Efficient designs for three-sequence stepped wedge trials with continuous recruitment.

BACKGROUND/AIMS: The standard approach to designing stepped wedge trials that recruit participants in a continuous stream is to divide time into periods of equal length. But the choice of design in such cases is infinitely more flexible: each cluster could cross from the control to the intervention at any point on the continuous time-scale. We consider the case of a stepped wedge design with clusters randomised to just three sequences (designs with small numbers of sequences may be preferred for their simplicity and practicality) and investigate the choice of design that minimises the variance of the treatment effect estimator under different assumptions about the intra-cluster correlation. METHODS: We make some simplifying assumptions in order to calculate the variance: in particular that we recruit the same number of participants, m, from each cluster over the course of the trial, and that participants present at regularly spaced intervals. We consider an intra-cluster correlation that decays exponentially with separation in time between the presentation of two individuals from the same cluster, from a value of ρ for two individuals who present at the same time, to a value of ρτ for individuals presenting at the start and end of the trial recruitment interval. We restrict attention to three-sequence designs with centrosymmetry - the property that if we reverse time and swap the intervention and control conditions then the design looks the same. We obtain an expression for the variance of the treatment effect estimator adjusted for effects of time, using methods for generalised least squares estimation, and we evaluate this expression numerically for different designs, and for different parameter values. RESULTS: There is a two-dimensional space of possible three-sequence, centrosymmetric stepped wedge designs with continuous recruitment. The variance of the treatment effect estimator for given ρ and τ can be plotted as a contour map over this space. The shape of this variance surface depends on τ and on the parameter mρ/(1-ρ), but typically indicates a broad, flat region of close-to-optimal designs. The 'standard' design with equally spaced periods and 1:1:1 allocation rarely performs well, however. CONCLUSIONS: In many different settings, a relatively simple design can be found (e.g. one based on simple fractions) that offers close-to-optimal efficiency in that setting. There may also be designs that are robustly efficient over a wide range of settings. Contour maps of the kind we illustrate can help guide this choice. If efficiency is offered as one of the justifications for using a stepped wedge design, then it is worth designing with optimal efficiency in mind.

Influence of vitamin D supplementation on bone mineral content, bone turnover markers, and fracture risk in South African schoolchildren: multicenter double-blind randomized placebo-controlled trial (ViDiKids).

Randomized controlled trials (RCTs) to determine the influence of vitamin D on BMC and fracture risk in children of Black African ancestry are lacking. We conducted a sub-study (n = 450) nested within a phase 3 RCT of weekly oral supplementation with 10 000 IU vitamin D3 vs placebo for 3 yr in HIV-uninfected Cape Town schoolchildren aged 6-11 yr. Outcomes were BMC at the whole body less head (WBLH) and LS and serum 25-hydroxyvitamin D3 (25(OH)D3), PTH, alkaline phosphatase, C-terminal telopeptide, and PINP. Incidence of fractures was a secondary outcome of the main trial (n = 1682). At baseline, mean serum 25(OH)D3 concentration was 70.0 nmol/L (SD 13.5), and 5.8% of participants had serum 25(OH)D3 concentrations <50 nmol/L. Among sub-study participants, end-trial serum 25(OH)D3 concentrations were higher for participants allocated to vitamin D vs placebo (adjusted mean difference [aMD] 39.9 nmol/L, 95% CI, 36.1 to 43.6) and serum PTH concentrations were lower (aMD -0.55 pmol/L, 95% CI, -0.94 to -0.17). However, no interarm differences were seen for WBLH BMC (aMD -8.0 g, 95% CI, -30.7 to 14.7) or LS BMC (aMD -0.3 g, 95% CI, -1.3 to 0.8) or serum concentrations of bone turnover markers. Fractures were rare among participants in the main trial randomized to vitamin D vs placebo (7/755 vs 10/758 attending at least 1 follow-up; adjusted odds ratio 0.70, 95% CI, 0.27 to 1.85). In conclusion, a 3-yr course of weekly oral vitamin D supplementation elevated serum 25(OH)D3 concentrations and suppressed serum PTH concentrations in HIV-uninfected South African schoolchildren of Black African ancestry but did not influence BMC or serum concentrations of bone turnover markers. Fracture incidence was low, limiting power to detect an effect of vitamin D on this outcome.

Vitamin D­the "sunshine vitamin"­is essential for helping the body to absorb calcium from the diet, which is laid down in bone to improve its strength. There is a lack of clinical trials testing whether vitamin D supplements can improve bone content of calcium and other minerals, or reduce risk of bone fractures (broken bones) in children of Black African ancestry. We therefore conducted such a study, recruiting 1682 schoolchildren aged 6­11 yr living in Cape Town, South Africa. We found that a weekly dose of 10 000 international units (250 micrograms) of vitamin D3, given by mouth for 3 yr, was effective in boosting vitamin D levels in trial participants who received it. However, this did not have any effect on bone content of calcium and other minerals. Relatively few children experienced a broken bone during the study, so we were unable to say with confidence whether or not vitamin D supplements might affect this outcome.

A tailored psychological intervention for anxiety and depression management in people with chronic obstructive pulmonary disease: TANDEM RCT and process evaluation.

Background: People with chronic obstructive pulmonary disease have high levels of anxiety and depression, which is associated with increased morbidity and poor uptake of effective treatments, such as pulmonary rehabilitation. Cognitive-behavioural therapy improves mental health of people with long-term conditions and could potentially increase uptake of pulmonary rehabilitation, enabling synergies that could enhance the mental health of people with chronic obstructive pulmonary disease. Aim: Our aim was to develop and evaluate the clinical effectiveness and cost effectiveness of a tailored cognitive-behavioural approach intervention, which links into, and optimises the benefits of, routine pulmonary rehabilitation. Design: We carried out a pragmatic multicentre randomised controlled trial using a 1.25 : 1 ratio (intervention : control) with a parallel process evaluation, including assessment of fidelity. Setting: Twelve NHS trusts and five Clinical Commissioning Groups in England were recruited into the study. The intervention was delivered in participant's own home or at a local NHS facility, and by telephone. Participants: Between July 2017 and March 2020 we recruited adults with moderate/very severe chronic obstructive pulmonary disease and mild/moderate anxiety and/or depression, meeting eligibility criteria for assessment for pulmonary rehabilitation. Carers of participants were invited to participate. Intervention: The cognitive-behavioural approach intervention (i.e. six to eight 40- to 60-minute sessions plus telephone support throughout pulmonary rehabilitation) was delivered by 31 trained respiratory healthcare professionals to participants prior to commencing pulmonary rehabilitation. Usual care included routine pulmonary rehabilitation referral. Main outcome measures: Co-primary outcomes were Hospital Anxiety and Depression Scale - anxiety and Hospital Anxiety and Depression Scale - depression at 6 months post randomisation. Secondary outcomes at 6 and 12 months included health-related quality of life, smoking status, uptake of pulmonary rehabilitation and healthcare use. Results: We analysed results from 423 randomised participants (intervention, n = 242; control, n = 181). Forty-three carers participated. Follow-up at 6 and 12 months was 93% and 82%, respectively. Despite good fidelity for intervention delivery, mean between-group differences in Hospital Anxiety and Depression Scale at 6 months ruled out clinically important effects (Hospital Anxiety and Depression Scale - anxiety mean difference -0.60, 95% confidence interval -1.40 to 0.21; Hospital Anxiety and Depression Scale - depression mean difference -0.66, 95% confidence interval -1.39 to 0.07), with similar results at 12 months. There were no between-group differences in any of the secondary outcomes. Sensitivity analyses did not alter these conclusions. More adverse events were reported for intervention participants than for control participants, but none related to the trial. The intervention did not generate quality-of-life improvements to justify the additional cost (adjusted mean difference £770.24, 95% confidence interval -£27.91 to £1568.39) to the NHS. The intervention was well received and many participants described positive affects on their quality of life. Facilitators highlighted the complexity of participants' lives and considered the intervention to be of potential valuable; however, the intervention would be difficult to integrate within routine clinical services. Our well-powered trial delivered a theoretically designed intervention with good fidelity. The respiratory-experienced facilitators were trained to deliver a low-intensity cognitive-behavioural approach intervention, but high-intensity cognitive-behavioural therapy might have been more effective. Our broad inclusion criteria specified objectively assessed anxiety and/or depression, but participants were likely to favour talking therapies. Randomisation was concealed and blinding of outcome assessment was breached in only 15 participants. Conclusions: The tailored cognitive-behavioural approach intervention delivered with fidelity by trained respiratory healthcare professionals to people with chronic obstructive pulmonary disease was neither clinically effective nor cost-effective. Alternative approaches that are integrated with routine long-term condition care are needed to address the unmet, complex clinical and psychosocial needs of this group of patients. Trial registration: This trial is registered as ISRCTN59537391. Funding: This award was funded by the National Institute for Health and Care Research (NIHR) Health Technology Assessment programme (NIHR award ref: 13/146/02) and is published in full in Health Technology Assessment; Vol. 28, No. 1. See the NIHR Funding and Awards website for further award information.

People with long-standing lung problems, such as chronic obstructive pulmonary disease, often also have anxiety and depression, which further reduces their quality of life. Two existing treatments could help. Pulmonary rehabilitation (a programme of exercise and education) improves both the physical and mental health of people with chronic obstructive pulmonary disease. Cognitive­behavioural therapy (a talking therapy) may reduce anxiety and depression. The TANDEM [Tailored intervention for Anxiety and Depression Management in chronic obstructive pulmonary disease (COPD)] intervention linked these two treatments by providing talking therapy based on cognitive­behavioural therapy during the waiting time following referral for pulmonary rehabilitation. The TANDEM treatment was delivered by respiratory healthcare professionals (e.g. nurses or physiotherapists) trained to deliver the talking therapy in six to eight weekly sessions. The sessions were conducted in the participant's home (or another convenient location), with brief telephone support during the pulmonary rehabilitation. Of 423 participants recruited to the study, 242 participants received TANDEM talking therapy and 181 participants received usual care (including a referral to pulmonary rehabilitation). We measured mental health, quality of life, social life, attendance at pulmonary rehabilitation and healthcare use in both groups at 6 and 12 months. Forty-three carers joined the study and we assessed their mental well-being. We interviewed patients, carers and health professionals to find out their views and experience of the TANDEM treatment. We also examined whether or not the TANDEM treatment was good value for money. The TANDEM treatment did not improve the mental or the physical health of people with chronic obstructive pulmonary disease. In addition, the TANDEM treatment cost the NHS an extra £770 per patient, which was not good value for money. The TANDEM treatment was well received, and many participants told us how it had helped them. Heath-care professionals noted how participants did not just have chronic obstructive pulmonary disease, but were coping with many physical, mental and social problems. The TANDEM intervention was not effective and, therefore, other strategies will be needed to help people with chronic obstructive pulmonary disease and mental health problems live with their condition.

The staircase cluster randomised trial design: A pragmatic alternative to the stepped wedge.

This article introduces the 'staircase' design, derived from the zigzag pattern of steps along the diagonal of a stepped wedge design schematic where clusters switch from control to intervention conditions. Unlike a complete stepped wedge design where all participating clusters must collect and provide data for the entire trial duration, clusters in a staircase design are only required to be involved and collect data for a limited number of pre- and post-switch periods. This could alleviate some of the burden on participating clusters, encouraging involvement in the trial and reducing the likelihood of attrition. Staircase designs are already being implemented, although in the absence of a dedicated methodology, approaches to sample size and power calculations have been inconsistent. We provide expressions for the variance of the treatment effect estimator when a linear mixed model for an outcome is assumed for the analysis of staircase designs in order to enable appropriate sample size and power calculations. These include explicit variance expressions for basic staircase designs with one pre- and one post-switch measurement period. We show how the variance of the treatment effect estimator is related to key design parameters and demonstrate power calculations for examples based on a real trial.

Effectiveness of group arts therapies (art therapy, dance movement therapy and music therapy) compared to group counselling for diagnostically heterogeneous psychiatric community patients: study protocol for a randomised controlled trial in mental health services (the ERA study).

BACKGROUND: Arts therapies are widely but inconsistently provided in community mental health. Whilst they are appealing to patients, evidence for their effectiveness is mixed. Trials to date have been limited to one art-form or diagnosis. Patients may hold strong preferences for or against an art-form whilst group therapies rely on heterogeneity to provide a range of learning experiences. This study will test whether manualised group arts therapies (art therapy, dance movement therapy and music therapy) are effective in reducing psychological distress for diagnostically heterogeneous patients in community mental health compared to active group counselling control. METHODS: A pragmatic multi-centre 2-arm randomised controlled superiority trial with health economic evaluation and nested process evaluation. Adults aged ≥ 18, living in the community with a primary diagnosis of psychosis, mood, or anxiety disorder will be invited to participate and provide written informed consent. Participants are eligible if they score ≥ 1.65 on the Global Severity Index of the Brief Symptom Inventory. Those eligible will view videos of arts therapies and be asked for their preference. Participants are randomised to either their preferred type of group arts therapy or counselling. Groups will run twice per week in a community venue for 20 weeks. Our primary outcome is symptom distress at the end of intervention. Secondary outcomes include observer-rated symptoms, social situation and quality of life. Data will be collected at baseline, post-intervention and 6 and 12 months post-intervention. Outcome assessors and trial statisticians will be blinded. Analysis will be intention-to-treat. Economic evaluation will assess the cost-effectiveness of group arts therapies. A nested process evaluation will consist of treatment fidelity analysis, exploratory analysis of group process measures and qualitative interviews with participants and therapists. DISCUSSION: This will be the first trial to account for patient preferences and diagnostic heterogeneity in group arts therapies. As with all group therapies, there are a number of logistical challenges to which we have had to further adapt due to the COVID-19 pandemic. Overall, the study will provide evidence as to whether there is an additive benefit or not to the use of the arts in group therapy in community mental health care. TRIAL REGISTRATION: ISRCTN, ISRCTN88805048 . Registered on 12 September 2018.

Tailored psychological intervention for anxiety or depression in COPD (TANDEM): a randomised controlled trial.

BACKGROUND: The TANDEM multicentre, pragmatic, randomised controlled trial evaluated whether a tailored psychological intervention based on a cognitive behavioural approach for people with COPD and symptoms of anxiety and/or depression improved anxiety or depression compared with usual care (control). METHODS: People with COPD and moderate to very severe airways obstruction and Hospital Anxiety and Depression Scale subscale scores indicating mild to moderate anxiety (HADS-A) and/or depression (HADS-D) were randomised 1.25:1 (242 intervention and 181 control). Respiratory health professionals delivered the intervention face-to-face over 6-8 weeks. Co-primary outcomes were HADS-A and HADS-D measured 6 months post-randomisation. Secondary outcomes at 6 and 12 months included: HADS-A and HADS-D (12 months), Beck Depression Inventory II, Beck Anxiety Inventory, St George's Respiratory Questionnaire, social engagement, the EuroQol instrument five-level version (EQ-5D-5L), smoking status, completion of pulmonary rehabilitation, and health and social care resource use. RESULTS: The intervention did not improve anxiety (HADS-A mean difference -0.60, 95% CI -1.40-0.21) or depression (HADS-D mean difference -0.66, 95% CI -1.39-0.07) at 6 months. The intervention did not improve any secondary outcomes at either time-point, nor did it influence completion of pulmonary rehabilitation or healthcare resource use. Deaths in the intervention arm (13/242; 5%) exceeded those in the control arm (3/181; 2%), but none were associated with the intervention. Health economic analysis found the intervention highly unlikely to be cost-effective. CONCLUSION: This trial has shown, beyond reasonable doubt, that this cognitive behavioural intervention delivered by trained and supervised respiratory health professionals does not improve psychological comorbidity in people with advanced COPD and depression or anxiety.

Systematic review of preoperative and intraoperative colorectal Anastomotic Leak Prediction Scores (ALPS).

OBJECTIVE: To systematically review preoperative and intraoperative Anastomotic Leak Prediction Scores (ALPS) and validation studies to evaluate performance and utility in surgical decision-making. Anastomotic leak (AL) is the most feared complication of colorectal surgery. Individualised leak risk could guide anastomosis and/or diverting stoma. METHODS: Systematic search of Ovid MEDLINE and Embase databases, 30 October 2020, identified existing ALPS and validation studies. All records including >1 risk factor, used to develop new, or to validate existing models for preoperative or intraoperative use to predict colorectal AL, were selected. Data extraction followed CHecklist for critical Appraisal and data extraction for systematic Reviews of prediction Modelling Studies guidelines. Models were assessed for applicability for surgical decision-making and risk of bias using Prediction model Risk Of Bias ASsessment Tool. RESULTS: 34 studies were identified containing 31 individual ALPS (12 colonic/colorectal, 19 rectal) and 6 papers with validation studies only. Development dataset patient populations were heterogeneous in terms of numbers, indication for surgery, urgency and stoma inclusion. Heterogeneity precluded meta-analysis. Definitions and timeframe for AL were available in only 22 and 11 ALPS, respectively. 26/31 studies used some form of multivariable logistic regression in their modelling. Models included 3-33 individual predictors. 27/31 studies reported model discrimination performance but just 18/31 reported calibration. 15/31 ALPS were reported with external validation, 9/31 with internal validation alone and 4 published without any validation. 27/31 ALPS and every validation study were scored high risk of bias in model analysis. CONCLUSIONS: Poor reporting practices and methodological shortcomings limit wider adoption of published ALPS. Several models appear to perform well in discriminating patients at highest AL risk but all raise concerns over risk of bias, and nearly all over wider applicability. Large-scale, precisely reported external validation studies are required. PROSPERO REGISTRATION NUMBER: CRD42020164804.

Implementation of a batched stepped wedge trial evaluating a quality improvement intervention for surgical teams to reduce anastomotic leak after right colectomy.

BACKGROUND: Large-scale quality improvement interventions demand robust trial designs with flexibility for delivery in different contexts, particularly during a pandemic. We describe innovative features of a batched stepped wedge trial, ESCP sAfe Anastomosis proGramme in CoLorectal SurgEry (EAGLE), intended to reduce anastomotic leak following right colectomy, and reflect on lessons learned about the implementation of quality improvement programmes on an international scale. METHODS: Surgical units were recruited and randomised in batches to receive a hospital-level education intervention designed to reduce anastomotic leak, either before, during, or following data collection. All consecutive patients undergoing right colectomy were included. Online learning, patient risk stratification and an in-theatre checklist constituted the intervention. The study was powered to detect an absolute risk reduction of anastomotic leak from 8.1 to 5.6%. Statistical efficiency was optimised using an incomplete stepped wedge trial design and study batches analysed separately then meta-analysed to calculate the intervention effect. An established collaborative group helped nurture strong working relationships between units/countries and a prospectively designed process evaluation will enable evaluation of both the intervention and its implementation. RESULTS: The batched trial design allowed sequential entry of clusters, targeted research training and proved to be robust to pandemic interruptions. Staggered start times in the incomplete stepped wedge design with long lead-in times can reduce motivation and engagement and require careful administration. CONCLUSION: EAGLE's robust but flexible study design allowed completion of the study across globally distributed geographical locations in spite of the pandemic. The primary outcome analysed in conjunction with the process evaluation will ensure a rich understanding of the intervention and the effects of the study design. TRIAL REGISTRATION: National Institute of Health Research Clinical Research Network portfolio IRAS ID: 272,250. Health Research Authority approval 18 October 2019. CLINICALTRIALS: gov, identifier NCT04270721, protocol ID RG_19196.

Vitamin D supplementation to prevent tuberculosis infection in South African schoolchildren: multicenter phase 3 double-blind randomized placebo-controlled trial (ViDiKids).

OBJECTIVES: To determine whether weekly oral supplementation with 10,000 IU vitamin D3 for 3 years reduces the risk of sensitization to M. tuberculosis in South African schoolchildren aged 6-11 years with negative QuantiFERON-tuberculosis (TB) Gold Plus (QFT-Plus) assay results at baseline. METHODS: We conducted a phase 3 randomized placebo-controlled trial in 1682 children attending 23 primary schools in Cape Town. The primary outcome was a positive end-trial QFT-Plus result, analyzed using a mixed effects logistic regression model with the school of attendance included as a random effect. RESULTS: 829 vs. 853 QFT-Plus-negative children were randomized to receive vitamin D3 vs. placebo, respectively. Mean end-study 25(OH)D concentrations in participants randomized to vitamin D vs. placebo were 104.3 vs 64.7 nmol/l, respectively (95% confidence interval for difference, 37.6 to 41.9 nmol/l). A total of 76/667 (11.4%) participants allocated to vitamin D vs. 89/687 (13.0%) participants allocated to placebo tested QFT-Plus positive at 3-year follow-up (adjusted odds ratio 0.86, 95% confidence interval 0.62-1.19, P = 0.35). CONCLUSION: Weekly oral supplementation with 10,000 IU vitamin D3 for 3 years elevated serum 25(OH)D concentrations among QFT-Plus-negative Cape Town schoolchildren but did not reduce their risk of QFT-Plus conversion.

Nonlinear effects and effect modification at the participant-level in IPD meta-analysis part 2: methodological guidance is available.

OBJECTIVES: To review methodological guidance for nonlinear covariate-outcome associations (NL), and linear effect modification and nonlinear effect modification (LEM and NLEM) at the participant level in individual participant data meta-analyses (IPDMAs) and their power requirements. STUDY DESIGN AND SETTING: We searched Medline, Embase, Web of Science, Scopus, PsycINFO and the Cochrane Library to identify methodology publications on IPDMA of LEM, NL or NLEM (PROSPERO CRD42019126768). RESULTS: Through screening 6,466 records we identified 54 potential articles of which 23 full texts were relevant. Nine further relevant publications were published before or after the literature search and were added. Of these 32 references, 21 articles considered LEM, 6 articles NL or NLEM and 6 articles described sample size calculations. A book described all four. Sample size may be calculated through simulation or closed form. Assessments of LEM or NLEM at the participant level need to be based on within-trial information alone. Nonlinearity (NL or NLEM) can be modeled using polynomials or splines to avoid categorization. CONCLUSION: Detailed methodological guidance on IPDMA of effect modification at participant-level is available. However, methodology papers for sample size and nonlinearity are rarer and may not cover all scenarios. On these aspects, further guidance is needed.

Nonlinear effects and effect modification at the participant-level in IPD meta-analysis part 1: analysis methods are often substandard.

OBJECTIVES: To review analysis methods used for linear effect modification (LEM), nonlinear covariate-outcome associations (NL) and nonlinear effect modification (NLEM) at the participant-level in individual participant data meta-analysis (IPDMA). STUDY DESIGN AND SETTING: We searched Medline, Embase, Web of Science, Scopus, PsycINFO and the Cochrane Library to identify IPDMA of randomized controlled trials (PROSPERO CRD42019126768). We investigated if and how IPDMA examined LEM, NL and NLEM, including whether aggregation bias was addressed and if power was considered. RESULTS: We screened 6,466 records, randomly sampled 207 and identified 100 IPDMA of LEM, NL or NLEM. Power for LEM was calculated a priori in 3 IPDMA. Of 100 IPDMA, 94 analyzed LEM, 4 NLEM and 8 NL. One-stage models were favoured for all three (56%, 100%, 50%, respectively). Two-stage models were used in 15%, 0% and 25% of IPDMA with unclear descriptions in 30%, 0% and 25%, respectively. Only 12% of one-stage LEM and NLEM IPDMA provided sufficient detail to confirm they had addressed aggregation bias. CONCLUSION: Investigation of effect modification at the participant-level is common in IPDMA projects, but methods are often open to bias or lack detailed descriptions. Nonlinearity of continuous covariates and power of IPDMA are rarely assessed.

The batched stepped wedge design: A design robust to delays in cluster recruitment.

Stepped wedge designs are an increasingly popular variant of longitudinal cluster randomized trial designs, and roll out interventions across clusters in a randomized, but step-wise fashion. In the standard stepped wedge design, assumptions regarding the effect of time on outcomes may require that all clusters start and end trial participation at the same time. This would require ethics approvals and data collection procedures to be in place in all clusters before a stepped wedge trial can start in any cluster. Hence, although stepped wedge designs are useful for testing the impacts of many cluster-based interventions on outcomes, there can be lengthy delays before a trial can commence. In this article, we introduce "batched" stepped wedge designs. Batched stepped wedge designs allow clusters to commence the study in batches, instead of all at once, allowing for staggered cluster recruitment. Like the stepped wedge, the batched stepped wedge rolls out the intervention to all clusters in a randomized and step-wise fashion: a series of self-contained stepped wedge designs. Provided that separate period effects are included for each batch, software for standard stepped wedge sample size calculations can be used. With this time parameterization, in many situations including when linear models are assumed, sample size calculations reduce to the setting of a single stepped wedge design with multiple clusters per sequence. In these situations, sample size calculations will not depend on the delays between the commencement of batches. Hence, the power of batched stepped wedge designs is robust to unexpected delays between batches.

Re-randomisation trials in multi-episode settings: Estimands and independence estimators.

Often patients may require treatment on multiple occasions. The re-randomisation design can be used in such multi-episode settings, as it allows patients to be re-enrolled and re-randomised for each new treatment episode they experience. We propose a set of estimands that can be used in multi-episode settings, focusing on issues unique to multi-episode settings, namely how each episode should be weighted, how the patient's treatment history in previous episodes should be handled, and whether episode-specific effects or average effects across all episodes should be used. We then propose independence estimators for each estimand, and show the manner in which many re-randomisation trials have been analysed in the past (a simple comparison between all intervention episodes vs. all control episodes) corresponds to a per-episode added-benefit estimand, that is, the average effect of the intervention across all episodes, over and above any benefit conferred from the intervention in previous episodes. We show this estimator is generally unbiased, and describe when other estimators will be unbiased. We conclude that (i) consideration of these estimands can help guide the choice of which analysis method is most appropriate; and (ii) the re-randomisation design with an independence estimator can be a useful approach in multi-episode settings.

Statistical analysis plan for the Early Youth Engagement in first episode psychosis (EYE-2) study: a pragmatic cluster randomised controlled trial of implementation, effectiveness and cost-effectiveness of a team-based motivational engagement intervention to improve engagement.

BACKGROUND: Early Intervention in Psychosis (EIP) services improve health outcomes for young people with psychosis in the medium-long term, but 25% of young people disengage in the first 12 months with costs to their mental health, families, society and health services. This study will evaluate the effectiveness of a team-based motivational engagement intervention, the Early Youth Engagement (EYE-2) intervention. METHODS AND DESIGN: The EYE-2 trial is a cluster randomised controlled trial comparing the EYE-2 intervention plus standardised EIP service to standardised EIP service alone, with randomisation at the clinical team (cluster) level. The study aimed to enrol 950 young people (aged 14-35 years) with first episode psychosis in 10 teams per arm. RESULTS: The primary outcome is time to disengagement: days from the date of allocation to care coordinator to date of the last contact following either refusal to engage with an EIP team or lack of response to EIP contact for 3 consecutive months which will be analysed using a shared frailty model. Secondary outcomes are Health of the Nation Outcome Scale (HoNOS), Process of Recovery Questionnaire (QPR), DIALOG (a service user-reported measure of quality of life and treatment satisfaction) and service use outcomes which will be analysed using mixed effects regression models. DISCUSSION: This paper is the detailed statistical analysis plan for the EYE-2 trial. Any changes to, or deviations from, this plan will be described and justified in the final trial report. TRIAL REGISTRATION: ISRCTN 51629746 . Prospectively registered on 7 May 2019. Date assigned 10 May 2019.

Independence estimators for re-randomisation trials in multi-episode settings: a simulation study.

BACKGROUND: Re-randomisation trials involve re-enrolling and re-randomising patients for each new treatment episode they experience. They are often used when interest lies in the average effect of an intervention across all the episodes for which it would be used in practice. Re-randomisation trials are often analysed using independence estimators, where a working independence correlation structure is used. However, research into independence estimators in the context of re-randomisation has been limited. METHODS: We performed a simulation study to evaluate the use of independence estimators in re-randomisation trials. We focussed on a continuous outcome, and the setting where treatment allocation does not affect occurrence of subsequent episodes. We evaluated different treatment effect mechanisms (e.g. by allowing the treatment effect to vary across episodes, or to become less effective on re-use, etc), and different non-enrolment mechanisms (e.g. where patients who experience a poor outcome are less likely to re-enrol for their second episode). We evaluated four different independence estimators, each corresponding to a different estimand (per-episode and per-patient approaches, and added-benefit and policy-benefit approaches). RESULTS: We found that independence estimators were unbiased for the per-episode added-benefit estimand in all scenarios we considered. We found independence estimators targeting other estimands (per-patient or policy-benefit) were unbiased, except when there was differential non-enrolment between treatment groups (i.e. when different types of patients from each treatment group decide to re-enrol for subsequent episodes). We found the use of robust standard errors provided close to nominal coverage in all settings where the estimator was unbiased. CONCLUSIONS: Careful choice of estimand can ensure re-randomisation trials are addressing clinically relevant questions. Independence estimators are a useful approach, and should be considered as the default estimator until the statistical properties of alternative estimators are thoroughly evaluated.

Optimal design of cluster randomized trials allowing unequal allocation of clusters and unequal cluster size between arms.

There are sometimes cost, scientific, or logistical reasons to allocate individuals unequally in an individually randomized trial. In cluster randomized trials we can allocate clusters unequally and/or allow different cluster size between trial arms. We consider parallel group designs with a continuous outcome, and optimal designs that require the smallest number of individuals to be measured given the number of clusters. Previous authors have derived the optimal allocation ratio for clusters under different variance and/or intracluster correlations (ICCs) between arms, allowing different but prespecified cluster sizes by arm. We derive closed-form expressions to identify the optimal proportions of clusters and of individuals measured for each arm, thereby defining optimal cluster sizes, when cluster size can be chosen freely. When ICCs differ between arms but the variance is equal, the optimal design allocates more than half the clusters to the arm with the higher ICC, but (typically only slightly) less than half the individuals and hence a smaller cluster size. We also describe optimal design under constraints on the number of clusters or cluster size in one or both arms. This methodology allows trialists to consider a range for the number of clusters in the trial and for each to identify the optimal design. Except if there is clear prior evidence for the ICC and variance by arm, a range of values will need to be considered. Researchers should choose a design with adequate power across the range, while also keeping enough clusters in each arm to permit the intended analysis method.

Clinical Impact of Rectal Hyposensitivity: A Cross-Sectional Study of 2,876 Patients With Refractory Functional Constipation.

INTRODUCTION: Normal bowel function requires intact sensory pathways. Diminished rectal sensation (rectal hyposensitivity [RH]) is associated with constipation, although its clinical importance remains unclear. METHODS: Consecutive patients (aged 18-80) attending a tertiary center (2004-2016) for investigation of refractory functional constipation (Rome IV core criteria defined, applied post hoc) were included. Patients completed a clinical symptom questionnaire and underwent anorectal physiologic investigations, including rectal sensory testing (balloon distension) to determine 3 well-established sensory thresholds. Multivariate regression analyses were performed to evaluate associations between RH, symptomology, and allied physiologic investigations. RESULTS: Of 2,876 patients meeting inclusion criteria, 722 (25%) had RH based on ≥1 elevated sensory thresholds (0: n = 2,154 [74.9%]; 1: n = 327 [11.4%]; 2: n = 209 [7.3%]; and 3: n = 186 [6.5%]). A linear relationship existed between increasing number of elevated sensory thresholds and constipation severity (Cleveland Clinic constipation score: mean difference per threshold [95% confidence interval] 0.69 [0.48-0.90]; P < 0.001). Several symptoms were significantly (P < 0.05) associated with RH including: infrequent defecation (odds ratio 1.29 [1.17-1.42]), painful evacuation (1.15 [1.05-1.27]), prolonged toileting (1.14 [1.05-1.24]), and digitation or enema use (1.18 [1.08-1.30]). On defecography, a "functional" evacuation disorder was also associated with RH (1.37 [1.25-1.50], P < 0.001), as was megarectum (2.52 [2.08-3.05], P < 0.001). DISCUSSION: RH occurs in 25% of patients with refractory functional constipation. Increased number of elevated sensory thresholds is associated with more severe constipation phenotype. These data, in the largest study to date, provide for the first time evidence to show that RH is a major pathophysiologic mechanism in constipation, with recognized clinical impact (http://links.lww.com/AJG/B765).(Equation is included in full-text article.).

The Early Youth Engagement in first episode psychosis (EYE-2) study: pragmatic cluster randomised controlled trial of implementation, effectiveness and cost-effectiveness of a team-based motivational engagement intervention to improve engagement.

BACKGROUND: Early Intervention in Psychosis (EIP) services improve health outcomes for young people with psychosis in the medium-long term, but 25% of young people disengage in the first 12 months with costs to their mental health, families, society and the NHS. This study will evaluate the effectiveness, cost-effectiveness and implementation of a team-based motivational Early Youth Engagement (EYE-2) intervention. METHOD: The study design is a cluster randomised controlled trial (RCT) with economic evaluation, comparing the EYE-2 intervention + standardised EIP service to standardised EIP service alone, with randomisation at the team level. A process evaluation will evaluate the delivery of the intervention qualitatively and quantitatively across contexts. The setting is 20 EIP teams in 5 sites: Manchester, South London, East Anglia, Thames Valley and Hampshire. Participants are young people (14-35 years) with first episode psychosis, and EIP staff. The intervention is the team-based motivational engagement (EYE-2) intervention, delivered alongside standardised EIP services, and supported by additional training, website, booklets and social groups. The comparator is the standardised EIP service. Both interventions are delivered by EIP clinicians. The primary outcome is time to disengagement (time in days from date of allocation to care coordinator to date of last contact following refusal to engage with EIP service, or lack of response to EIP contact for a consecutive 3-month period). Secondary outcomes include mental and physical health, deaths, social and occupational function, recovery, satisfaction and service use at 6, 12, 18 and 24 months. A 12-month within-trial economic evaluation will investigate cost-effectiveness from a societal perspective and from an NHS perspective. DISCUSSION: The trial will provide the first test of an engagement intervention in standardised care, with the potential for significant impact on the mental health and wellbeing of young people and their families, and economic benefits for services. The intervention will be highly scalable, supported by the toolkit including manuals, commissioning guide, training and resources, adapted to meet the needs of the diverse EIP population, and based on an in-depth process evaluation. TRIAL REGISTRATION: ISRCTN 51629746 prospectively registered 7th May 2019. Date assigned 10th May 2019.

Key concepts in clinical epidemiology: Stepped wedge trials.

A stepped wedge trial evaluates an intervention that is implemented over a number of time periods according to a staggered timetable. Stepped wedge trials are usually cluster randomized, the intervention being delivered at some geographical, service or other cluster level. There is considerable variety in the design and conduct of stepped wedge trials in practice. The analysis of a stepped wedge trial often assumes that the effect of the intervention is maintained at a constant level once it has been implemented. It is important when estimating this effect to adjust for a period effect or underlying secular trend, since time is confounded with intervention, and to account for the clustering of outcomes. The advantage often cited for a stepped wedge design is that every cluster ends up getting the intervention, though in any trial design we can offer the intervention preferentially to control clusters after the trial has finished. The real advantage of a stepped wedge design is likely to be practicality or statistical efficiency.