The hunt for efficient, incomplete designs for stepped wedge trials with continuous recruitment and continuous outcome measures

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 ρ τ 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 m ρ / ( 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.

Adherence to key recommendations for design and analysis of stepped-wedge cluster randomized trials: A review of trials published 2016-2022

BACKGROUND/AIMS

The stepped-wedge cluster randomized trial (SW-CRT), in which clusters are randomized to a time at which they will transition to the intervention condition - rather than a trial arm - is a relatively new design. SW-CRTs have additional design and analytical considerations compared to conventional parallel arm trials. To inform future methodological development, including guidance for trialists and the selection of parameters for statistical simulation studies, we conducted a review of recently published SW-CRTs. Specific objectives were to describe (1) the types of designs used in practice, (2) adherence to key requirements for statistical analysis, and (3) practices around covariate adjustment. We also examined changes in adherence over time and by journal impact factor.

METHODS

We used electronic searches to identify primary reports of SW-CRTs published 2016-2022. Two reviewers extracted information from each trial report and its protocol, if available, and resolved disagreements through discussion.

RESULTS

We identified 160 eligible trials, randomizing a median (Q1-Q3) of 11 (8-18) clusters to 5 (4-7) sequences. The majority (122, 76%) were cross-sectional (almost all with continuous recruitment), 23 (14%) were closed cohorts and 15 (9%) open cohorts. Many trials had complex design features such as multiple or multivariate primary outcomes (50, 31%) or time-dependent repeated measures (27, 22%). The most common type of primary outcome was binary (51%); continuous outcomes were less common (26%). The most frequently used method of analysis was a generalized linear mixed model (112, 70%); generalized estimating equations were used less frequently (12, 8%). Among 142 trials with fewer than 40 clusters, only 9 (6%) reported using methods appropriate for a small number of clusters. Statistical analyses clearly adjusted for time effects in 119 (74%), for within-cluster correlations in 132 (83%), and for distinct between-period correlations in 13 (8%). Covariates were included in the primary analysis of the primary outcome in 82 (51%) and were most often individual-level covariates; however, clear and complete pre-specification of covariates was uncommon. Adherence to some key methodological requirements (adjusting for time effects, accounting for within-period correlation) was higher among trials published in higher versus lower impact factor journals. Substantial improvements over time were not observed although a slight improvement was observed in the proportion accounting for a distinct between-period correlation.

CONCLUSIONS

Future methods development should prioritize methods for SW-CRTs with binary or time-to-event outcomes, small numbers of clusters, continuous recruitment designs, multivariate outcomes, or time-dependent repeated measures. Trialists, journal editors, and peer reviewers should be aware that SW-CRTs have additional methodological requirements over parallel arm designs including the need to account for period effects as well as complex intracluster correlations.

Information content of stepped wedge designs under the working independence assumption

The stepped wedge design is increasingly popular in pragmatic trials and implementation science research studies for evaluating system-level interventions that are perceived to be beneficial to patient populations. An important step in planning a stepped wedge design is to understand the efficiency of the treatment effect estimator and hence the power of the study. We develop several novel analytical results for designing stepped wedge cluster randomized trials analyzed through generalized estimating equations under a misspecified working independence correlation structure. We first contribute a general variance expression of the treatment effect estimator when data collection is scheduled for each cluster-period. Because resource and patient-centered considerations may intentionally call for an incomplete design with outcome data being omitted for certain cluster-periods, we further derive the information content based on the robust sandwich variance to identify data elements that may be preferentially omitted with minimum loss of precision in estimating the treatment effect. We prove that centrosymmetric pairs of cluster-periods, treatment sequences and periods have identical information content and thus contribute equally to the treatment effect estimation, as long as the true covariance structure for the cluster-period means remains centrosymmetric. Finally, we provide an example of how to obtain an incomplete stepped wedge design that admits a more efficient independence GEE estimator but requires less data collection effort. Our results elegantly extend existing ones from linear mixed models coupled with model-based variances to accommodate a misspecified independence working correlation structure through the robust sandwich variances.

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.

Optimal study designs for cluster randomised trials: An overview of methods and results

There are multiple possible cluster randomised trial designs that vary in when the clusters cross between control and intervention states, when observations are made within clusters, and how many observations are made at each time point. Identifying the most efficient study design is complex though, owing to the correlation between observations within clusters and over time. In this article, we present a review of statistical and computational methods for identifying optimal cluster randomised trial designs. We also adapt methods from the experimental design literature for experimental designs with correlated observations to the cluster trial context. We identify three broad classes of methods: using exact formulae for the treatment effect estimator variance for specific models to derive algorithms or weights for cluster sequences; generalised methods for estimating weights for experimental units; and, combinatorial optimisation algorithms to select an optimal subset of experimental units. We also discuss methods for rounding experimental weights, extensions to non-Gaussian models, and robust optimality. We present results from multiple cluster trial examples that compare the different methods, including determination of the optimal allocation of clusters across a set of cluster sequences and selecting the optimal number of single observations to make in each cluster-period for both Gaussian and non-Gaussian models, and including exchangeable and exponential decay covariance structures.

The thriving kids and parents schools project: protocol of an incomplete stepped wedged cluster randomised trial evaluating the effectiveness of a Triple P seminar series

BACKGROUND

The COVID-19 pandemic disrupted the normality of daily life for many children, their families, and schools, resulting in heightened levels of anxiety, depression, social isolation, and loneliness among young people. An integrated public health model of interventions is needed to address the problem and to safeguard the mental health and wellbeing of children. The Triple P - Positive Parenting Program is one system of parenting support with a strong evidence-base and wide international reach. When implemented as a public health approach, Triple P has demonstrated population level positive effects on child wellbeing. This study will be the first large-scale, multi-site randomised controlled trial of a newly developed, low-intensity variant of Triple P, a school-based seminar series, as a response to the impacts of the pandemic.

METHODS

The evaluation will employ an Incomplete Batched Stepped Wedge Cluster Randomised Trial Design. At least 300 Australian primary schools, from South Australia, Queensland, and Victoria will be recruited and randomised in three batches. Within each batch, schools will be randomly assigned to either start the intervention immediately or start in six weeks. Parents will be recruited from participating schools. The Triple P seminar series includes three seminars titled: "The Power of Positive Parenting", "Helping Your Child to Manage Anxiety", and "Keeping your Child Safe from Bullying". Parents will complete measures about child wellbeing, parenting, parenting self-regulation and other key intervention targets at baseline, six weeks after baseline, and 12 weeks after baseline. Intervention effectiveness will be evaluated with a Multilevel Piecewise Latent Growth Curve Modelling approach. Data collection is currently underway, and the current phase of the project is anticipated to be completed in January 2024.

DISCUSSION

The findings from this study will extend the current knowledge of the effects of evidence-based parenting support delivered through brief, universally offered, low intensity, school-based parenting seminars in a post pandemic world.

TRIAL REGISTRATION

The trial is registered at the Australian New Zealand Clinical Trials Registry (Trial Registration Number: ACTRN12623000852651).

Generalizing the information content for stepped wedge designs: A marginal modeling approach

Stepped wedge trials are increasingly adopted because practical constraints necessitate staggered roll-out. While a complete design requires clusters to collect data in all periods, resource and patient-centered considerations may call for an incomplete stepped wedge design to minimize data collection burden. To study incomplete designs, we expand the metric of information content to discrete outcomes. We operate under a marginal model with general link and variance functions, and derive information content expressions when data elements (cells, sequences, periods) are omitted. We show that the centrosymmetric patterns of information content can hold for discrete outcomes with the variance-stabilizing link function. We perform numerical studies under the canonical link function, and find that while the patterns of information content for cells are approximately centrosymmetric for all examined underlying secular trends, the patterns of information content for sequences or periods are more sensitive to the secular trend, and may be far from centrosymmetric.

Evaluation of combinatorial optimisation algorithms for c-optimal experimental designs with correlated observations

We show how combinatorial optimisation algorithms can be applied to the problem of identifying c-optimal experimental designs when there may be correlation between and within experimental units and evaluate the performance of relevant algorithms. We assume the data generating process is a generalised linear mixed model and show that the c-optimal design criterion is a monotone supermodular function amenable to a set of simple minimisation algorithms. We evaluate the performance of three relevant algorithms: the local search, the greedy search, and the reverse greedy search. We show that the local and reverse greedy searches provide comparable performance with the worst design outputs having variance < 10 % greater than the best design, across a range of covariance structures. We show that these algorithms perform as well or better than multiplicative methods that generate weights to place on experimental units. We extend these algorithms to identifying modle-robust c-optimal designs.

Supplementary Information

The online version contains supplementary material available at 10.1007/s11222-023-10280-w.

The impact of iterative removal of low-information cluster-period cells from a stepped wedge design

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.

Enhancing doctor-patient relationships in community health care institutions: the Patient Oriented Four Habits Model (POFHM) trial-a stepped wedge cluster randomized trial protocol

BACKGROUND

The poor relationship between doctors and patients is a long-standing, global problem. However, current interventions tend to focus on the training of physicians, while patient-targeted interventions still need to be improved. Considering that patients play a significant role in outpatient consultations, we developed a protocol to assess the effectiveness of the Patient Oriented Four Habits Model (POFHM) in improving doctor-patient relationships.

METHODS

A cross-sectional incomplete stepped-wedge cluster randomized trial design will be conducted in 8 primary healthcare institutions (PHCs). Following phase I of "usual care" as control measures for each PHC, either a patient- or doctor-only intervention will be implemented in phase II. In phase III, both patients and doctors will be involved in the intervention. This study will be conducted simultaneously in Nanling County and West Lake District. The primary outcomes will be evaluated after patients complete their visit: (1) patient literacy, (2) sense of control and (3) quality of doctor-patient communication. Finally, a mixed-effects model and subgroup analysis will be used to evaluate the effectiveness of the interventions.

DISCUSSION

Fostering good consultation habits for the patient is a potentially effective strategy to improve the quality of doctor-patient communication. This study evaluates the implementation process and develops a rigorous quality control manual using a theoretical domain framework under the collective culture of China. The results of this trial will provide substantial evidence of the effectiveness of patient-oriented interventions. The POFHM can benefit the PHCs and provide a reference for countries and regions where medical resources are scarce and collectivist cultures dominate.

TRIAL REGISTRATION

AsPredicted #107,282 on Sep 18, 2022; https://aspredicted.org/QST_MHW.

Assessing the implementation and effectiveness of early integrated palliative care in long-term care facilities in France: an interventional mixed-methods study protocol

BACKGROUND

Majority of residents in long-term care facilities (LTCF) have limited and delayed access to palliative care even though many suffer from incurable chronic illnesses that will likely require the provision of palliative care. We present the study protocol of "PADI-Palli", an intervention aims to advance early integrated palliative care into standard care delivered in LTCF. This study will assess the effectiveness of early integrated palliative care on palliative care accessibility for older persons in LTCF, and identify the key factors for the successful implementation of early integrated palliative care and its sustainability in the LTCF context.

METHODS

This multicentre interventional study utilises a pragmatic research design with a convergent parallel mixed-methods approach. The qualitative study will use a case study design and the quantitative study will use a stepped wedge cluster randomised trial. In total, 21 participating LTCF from three French regions will be randomly allocated to one of seven clusters. The clusters will cross over from the usual care to the active intervention condition over the course of the study. The primary outcome relates to the accurate identification of palliative care needs and early access to palliative care for LTCF residents. Secondary outcomes are quality of care, quality of life for residents and their families, and quality of life at work for professionals. Measurements will be performed before and after the intervention. Implementation and evaluation of PADI-Palli intervention is grounded in the Consolidated Framework for Implementation Research.

DISCUSSION

Existing evidence demonstrates that early integrated palliative care in cancer care leads to a significant improvement in patient outcomes and processes of care. Little is known, however, about early integrated palliative care in the context of LTCF for older persons. This study has the potential to fill this gap in the literature by providing evidence on the effectiveness of early integrated palliative care for older persons in LTCF. Moreover, this study will provide a better understanding of the relevant contextual elements that facilitate or hinder early integrated palliative care implementation and transferability. If proven effective, this intervention can be scaled to other care settings in which older persons require palliative care.

TRIAL REGISTRATION

ClinicalTrials.gov ID: NCT04708002; National registration: ID-RCB number: 2020-A01832-37.

Sample size calculators for planning stepped-wedge cluster randomized trials: a review and comparison

Recent years have seen a surge of interest in stepped-wedge cluster randomized trials (SW-CRTs). SW-CRTs include several design variations and methodology is rapidly developing. Accordingly, a variety of power and sample size calculation software for SW-CRTs has been developed. However, each calculator may support only a selected set of design features and may not be appropriate for all scenarios. Currently, there is no resource to assist researchers in selecting the most appropriate calculator for planning their trials. In this paper, we review and classify 18 existing calculators that can be implemented in major platforms, such as R, SAS, Stata, Microsoft Excel, PASS and nQuery. After reviewing the main sample size considerations for SW-CRTs, we summarize the features supported by the available calculators, including the types of designs, outcomes, correlation structures and treatment effects; whether incomplete designs, cluster-size variation or secular trends are accommodated; and the analytical approach used. We then discuss in more detail four main calculators and identify their strengths and limitations. We illustrate how to use these four calculators to compute power for two real SW-CRTs with a continuous and binary outcome and compare the results. We show that the choice of calculator can make a substantial difference in the calculated power and explain these differences. Finally, we make recommendations for implementing sample size or power calculations using the available calculators. An R Shiny app is available for users to select the calculator that meets their requirements (https://douyang.shinyapps.io/swcrtcalculator/).