Fast computation by block permanents of cumulative distribution functions of order statistics from several populations

The joint cumulative distribution function for order statistics arising from several different populations is given in terms of the distribution function of the populations. The computational cost of the formula in the case of two populations is still exponential in the worst case, but it is a dramatic improvement compared to the general formula by Bapat and Beg. In the case when only the joint distribution function of a subset of the order statistics of fixed size is needed, the complexity is polynomial, for the case of two populations.Comment: 21 pages, 3 figure

Learning to bridge the gap between adaptive management and organisational culture

Adaptive management is the problem-solving approach of choice proposed for complex and multistakeholder environments, which are, at best, only partly predictable. We discuss the implications of this approach as applicable to scientists, who have to overcome certain entrained behaviour patterns in order to participate effectively in an adaptive management process. The challenge does not end there. Scientists and managers soon discover that an adaptive management approach does not only challenge conventional scientific and management behaviour but also clashes with contemporary organisational culture. We explore the shortcomings and requirements of organisations with regard to enabling adaptive management. Our overall conclusion relates to whether organisations are learning-centred or not. Do we continue to filter out unfamiliar information which does not fit our world view and avoid situations where we might fail, or do we use new and challenging situations to reframe the question and prepare ourselves for continued learning? Conservation implications: For an organisation to effectively embrace adaptive management, its mangers and scientists may first have to adapt their own beliefs regarding their respective roles. Instead of seeking certainty for guiding decisions, managers and scientists should acknowledge a degree of uncertainty inherent to complex social and ecological systems and seek to learn from the patterns emerging from every decision and action. The required organisational culture is one of ongoing and purposeful learning with all relevant stakeholders. Such a learning culture is often talked about but rarely practised in the organisational environment

Using realist review to inform intervention development: Methodological illustration and conceptual platform for collaborative care in offender mental health

BackgroundThis paper reports how we used a realist review, as part of a wider project to improve collaborative mental health care for prisoners with common mental health problems, to develop a conceptual platform. The importance of offenders gaining support for their mental health, and the need for practitioners across the health service, the criminal justice system, and the third sector to work together to achieve this is recognised internationally. However, the literature does not provide coherent analyses of how these ambitions can be achieved. This paper demonstrates how a realist review can be applied to inform complex intervention development that spans different locations, organisations, professions, and care sectors.MethodsWe applied and developed a realist review for the purposes of intervention development, using a three-stage process. (1) An iterative database search strategy (extending beyond criminal justice and offender health) and groups of academics, practitioners, and people with lived experience were used to identify explanatory accounts (n = 347). (2) From these accounts, we developed consolidated explanatory accounts (n = 75). (3) The identified interactions between practitioners and offenders (within their organisational, social, and cultural contexts) were specified in a conceptual platform. We also specify, step by step, how these explanatory accounts were documented, consolidated, and built into a conceptual platform. This addresses an important methodological gap for social scientists and intervention developers about how to develop and articulate programme and implementation theory underpinning complex interventions.ResultsAn integrated person-centred system is proposed to improve collaborative mental health care for offenders with common mental health problems (near to and after release) by achieving consistency between the goals of different sectors and practitioners, enabling practitioners to apply scientific and experiential knowledge in working judiciously and reflectively, and building systems and aligning resources that are centred on offenders’ health and social care needs.ConclusionsAs part of a broader programme of work, a realist review can make an important contribution to the specification of theoretically informed interventions that have the potential to improve health outcomes. Our conceptual platform has potential application in related systems of health and social care where integrated, and person-centred care is a goal

Evaluation of a complex intervention (Engager) for prisoners with common mental health problems, near to and after release: study protocol for a randomised controlled trial.

INTRODUCTION: The 'Engager' programme is a 'through-the-gate' intervention designed to support prisoners with common mental health problems as they transition from prison back into the community. The trial will evaluate the clinical and cost-effectiveness of the Engager intervention. METHODS AND ANALYSIS: The study is a parallel two-group randomised controlled trial with 1:1 individual allocation to either: (a) the Engager intervention plus standard care (intervention group) or (b) standard care alone (control group) across two investigation centres (South West and North West of England). Two hundred and eighty prisoners meeting eligibility criteria will take part. Engager is a person-centred complex intervention delivered by practitioners and aimed at addressing offenders' mental health and social care needs. It comprises one-to-one support for participants prior to release from prison and for up to 20 weeks postrelease. The primary outcome is change in psychological distress measured by the Clinical Outcomes in Routine Evaluation-Outcome Measure at 6 months postrelease. Secondary outcomes include: assessment of subjective met/unmet need, drug and alcohol use, health-related quality of life and well-being-related quality of life measured at 3, 6 and 12 months postrelease; change in objective social domains, drug and alcohol dependence, service utilisation and perceived helpfulness of services and change in psychological constructs related to desistence at 6 and 12 months postrelease; and recidivism at 12 months postrelease. A process evaluation will assess fidelity of intervention delivery, test hypothesised mechanisms of action and look for unintended consequences. An economic evaluation will estimate the cost-effectiveness. ETHICS AND DISSEMINATION: This study has been approved by the Wales Research Ethics Committee 3 (ref: 15/WA/0314) and the National Offender Management Service (ref: 2015-283). Findings will be disseminated to commissioners, clinicians and service users via papers and presentations. TRIAL REGISTRATION NUMBER: ISRCTN11707331; Pre-results

Interrogating intervention delivery and participants' emotional states to improve engagement and implementation: A realist informed multiple case study evaluation of Engager.

BACKGROUND: 'Engager' is an innovative 'through-the-gate' complex care intervention for male prison-leavers with common mental health problems. In parallel to the randomised-controlled trial of Engager (Trial registration number: ISRCTN11707331), a set of process evaluation analyses were undertaken. This paper reports on the depth multiple case study analysis part of the process evaluation, exploring how a sub-sample of prison-leavers engaged and responded to the intervention offer of one-to-one support during their re-integration into the community. METHODS: To understand intervention delivery and what response it elicited in individuals, we used a realist-informed qualitative multiple 'case' studies approach. We scrutinised how intervention component delivery lead to outcomes by examining underlying causal pathways or 'mechanisms' that promoted or hindered progress towards personal outcomes. 'Cases' (n = 24) were prison-leavers from the intervention arm of the trial. We collected practitioner activity logs and conducted semi-structured interviews with prison-leavers and Engager/other service practitioners. We mapped data for each case against the intervention logic model and then used Bhaskar's (2016) 'DREIC' analytic process to categorise cases according to extent of intervention delivery, outcomes evidenced, and contributing factors behind engagement or disengagement and progress achieved. RESULTS: There were variations in the dose and session focus of the intervention delivery, and how different participants responded. Participants sustaining long-term engagement and sustained change reached a state of 'crises but coping'. We found evidence that several components of the intervention were key to achieving this: trusting relationships, therapeutic work delivered well and over time; and an in-depth shared understanding of needs, concerns, and goals between the practitioner and participants. Those who disengaged were in one of the following states: 'Crises and chaos', 'Resigned acceptance', 'Honeymoon' or 'Wilful withdrawal'. CONCLUSIONS: We demonstrate that the 'implementability' of an intervention can be explained by examining the delivery of core intervention components in relation to the responses elicited in the participants. Core delivery mechanisms often had to be 'triggered' numerous times to produce sustained change. The improvements achieved, sustained, and valued by participants were not always reflected in the quantitative measures recorded in the RCT. The compatibility between the practitioner, participant and setting were continually at risk of being undermined by implementation failure as well as changing external circumstances and participants' own weaknesses. TRIAL REGISTRATION NUMBER: ISRCTN11707331, Wales Research Ethics Committee, Registered 02-04-2016-Retrospectively registered https://doi.org/10.1186/ISRCTN11707331

Building programme theory to develop more adaptable and scalable complex interventions: Realist formative process evaluation prior to full trial

Medical Research Council guidelines recognise the need to optimise complex interventions prior to full trial through greater understanding of underlying theory and formative process evaluation, yet there are few examples. A realist approach to formative process evaluation makes a unique contribution through a focus on theory formalisation and abstraction. The success of an intervention is dependent on the extent to which it gels or jars with existing provision and can be successfully transferred to new contexts. Interventions with underlying programme theory about how they work, for whom, and under which circumstances will be better able to adapt to work with (rather than against) different services, individuals, and settings. In this methodological article, we describe and illustrate how a realist approach to formative process evaluation develops contextualised intervention theory that can underpin more adaptable and scalable interventions. We discuss challenges and benefits of this approach