89 interviews included doctors who were not accessible, did not know the residents and lacked information in homes when prescribing; home staff’s high workload, lack of medicines training and drug round interruptions; lack of team work among home, practice and pharmacy; inefficient ordering systems; inaccurate medicine records and prevalence of verbal communication; and difficult to fill (and check) medication administration systems. Conclusions: That two thirds of residents were exposed to one or more medication errors is of concern. The will to improve exists, but there is a lack of overall responsibility. Action is required from all concerned.

Drug holidays from ADHD medication: international experience over the past four decades

Objective: ADHD is managed by stimulants that are effective but can cause growth retardation. Prescribers should ideally monitor children and trial a “drug holiday” to enable catch-up growth. Our aim was to map the experience of drug holidays from ADHD medication in children and adolescents. Method: A comprehensive search of the literature identified 22 studies published during the period 1972 to 2013. Results: Drug holidays are prevalent in 25% to 70% of families and are more likely to be exercised during school holidays. They test whether medication is still needed and are also considered for managing medication side effects and drug tolerance. The impact of drug holidays was reported in terms of side effects and ADHD symptoms. There was evidence of a positive impact on child growth with longer breaks from medication, and shorter breaks could reduce insomnia and improve appetite. Conclusion: Drug holidays from ADHD medication could be a useful tool with multiple purposes: assessment, management, prevention, and negotiation.

Memory for medication side effects in younger and older adults: the role of subjective and objective importance

Older adults often experience memory impairments, but can sometimes use selective processing and schematic support to remember important information. The current experiments investigate to what degree younger and healthy older adults remember medication side effects that were subjectively or objectively important to remember. Participants studied a list of common side effects, and rated how negative these effects were if they were to experience them, and were then given a free recall test. In Experiment 1, the severity of the side effects ranged from mild (e.g., itching) to severe (e.g., stroke), and in Experiment 2, certain side effects were indicated as critical to remember (i.e., “contact your doctor if you experience this”). There were no age differences in terms of free recall of the side effects, and older adults remembered more severe side effects relative to mild effects. However, older adults were less likely to recognize critical side effects on a later recognition test, relative to younger adults. The findings suggest that older adults can selectively remember medication side effects, but have difficulty identifying familiar but potentially critical side effects, and this has implications for monitoring medication use in older age.