Drawing and Mathematics

In this paper we consider various ways that drawing occurs in mathematics. We describe, and give examples of, drawing-based mathematical proof: in this context drawing is a language for communicating mathematical reasoning. We then describe our artistic collaboration, where drawing functions both as a language for interdisciplinary communication, essential to the formative process, and as the artwork itself

Protocol for the economic evaluation of metacognitive therapy for cardiac rehabilitation participants with symptoms of anxiety and/or depression

INTRODUCTION: Cardiac rehabilitation (CR) is offered to reduce the risk of further cardiac events and to improve patients' health and quality of life following a cardiac event. Psychological care is a common component of CR as symptoms of depression and/or anxiety are more prevalent in this population, however evidence for the cost-effectiveness of current interventions is limited. Metacognitive therapy (MCT), is a recent treatment development that is effective in treating anxiety and depression in mental health settings and is being evaluated in CR patients. This protocol describes the planned approach to the economic evaluation of MCT for CR patients. METHODS AND ANALYSIS: The economic evaluation work will consist of a within-trial analysis and an economic model. The PATHWAY Group MCT study has been prospectively designed to collect comprehensive self-reported resource use and health outcome data, including the EQ-5D, within a randomised controlled trial study design (UK Clinical Trials Gateway). A within-trial economic evaluation and economic model will compare the cost-effectiveness of MCT plus usual care (UC) to UC, from a health and social care perspective in the UK. The within-trial analysis will use intention-to-treat and estimate total costs and quality-adjusted life-years (QALYs) for the trial follow-up. Single imputation will be used to impute missing baseline variables. Multiple imputation will be used to impute values missing at follow-up. Items of resource use will be multiplied by published national healthcare costs. Regression analysis will be used to estimate net costs and net QALYs and these estimates will be bootstrapped to generate 10 000 net pairs of costs and QALYs to inform the probability of cost-effectiveness. A decision analytical economic model will be developed to synthesise trial data with the published literature over a longer time frame. Sensitivity analysis will explore uncertainty. Guidance of the methods for economic models will be followed and dissemination will adhere to reporting guidelines. ETHICS AND DISSEMINATION: The economic evaluation includes a within-trial analysis. The trial which included the collection of this data was reviewed and approved by Ethics. Ethics approval was obtained by the Preston Research Ethics Committee (project ID 156862). The modelling analysis is not applicable for Ethics as it will use data from the trial (secondary analysis) and the published literature. Results of the main trial and economic evaluation will be published in the peer-reviewed National Institute for Health Research (NIHR) journals library (Programme Grants for Applied Research), submitted to a peer-reviewed journal and presented at appropriate conferences. TRIAL REGISTRATION NUMBER: ISRCTN74643496; Pre-results

Genome-Wide Copy Number Variation Analysis in Extended Families and Unrelated Individuals Characterized for Musical Aptitude and Creativity in Music

Peer reviewe

Cognitive behavioural therapy for clozapine-resistant schizophrenia: the FOCUS RCT

Background: Clozapine (clozaril, Mylan Products Ltd) is a first-choice treatment for people with schizophrenia who have a poor response to standard antipsychotic medication. However, a significant number of patients who trial clozapine have an inadequate response and experience persistent symptoms, called clozapine-resistant schizophrenia (CRS). There is little evidence regarding the clinical effectiveness of pharmacological or psychological interventions for this population. Objectives: To evaluate the clinical effectiveness and cost-effectiveness of cognitive–behavioural therapy (CBT) for people with CRS and to identify factors predicting outcome. Design: The Focusing on Clozapine Unresponsive Symptoms (FOCUS) trial was a parallel-group, randomised, outcome-blinded evaluation trial. Randomisation was undertaken using permuted blocks of random size via a web-based platform. Data were analysed on an intention-to-treat (ITT) basis, using random-effects regression adjusted for site, age, sex and baseline symptoms. Cost-effectiveness analyses were carried out to determine whether or not CBT was associated with a greater number of quality-adjusted life-years (QALYs) and higher costs than treatment as usual (TAU). Setting: Secondary care mental health services in five cities in the UK. Participants: People with CRS aged up to 16 years, with an International Classification of Diseases, Tenth Revision (ICD-10) schizophrenia spectrum diagnoses and who are experiencing psychotic symptoms. Interventions: Individual CBT included up to 30 hours of therapy delivered over 9 months. The comparator was TAU, which included care co-ordination from secondary care mental health services. Main outcome measures: The primary outcome was the Positive and Negative Syndrome Scale (PANSS) total score at 21 months and the primary secondary outcome was PANSS total score at the end of treatment (9 months post randomisation). The health benefit measure for the economic evaluation was the QALY, estimated from the EuroQol-5 Dimensions, five-level version (EQ-5D-5L), health status measure. Service use was measured to estimate costs. Results: Participants were allocated to CBT (n = 242) or TAU (n = 245). There was no significant difference between groups on the prespecified primary outcome [PANSS total score at 21 months was 0.89 points lower in the CBT arm than in the TAU arm, 95% confidence interval (CI) –3.32 to 1.55 points; p = 0.475], although PANSS total score at the end of treatment (9 months) was significantly lower in the CBT arm (–2.40 points, 95% CI –4.79 to –0.02 points; p = 0.049). CBT was associated with a net cost of £5378 (95% CI –£13,010 to £23,766) and a net QALY gain of 0.052 (95% CI 0.003 to 0.103 QALYs) compared with TAU. The cost-effectiveness acceptability analysis indicated a low likelihood that CBT was cost-effective, in the primary and sensitivity analyses (probability < 50%). In the CBT arm, 107 participants reported at least one adverse event (AE), whereas 104 participants in the TAU arm reported at least one AE (odds ratio 1.09, 95% CI 0.81 to 1.46; p = 0.58). Conclusions: Cognitive–behavioural therapy for CRS was not superior to TAU on the primary outcome of total PANSS symptoms at 21 months, but was superior on total PANSS symptoms at 9 months (end of treatment). CBT was not found to be cost-effective in comparison with TAU. There was no suggestion that the addition of CBT to TAU caused adverse effects. Future work could investigate whether or not specific therapeutic techniques of CBT have value for some CRS individuals, how to identify those who may benefit and how to ensure that effects on symptoms can be sustained. Trial registration: Current Controlled Trials ISRCTN99672552

Identification and Functional Characterization of <i>G6PC2</i> Coding Variants Influencing Glycemic Traits Define an Effector Transcript at the <i>G6PC2-ABCB11</i> Locus

Genome wide association studies (GWAS) for fasting glucose (FG) and insulin (FI) have identified common variant signals which explain 4.8% and 1.2% of trait variance, respectively. It is hypothesized that low-frequency and rare variants could contribute substantially to unexplained genetic variance. To test this, we analyzed exome-array data from up to 33,231 non-diabetic individuals of European ancestry. We found exome-wide significant (P<5×10-7) evidence for two loci not previously highlighted by common variant GWAS: GLP1R (p.Ala316Thr, minor allele frequency (MAF)=1.5%) influencing FG levels, and URB2 (p.Glu594Val, MAF = 0.1%) influencing FI levels. Coding variant associations can highlight potential effector genes at (non-coding) GWAS signals. At the G6PC2/ABCB11 locus, we identified multiple coding variants in G6PC2 (p.Val219Leu, p.His177Tyr, and p.Tyr207Ser) influencing FG levels, conditionally independent of each other and the non-coding GWAS signal. In vitro assays demonstrate that these associated coding alleles result in reduced protein abundance via proteasomal degradation, establishing G6PC2 as an effector gene at this locus. Reconciliation of single-variant associations and functional effects was only possible when haplotype phase was considered. In contrast to earlier reports suggesting that, paradoxically, glucose-raising alleles at this locus are protective against type 2 diabetes (T2D), the p.Val219Leu G6PC2 variant displayed a modest but directionally consistent association with T2D risk. Coding variant associations for glycemic traits in GWAS signals highlight PCSK1, RREB1, and ZHX3 as likely effector transcripts. These coding variant association signals do not have a major impact on the trait variance explained, but they do provide valuable biological insights

Effects of antiplatelet therapy on stroke risk by brain imaging features of intracerebral haemorrhage and cerebral small vessel diseases: subgroup analyses of the RESTART randomised, open-label trial

Background Findings from the RESTART trial suggest that starting antiplatelet therapy might reduce the risk of recurrent symptomatic intracerebral haemorrhage compared with avoiding antiplatelet therapy. Brain imaging features of intracerebral haemorrhage and cerebral small vessel diseases (such as cerebral microbleeds) are associated with greater risks of recurrent intracerebral haemorrhage. We did subgroup analyses of the RESTART trial to explore whether these brain imaging features modify the effects of antiplatelet therapy

Cognitive behavioural therapy for clozapine-resistant schizophrenia: the FOCUS RCT

Background: Clozapine (clozaril, Mylan Products Ltd) is a first-choice treatment for people withschizophrenia who have a poor response to standard antipsychotic medication. However, a significant number of patients who trial clozapine have an inadequate response and experience persistent symptoms, called clozapine-resistant schizophrenia (CRS). There is little evidence regarding the clinical effectiveness of pharmacological or psychological interventions for this population.Objectives: To evaluate the clinical effectiveness and cost-effectiveness of cognitive–behavioural therapy (CBT) for people with CRS and to identify factors predicting outcome.Design: The Focusing on Clozapine Unresponsive Symptoms (FOCUS) trial was a parallel-group, randomised, outcome-blinded evaluation trial. Randomisation was undertaken using permuted blocks ofrandom size via a web-based platform. Data were analysed on an intention-to-treat (ITT) basis, using random-effects regression adjusted for site, age, sex and baseline symptoms. Cost-effectiveness analyses were carried out to determine whether or not CBT was associated with a greater number of quality-adjusted life-years (QALYs) and higher costs than treatment as usual (TAU).Setting: Secondary care mental health services in five cities in the UK.Participants: People with CRS aged up to 16 years, with an International Classification of Diseases, Tenth Revision (ICD-10) schizophrenia spectrum diagnoses and who are experiencing psychotic symptoms. Interventions: Individual CBT included up to 30 hours of therapy delivered over 9 months. The comparator was TAU, which included care co-ordination from secondary care mental health services.Main outcome measures: The primary outcome was the Positive and Negative Syndrome Scale (PANSS) total score at 21 months and the primary secondary outcome was PANSS total score at the end of treatment (9 months post randomisation). The health benefit measure for the economic evaluation was the QALY, estimated from the EuroQol-5 Dimensions, five-level version (EQ-5D-5L), health status measure. Service use was measured to estimate costs.Results: Participants were allocated to CBT (n = 242) or TAU (n = 245). There was no significant difference between groups on the prespecified primary outcome [PANSS total score at 21 months was 0.89 points lower in the CBT arm than in the TAU arm, 95% confidence interval (CI) –3.32 to 1.55 points; p = 0.475], although PANSS total score at the end of treatment (9 months) was significantly lower in the CBT arm (–2.40 points, 95% CI –4.79 to –0.02 points; p = 0.049). CBT was associated with a net cost of £5378(95% CI –£13,010 to £23,766) and a net QALY gain of 0.052 (95% CI 0.003 to 0.103 QALYs) compared with TAU. The cost-effectiveness acceptability analysis indicated a low likelihood that CBT was cost-effective, in the primary and sensitivity analyses (probability < 50%). In the CBT arm, 107 participants reported at least one adverse event (AE), whereas 104 participants in the TAU arm reported at least one AE (odds ratio 1.09, 95% CI 0.81 to 1.46; p = 0.58).Conclusions: Cognitive–behavioural therapy for CRS was not superior to TAU on the primary outcome of total PANSS symptoms at 21 months, but was superior on total PANSS symptoms at 9 months (end of treatment). CBT was not found to be cost-effective in comparison with TAU. There was no suggestion that the addition of CBT to TAU caused adverse effects. Future work could investigate whether or not specific therapeutic techniques of CBT have value for some CRS individuals, how to identify those who may benefitand how to ensure that effects on symptoms can be sustained

Identification and functional characterization of G6PC2 coding variants influencing glycemic traits define an effector transcript at the G6PC2-ABCB11 locus.

Genome wide association studies (GWAS) for fasting glucose (FG) and insulin (FI) have identified common variant signals which explain 4.8% and 1.2% of trait variance, respectively. It is hypothesized that low-frequency and rare variants could contribute substantially to unexplained genetic variance. To test this, we analyzed exome-array data from up to 33,231 non-diabetic individuals of European ancestry. We found exome-wide significant (P<5×10-7) evidence for two loci not previously highlighted by common variant GWAS: GLP1R (p.Ala316Thr, minor allele frequency (MAF)=1.5%) influencing FG levels, and URB2 (p.Glu594Val, MAF = 0.1%) influencing FI levels. Coding variant associations can highlight potential effector genes at (non-coding) GWAS signals. At the G6PC2/ABCB11 locus, we identified multiple coding variants in G6PC2 (p.Val219Leu, p.His177Tyr, and p.Tyr207Ser) influencing FG levels, conditionally independent of each other and the non-coding GWAS signal. In vitro assays demonstrate that these associated coding alleles result in reduced protein abundance via proteasomal degradation, establishing G6PC2 as an effector gene at this locus. Reconciliation of single-variant associations and functional effects was only possible when haplotype phase was considered. In contrast to earlier reports suggesting that, paradoxically, glucose-raising alleles at this locus are protective against type 2 diabetes (T2D), the p.Val219Leu G6PC2 variant displayed a modest but directionally consistent association with T2D risk. Coding variant associations for glycemic traits in GWAS signals highlight PCSK1, RREB1, and ZHX3 as likely effector transcripts. These coding variant association signals do not have a major impact on the trait variance explained, but they do provide valuable biological insights

Genome-wide DNA methylation map of human neutrophils reveals widespread inter-individual epigenetic variation

The extent of variation in DNA methylation patterns in healthy individuals is not yet well documented. Identification of inter-individual epigenetic variation is important for understanding phenotypic variation and disease susceptibility. Using neutrophils from a cohort of healthy individuals, we generated base-resolution DNA methylation maps to document inter-individual epigenetic variation. We identified 12851 autosomal inter-individual variably methylated fragments (iVMFs). Gene promoters were the least variable, whereas gene body and upstream regions showed higher variation in DNA methylation. The iVMFs were relatively enriched in repetitive elements compared to non-iVMFs, and were associated with genome regulation and chromatin function elements. Further, variably methylated genes were disproportionately associated with regulation of transcription, responsive function and signal transduction pathways. Transcriptome analysis indicates that iVMF methylation at differentially expressed exons has a positive correlation and local effect on the inclusion of that exon in the mRNA transcript