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The choice of an adequate sample size for a Cox regression analysis is generally based on the rule of thumb derived from simulation studies of a minimum of 10 events per variable (EPV). One simulation study suggested scenarios in which the 10 EPV rule can be relaxed. The effect of a range of binary predictors with varying prevalence, reflecting clinical practice, has not yet been fully investigated. We conducted an extended resampling study using a large general-practice data set, comprising over 2 million anonymized patient records, to examine the EPV requirements for prediction models with low-prevalence binary predictors developed using Cox regression. The performance of the models was then evaluated using an independent external validation data set. We investigated both fully specified models and models derived using variable selection. Our results indicated that an EPV rule of thumb should be data driven and that EPV ≥ 20 ​ generally eliminates bias in regression coefficients when many low-prevalence predictors are included in a Cox model. Higher EPV is needed when low-prevalence predictors are present in a model to eliminate bias in regression coefficients and improve predictive accuracy.

Prediction models in credit scoring usually involve the use of data sets with highly imbalanced distributions of the event of interest (default). Logistic regression, which is widely used to estimate the probability of default, PD, often suffers from the problem of separation when the event of interest is rare and consequently poor predictive performance of the minority class in small samples. A common solution is to discard majority class examples, to duplicate minority class examples or to use a combination of both to balance the data. These methods may overfit data. It is unclear how penalized regression models such as Firth’s estimator, which reduces bias and mean-square error relative to classical logistic regression, performs in modelling PD. We review some methods for class imbalanced data and compare them in a simulation study using the Taiwan credit card data. We emphasize the effect of events per variable for developing an accurate model—an often neglected concept in PD-modelling. The data balancing techniques that are considered are the random oversampling examples and synthetic minority oversampling technique methods. The results indicate that the synthetic minority oversampling technique improved predictive accuracy of PD regardless of sample size. Among the penalized regression models that are analysed, the log-F prior and ridge regression methods are preferred.

Sample selection arises when the outcome of interest is partially observed in a study. A common challenge is the requirement for exclusion restrictions. That is, some of the covariates affecting missingness mechanism do not affect the outcome. The drive to establish this requirement often leads to the inclusion of irrelevant variables in the model. A suboptimal solution is the use of classical variable selection criteria such as AIC and BIC, and traditional variable selection procedures such as stepwise selection. These methods are unstable when there is limited expert knowledge about the variables to include in the model. To address this, we propose the use of adaptive Lasso for variable selection and parameter estimation in both the selection and outcome submodels simultaneously in the absence of exclusion restrictions. By using the maximum likelihood estimator of the sample selection model, we constructed a loss function similar to the least squares regression problem up to a constant, and minimized its penalized version using an efficient algorithm. We show that the estimator, with proper choice of regularization parameter, is consistent and possesses the oracle properties. The method is compared to Lasso and adaptively weighted L1 penalized Two-step method. We applied the methods to the well-known Ambulatory Expenditure Data.

IntroductionCardiac rehabilitation (CR) delivered by rehabilitation specialists in a healthcare setting is effective in improving functional capacity and reducing readmission rates after cardiac surgery. It is also associated with a reduction in cardiac mortality and recurrent myocardial infarction. This trial assesses the feasibility of a home-based CR programme delivered using a mobile application (app).MethodsThe Rehabilitation through Exercise prescription for Cardiac patients using an Artificial intelligence web-based Programme (RECAP) randomised controlled feasibility trial is a single-centre prospective study, in which patients will be allocated on a 1:1 ratio to a home-based CR programme delivered using a mobile app with accelerometers or standard hospital-based rehabilitation classes. The home-based CR programme will employ artificial intelligence to prescribe exercise goals to the participants on a weekly basis. The trial will recruit 70 patients in total. The primary objectives are to evaluate participant recruitment and dropout rates, assess the feasibility of randomisation, determine acceptability to participants and staff, assess the rates of potential outcome measures and determine hospital resource allocation to inform the design of a larger randomised controlled trial for clinical efficacy and health economic evaluation. Secondary objectives include evaluation of health-related quality of life and 6 minute walk distance.Ethics and disseminationRECAP trial received a favourable outcome from the Berkshire research ethics committee in September 2022 (IRAS 315483).Trial results will be made available through publication in peer-reviewed journals and presented at relevant scientific meetings.Trial registration numberISRCTN97352737.

Background Autism Adapted Safety Plans (AASP) have been proposed to help prevent self-harm and suicidality among autistic adults. The introduction of such plans not only needs to be clinically effective but also cost-effective. The aim of this work was to establish how the cost-effectiveness of AASP could be assessed. Specifically, whether tools and techniques used to collect data for health economic evaluation of the intervention are feasible and acceptable to autistic people. Methods A feasibility and external pilot randomised controlled trial of the AASP intervention was conducted. Autistic adults recruited from diverse locations in England and Wales were randomised to either: AASP and usual care, or usual care only. Health economics tools (bespoke and adapted) were developed and focus groups were undertaken with participants, including autistic adults ( n  = 15), their family members/carers ( n  = 5), and service providers ( n  = 10), to determine their acceptability and feasibility. Tools considered worth further exploration were interviewer administered to participants during the pilot trial at baseline and at 6 months. Interviewer notes were used to record any issues reported while completing the tools. Response rates on the questions and completeness of the tools, along with participant feedback in the interviewer notes was assessed. Results Standard Gamble and Time-Trade Off approaches to measure health status were judged inappropriate to measure health outcomes with autistic adults experiencing suicidal ideation and with a history of self-harm. Contingent valuation and discrete choice experiments were also considered inappropriate, due to the heavy cognitive burden on respondents. The EQ-5D-5L/VAS, resource utilisation questionnaire and time-travel questionnaire were considered acceptable by participants. Response and completion rates (as a percentage of all returned questionnaires) for resource utilisation questionnaire (> 85%), time-travel questionnaire (> 79%), EQ-5D-5L (> 96%) and EQ-5D-VAS (> 87%) were good in general. Participants needed clear guidance and interviewer support to enable questionnaire completion. Conclusions It is feasible and acceptable to collect relevant data on resource utilisation, and costs of accessing care and the EQ-5D-5L in a future definitive trial. Clear guidance and interviewer support on how to complete the questionnaires and explanations of the importance of questions to the research would help autistic participants completing the health economic tools. Trial registration ISRCTN70594445; Trial Registration Date: 06/07/2020.

Non-random sampling is a source of bias in empirical research. It is common for the outcomes of interest (e.g. wage distribution) to be skewed in the source population. Sometimes, the outcomes are further subjected to sample selection, which is a type of missing data, resulting in partial observability. Thus, methods based on complete cases for skew data are inadequate for the analysis of such data and a general sample selection model is required. Heckman proposed a full maximum likelihood estimation method under the normality assumption for sample selection problems, and parametric and non-parametric extensions have been proposed. We generalize Heckman selection model to allow for underlying skew-normal distributions. Finite-sample performance of the maximum likelihood estimator of the model is studied via simulation. Applications illustrate the strength of the model in capturing spurious skewness in bounded scores, and in modelling data where logarithm transformation could not mitigate the effect of inherent skewness in the outcome variable.

Manufacturing organisations have contributed to a poor living environment via unsustainable practices in the production process and the entire service delivery operation. More importantly, the health performance of manufacturing employees may also be affected by unsustainable production practices in the industry. Therefore, the green supply chain management (GSCM) practice has become a topical issue in recent decades due to its significant impact on the ecosystem at large. Via green practices, various performances have been achieved in organisations; meanwhile, the relationships between the practices and performance metrics in most developing countries are unclear, although there have been supposed general submissions. In addition, the study of relationships in a leading business conglomerate in developing nations is rare. Therefore, this paper investigated relationships between GSCM practices and performance metrics in a leading manufacturing organisation in Africa by using a close-up study approach with data collected from 154 respondents. The data were analysed using multiple methods such as factor analysis to consolidate the measured variables; correlation, multiple regression analysis with stepwise estimation, and structural equation modelling (SEM) were used to examine the relationships between GSCM practices and performance. The results of these analyses revealed that environmental performance is significantly predicted by the measure of the organisation’s commitment to GSCM vision, while financial performance is significantly impacted by eco-centric consumption and education. This study concludes that inhouse-drafted strategies based on the insight from the study will facilitate the optimisation of GSCM practices.

IntroductionHallucinations (hearing or seeing things that others do not) are a common feature of psychosis, causing significant distress and disability. Existing treatments such as cognitive–behavioural therapy for psychosis (CBTp) have modest benefits, and there is a lack of CBTp-trained staff. Shorter, targeted treatments that focus on specific symptoms delivered by a non-specialist workforce could substantially increase access to treatment.Managing Unusual Sensory Experiences (MUSE) explains why people have hallucinations and helps the person to develop and use coping strategies to reduce distress. MUSE focuses only on hallucinations, and treatment is short (four to six, 1-hour sessions per week). It is a digital intervention, run on National Health Service (NHS) laptops, which provides information about hallucinations in an engaging way, using audio, video and animated content. Crucially, it is designed for use by non-specialist staff like community psychiatric nurses.Methods and analysisThe study is a two-arm feasibility randomised controlled trial comparing MUSE and treatment as usual (TAU) (n=40) to TAU alone (n=40), recruiting across two NHS Trusts, using 1:1 allocation and blind assessments before and after treatment (2 months) and at follow-up (3 months). Quantitative information on recruitment rates, adherence and completion of outcome assessments will be collected. Qualitative interviews will capture service users’ experience of therapy and clinicians’ experiences of the training and supervision in MUSE. Clinicians will also be asked about factors affecting uptake, adherence and facilitators/barriers to implementation. Analyses will focus on feasibility outcomes and provide initial estimates of intervention effects. Thematic analysis of the qualitative interviews will assess the acceptability of the training, intervention and trial procedures.Ethics and disseminationThe trial has received NHS Ethical and Health Research Authority approval. Findings will be disseminated directly to participants and services, as well as through peer-reviewed publications and conference presentations.Trial registration number ISRCTN16793301.

Background Suicide prevention is a national priority for the UK government. Autistic people are at greater risk of experiencing self-harm and suicidal thoughts and behaviours than the general population. Safety plans are widely used in suicide prevention but have not yet been designed with and for autistic people. We developed the first safety plan specifically targeting suicidality in autistic adults: the Autism Adapted Safety Plan (AASP). It consists of a prioritised list of hierarchical steps that can be used prior to or during a crisis to mitigate risk of self-harm and suicidal behaviour. This is a pilot study that aims to assess the feasibility and acceptability of the AASPs and the research processes, including the response rates, potential barriers and reach of AASPs, methods of recruitment, what comprises usual care, and economic evaluation methods/tools. Methods This is an external pilot randomised controlled trial of a suicide prevention tool aimed at mitigating the risk of self-harm and suicidal behaviour in autistic adults: AASPs. Participants will be assessed at baseline and followed up 1 month and 6 months later. Assessments include questions about self-harm, suicidality, service use, and their experience of the AASP/taking part in the study. Autistic adults who have a clinical autism diagnosis and self-reported history of self-harm, suicidal thoughts, or suicidal behaviours within the last 6 months will be invited to take part in the study. Informed consent will be obtained. Participants will be recruited via community and third sector services (including community settings, autism charities, and mental health charities). They may also “self-refer” into the study through social media recruitment and word of mouth. Ninety participants will be randomised to either develop an AASP or receive their usual care in a 1:1 ratio. Discussion The present study will provide an evaluation of the suitability of the processes that would be undertaken in a larger definitive study, including recruitment, randomisation, methods, questionnaires, outcome measures, treatment, and follow-up assessments. Trial registration ISRCTN70594445, Protocol v4: 8/2/22.

IntroductionAnthracyclines are included in chemotherapy regimens to treat several different types of cancer and are extremely effective. However, it is recognised that a significant side effect is cardiotoxicity; anthracyclines can cause irreversible damage to cardiac cells and ultimately impaired cardiac function and heart failure, which may only be evident years after exposure. The PROACT trial will establish the effectiveness of the ACE inhibitor enalapril maleate (enalapril) in preventing cardiotoxicity in patients with breast cancer and non-Hodgkin’s lymphoma (NHL) receiving anthracycline-based chemotherapy.Methods and analysisPROACT is a prospective, randomised, open-label, blinded end-point, superiority trial which will recruit adult patients being treated for breast cancer and NHL at NHS hospitals throughout England. The trial aims to recruit 106 participants, who will be randomised to standard care (high-dose anthracycline-based chemotherapy) plus enalapril (intervention) or standard care alone (control). Patients randomised to the intervention arm will receive enalapril (starting at 2.5 mg two times per day and titrating up to a maximum dose of 10 mg two times per day), commencing treatment at least 2 days prior to starting chemotherapy and finishing 3 weeks after their last anthracycline dose. The primary outcome is the presence or absence of cardiac troponin T release at any time during anthracycline treatment, and 1 month after the last dose of anthracycline. Secondary outcomes will focus on cardiac function measured using echocardiogram assessment, adherence to enalapril and side effects.Ethics and disseminationA favourable opinion was given following research ethics committee review by West Midlands—Edgbaston REC, Ref: 17/WM/0248. Trial findings will be disseminated through engagement with patients, the oncology and cardiology communities, NHS management and commissioning groups and through peer-reviewed publication.Trial registration numberNCT03265574.