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Background We consider the design of stepped wedge trials with continuous recruitment and continuous outcome measures. Suppose we recruit from a fixed number of clusters where eligible participants present continuously, and suppose we have fine control over when each cluster crosses to the intervention. Suppose also that we want to minimise the number of participants, leading us to consider “incomplete” designs (i.e. without full recruitment). How can we schedule recruitment and cross-over at different clusters to recruit efficiently while achieving good precision? Methods The large number of possible designs can make exhaustive searches impractical. Instead we consider an algorithm using iterative improvements to hunt for an efficient design. At each iteration (starting from a complete design) a single participant – the one with the smallest impact on precision – is removed, and small changes preserving total sample size are made until no further improvement in precision can be found. Results Striking patterns emerge. Solutions typically focus recruitment and cross-over on the leading diagonal of the cluster-by-time diagram, but in some scenarios clusters form distinct phases resembling before-and-after designs. Conclusions There is much to be learned about optimal design for incomplete stepped wedge trials. Algorithmic searches could offer a practical approach to trial design in complex settings generally.

Randomised trials with long-term follow-up can provide estimates of the long-term effects of health interventions. However, analysis of long-term outcomes in randomised trials may be complicated by problems with the administration of treatment such as non-adherence, treatment switching and co-intervention, and problems obtaining outcome measurements arising from loss to follow-up and death of participants. Methods for dealing with these issues that involve conditioning on post-randomisation variables are unsatisfactory because they may involve the comparison of non-exchangeable groups and generate estimates that do not have a valid causal interpretation. We describe approaches to analysis that potentially provide estimates of causal effects when such issues arise. Brief descriptions are provided of the use of instrumental variable and propensity score methods in trials with imperfect adherence, marginal structural models and g-estimation in trials with treatment switching, mixed longitudinal models and multiple imputation in trials with loss to follow-up, and a sensitivity analysis that can be used when trial follow-up is truncated by death or other events. Clinical trialists might consider these methods both at the design and analysis stages of randomised trials with long-term follow-up.

Background The aim of this study was to examine the relationship between psychological characteristics and physical activity levels, measured as the average number of steps per day, in people with knee osteoarthritis (OA). Methods This study analysed baseline data from a randomized controlled trial (Australian New Zealand Clinical Trials Registry reference: ACTRN12612000308897). A total of 167 adults aged over 50 years, with knee pain rated as four or more on an 11-point numeric rating scale, and knee OA diagnosed using American College of Rheumatology clinical criteria, were recruited from the community (62 men and 105 women, mean age, 62.2 ± 7.5 years). The average number of steps per day over seven consecutive days was measured using an accelerometer-based device. Psychological characteristics evaluated were: depressive symptoms (Depression Anxiety Stress Scale), self-efficacy (Arthritis Self-Efficacy Scale for pain and other symptoms), fear of movement (Brief Fear of Movement Scale for Osteoarthritis), and pain catastrophizing (Pain Catastrophizing Scale). The association between the average number of steps per day and psychological characteristics was analyzed using a multiple linear regression analysis, with the average number of steps per day as the dependent variable, adjusting for each psychological characteristic separately, and age, sex, body mass index, and pain entered as covariates. Results There was evidence that the amount of physical activity was associated with fear of movement (coefficient [B]: − 117, 95% confidence interval [95%CI]: − 227 to − 8) and with pain catastrophizing (B: -44, 95%CI: − 86 to − 1). The association with self-efficacy was similar (B:117, 95%CI: − 12 to 246). However, the direction of the association with depressive symptoms was less clear (B: -59, 95%CI: − 138 to 19). Conclusions The results of this study revealed that the relationship was such that lower fear of movement and lower pain catastrophizing may be associated with more steps per day. It may be hypothesized that fear of moving and pain catastrophizing lead to activity avoidance and that strategies to improve these disease-related psychological aspects may be useful in enhancing physical activity participation, although this hypothesis is highly speculative and needs further testing given the cross-sectional design of this study.

Background Simulation is an important tool for assessing the performance of statistical methods for the analysis of data and for the planning of studies. While methods are available for the simulation of correlated binary random variables, all have significant practical limitations for simulating outcomes from longitudinal cluster randomised trial designs, such as the cluster randomised crossover and the stepped wedge trial designs. For these trial designs as the number of observations in each cluster increases these methods either become computationally infeasible or their range of allowable correlations rapidly shrinks to zero. Methods In this paper we present a simple method for simulating binary random variables with a specified vector of prevalences and correlation matrix. This method allows for the outcome prevalence to change due to treatment or over time, and for a ‘nested exchangeable’ correlation structure, in which observations in the same cluster are more highly correlated if they are measured in the same time period than in different time periods, and where different individuals are measured in each time period. This means that our method is also applicable to more general hierarchical clustered data contexts, such as students within classrooms within schools. The method is demonstrated by simulating 1000 datasets with parameters matching those derived from data from a cluster randomised crossover trial assessing two variants of stress ulcer prophylaxis. Results Our method is orders of magnitude faster than the most well known general simulation method while also allowing a much wider range of correlations than alternative methods. An implementation of our method is available in an R package NestBin . Conclusions This simulation method is the first to allow for practical and efficient simulation of large datasets of binary outcomes with the commonly used nested exchangeable correlation structure. This will allow for much more effective testing of designs and inference methods for longitudinal cluster randomised trials with binary outcomes.

Background Standard stepped wedge trials, where clusters switch from the control to the intervention condition in a staggered manner, can be costly and burdensome. Recent work has shown that the amount of information contributed by each cluster in each period differs, with some cluster-periods contributing a relatively small amount of information. We investigate the patterns of the information content of cluster-period cells upon iterative removal of low-information cells, assuming a model for continuous outcomes with constant cluster-period size, categorical time period effects, and exchangeable and discrete-time decay intracluster correlation structures. Methods We sequentially remove pairs of “centrosymmetric” cluster-period cells from an initially complete stepped wedge design which contribute the least amount of information to the estimation of the treatment effect. At each iteration, we update the information content of the remaining cells, determine the pair of cells with the lowest information content, and repeat this process until the treatment effect cannot be estimated. Results We demonstrate that as more cells are removed, more information is concentrated in the cells near the time of the treatment switch, and in “hot-spots” in the corners of the design. For the exchangeable correlation structure, removing the cells from these hot-spots leads to a marked reduction in study precision and power, however the impact of this is lessened for the discrete-time decay structure. Conclusions Removing cluster-period cells distant from the time of the treatment switch may not lead to large reductions in precision or power, implying that certain incomplete designs may be almost as powerful as complete designs.

Background Staircase designs are incomplete stepped wedge designs that, unlike standard stepped wedge designs, require clusters to contribute data for only a limited number of trial periods. Previous work has provided formulae based on asymptotic results for the calculation of the power of staircase designs to detect treatment effects of interest. Methods We conduct a simulation study to assess the finite sample performance of these formulae, and the impact of misspecifying the correlation structure when analysing data from staircase designs on inference for the treatment effect, under a range of realistic trial settings. This study focuses on basic staircase designs with one control period followed by one intervention period in each sequence. We simulate staircase trial datasets with continuous outcomes and a repeated cross-sectional measurement scheme under exchangeable and block-exchangeable intracluster correlation structures, and then fit linear mixed models with linear and categorical time period effects. For settings with a small number of clusters, Kenward-Roger and Satterthwaite small-sample corrections are applied. Comparisons are made between nominal and observed Type I error rates, and theoretically-derived study power and empirical power. The impact on inference for the treatment effect when misspecifying the intracluster correlation structure is assessed through considering performance metrics including bias and 95% confidence interval coverage. Results Data analysis assuming an exchangeable correlation structure and application of the Satterthwaite correction controls Type I error well when the correlation structure is correctly specified, and there are a sufficient number of clusters. For the true block-exchangeable model, when fitting the correct model with the Satterthwaite correction, the observed Type I error (empirical power) can be higher (lower) than the nominal (i.e., theoretical) value when there is only 1 cluster per sequence, but otherwise, it aligns well with the nominal (theoretical) value. Misspecification of the correlation structure (fitting an exchangeable model when the true structure is block-exchangeable) can lead to inflated Type I error and poor confidence interval coverage. Conclusions Staircase designs with one cluster per sequence should be used with caution. Additionally, using a correlation structure that allows for decay is preferable for making valid inferences for the estimation of the treatment effect.

Background Stepped wedge trials are an appealing and potentially powerful cluster randomized trial design. However, they are frequently implemented with a small number of clusters. Standard analysis methods for these trials such as a linear mixed model with estimation via maximum likelihood or restricted maximum likelihood (REML) rely on asymptotic properties and have been shown to yield inflated type I error when applied to studies with a small number of clusters. Small-sample methods such as the Kenward-Roger approximation in combination with REML can potentially improve estimation of the fixed effects such as the treatment effect. A Bayesian approach may also be promising for such multilevel models but has not yet seen much application in cluster randomized trials. Methods We conducted a simulation study comparing the performance of REML with and without a Kenward-Roger approximation to a Bayesian approach using weakly informative prior distributions on the intracluster correlation parameters. We considered a continuous outcome and a range of stepped wedge trial configurations with between 4 and 40 clusters. To assess method performance we calculated bias and mean squared error for the treatment effect and correlation parameters and the coverage of 95% confidence/credible intervals and relative percent error in model-based standard error for the treatment effect. Results Both REML with a Kenward-Roger standard error and degrees of freedom correction and the Bayesian method performed similarly well for the estimation of the treatment effect, while intracluster correlation parameter estimates obtained via the Bayesian method were less variable than REML estimates with different relative levels of bias. Conclusions The use of REML with a Kenward-Roger approximation may be sufficient for the analysis of stepped wedge cluster randomized trials with a small number of clusters. However, a Bayesian approach with weakly informative prior distributions on the intracluster correlation parameters offers a viable alternative, particularly when there is interest in the probability-based inferences permitted within this paradigm.

Background Knee osteoarthritis (OA) is a global problem that causes significant pain and physical dysfunction, substantially impacting on quality of life and imposing enormous cost to the healthcare system. Exercise is pivotal to OA management, yet uptake by people with knee OA is inadequate. Limited access to appropriately skilled health professionals, such as physiotherapists, for prescription of an exercise program and support with exercise is a major barrier to optimal care. Internet-enabled video consultations permit widespread reach. However, services offering video consultations with physiotherapists for musculoskeletal conditions are scant in Australia where there is typically no Government or private health insurer funding for such services. The paucity of robust evidence demonstrating video consultations with physiotherapists are clinically effective, safe and cost-effective for knee OA is hampering implementation of, and willingness of healthcare policymakers to pay for, these services. Methods This is an assessor- and participant-blinded, two-arm, pragmatic, comparative effectiveness non-inferiority randomised controlled trial (RCT) conducted in Australia. We are recruiting 394 people from the community with chronic knee pain consistent with a clinical diagnosis of knee OA. Participants are randomly allocated to receive physiotherapy care via i) video-conferencing or; ii) face-to-face consultations. Participants are provided five consultations (30–45 min each) with a physiotherapist over 3 months for prescription of a home-based strengthening exercise program (to be conducted independently at home) and physical activity plan, as well as OA education. Participants in both groups are provided with educational booklets and simple exercise equipment via post. The co-primary outcomes are change in self-reported i) knee pain on walking; and ii) physical function, with a primary end-point of 3 months and a secondary end-point of 9 months. Secondary outcomes include changes in other clinical outcomes (health-related quality of life; therapeutic relationship; global ratings of change; satisfaction with care; self-efficacy; physical activity levels), time and financial costs of attending consultations, healthcare usage and convenience. Non-inferiority will be assessed using the per-protocol dataset. Discussion Findings will determine if video consultations with physiotherapists are non-inferior to traditional face-to-face consultations for management of people with knee OA. Trial registration Australian New Zealand Clinical Trials Registry, ACTRN12619001240134. http://www.anzctr.org.au/Trial/Registration/TrialReview.aspx?id=377672&isReview=true

IntroductionWomen living in rural and regional Australia often experience difficulties in accessing long-acting reversible contraception (LARC) and medical abortion services. Nurse-led models of care can improve access to these services but have not been evaluated in Australian general practice. The primary aim of the ORIENT trial (ImprOving Rural and regIonal accEss to long acting reversible contraceptioN and medical abortion through nurse-led models of care, Tasksharing and telehealth) is to assess the effectiveness of a nurse-led model of care in general practice at increasing uptake of LARC and improving access to medical abortion in rural and regional areas.Methods and analysisORIENT is a stepped-wedge pragmatic cluster-randomised controlled trial. We will enrol 32 general practices (clusters) in rural or regional Australia, that have at least two general practitioners, one practice nurse and one practice manager. The nurse-led model of care (the intervention) will be codesigned with key women’s health stakeholders. Clusters will be randomised to implement the model sequentially, with the comparator being usual care. Clusters will receive implementation support through clinical upskilling, educational outreach and engagement in an online community of practice. The primary outcome is the change in the rate of LARC prescribing comparing control and intervention phases; secondary outcomes include change in the rate of medical abortion prescribing and provision of related telehealth services. A within-trial economic analysis will determine the relative costs and benefits of the model on the prescribing rates of LARC and medical abortion compared with usual care. A realist evaluation will provide contextual information regarding model implementation informing considerations for scale-up. Supporting nurses to work to their full scope of practice has the potential to increase LARC and medical abortion access in rural and regional Australia.Ethics and disseminationEthics approval was obtained from the Monash University Human Research Ethics Committee (Project ID: 29476). Findings will be disseminated via multiple avenues including a knowledge exchange workshop, policy briefs, conference presentations and peer-reviewed publications.Trial registration numberThis trial is registered with the Australian New Zealand Clinical Trials Registry (ACTRN12622000086763).

Background There are numerous approaches available to analyse data from cluster randomised trials. These include cluster-level summary methods and individual-level methods accounting for clustering, such as generalised estimating equations and generalised linear mixed models. There has been much methodological work showing that estimates of treatment effects can vary depending on the choice of approach, particularly when estimating odds ratios, essentially because the different approaches target different estimands. Methods In this manuscript, we describe the protocol for a planned re-analysis of data from a large number of cluster randomised trials. Our main objective is to examine empirically whether and how odds ratios estimated using different approaches (for both primary and secondary binary outcomes) vary in cluster randomised trials. We describe the methods that will be used to identify the datasets for inclusion and how they will be analysed and reported. Discussion There have been a number of small comparisons of empirical differences between the different approaches to analysis for CRTs. The systematic approach outlined in this protocol will allow a much deeper understanding of when there are important choices around the model approach and in which settings. This will be of importance given the heightened awareness of the importance of estimands and the specification of statistical analysis plans.