Stepped-wedge cluster randomised controlled trials : a generic framework including parallel and multiple-level designs

Stepped-wedge cluster randomised trials (SW-CRTs) are being used with increasing frequency in health service evaluation. Conventionally, these studies are cross-sectional in design with equally spaced steps, with an equal number of clusters randomised at each step and data collected at each and every step. Here we introduce several variations on this design and consider implications for power. One modification we consider is the incomplete cross-sectional SW-CRT, where the number of clusters varies at each step or where at some steps, for example, implementation or transition periods, data are not collected. We show that the parallel CRT with staggered but balanced randomisation can be considered a special case of the incomplete SW-CRT. As too can the parallel CRT with baseline measures. And we extend these designs to allow for multiple layers of clustering, for example, wards within a hospital. Building on results for complete designs, power and detectable difference are derived using a Wald test and obtaining the variance–covariance matrix of the treatment effect assuming a generalised linear mixed model. These variations are illustrated by several real examples. We recommend that whilst the impact of transition periods on power is likely to be small, where they are a feature of the design they should be incorporated. We also show examples in which the power of a SW-CRT increases as the intra-cluster correlation (ICC) increases and demonstrate that the impact of the ICC is likely to be smaller in a SW-CRT compared with a parallel CRT, especially where there are multiple levels of clustering. Finally, through this unified framework, the efficiency of the SW-CRT and the parallel CRT can be compared

Optimal Study Designs for Cluster Randomised Trials: An Overview of Methods and Results

There are multiple 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 that 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 weights to whole numbers of clusters and extensions to non-Gaussian models. We present results from multiple cluster trial examples that compare the different methods, including problems involving determining 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

Systematic review finds major deficiencies in sample size methodology and reporting for stepped-wedge cluster randomised trials

BACKGROUND: Stepped-wedge cluster randomised trials (SW-CRT) are increasingly being used in health policy and services research, but unless they are conducted and reported to the highest methodological standards, they are unlikely to be useful to decision-makers. Sample size calculations for these designs require allowance for clustering, time effects and repeated measures. METHODS: We carried out a methodological review of SW-CRTs up to October 2014. We assessed adherence to reporting each of the 9 sample size calculation items recommended in the 2012 extension of the CONSORT statement to cluster trials. RESULTS: We identified 32 completed trials and 28 independent protocols published between 1987 and 2014. Of these, 45 (75%) reported a sample size calculation, with a median of 5.0 (IQR 2.5–6.0) of the 9 CONSORT items reported. Of those that reported a sample size calculation, the majority, 33 (73%), allowed for clustering, but just 15 (33%) allowed for time effects. There was a small increase in the proportions reporting a sample size calculation (from 64% before to 84% after publication of the CONSORT extension, p=0.07). The type of design (cohort or cross-sectional) was not reported clearly in the majority of studies, but cohort designs seemed to be most prevalent. Sample size calculations in cohort designs were particularly poor with only 3 out of 24 (13%) of these studies allowing for repeated measures. DISCUSSION: The quality of reporting of sample size items in stepped-wedge trials is suboptimal. There is an urgent need for dissemination of the appropriate guidelines for reporting and methodological development to match the proliferation of the use of this design in practice. Time effects and repeated measures should be considered in all SW-CRT power calculations, and there should be clarity in reporting trials as cohort or cross-sectional designs

Statistical efficiency and optimal design for stepped cluster studies under linear mixed effects models

In stepped cluster designs the intervention is introduced into some (or all) clusters at different times and persists until the end of the study. Instances include traditional parallel cluster designs and the more recent stepped‐wedge designs. We consider the precision offered by such designs under mixed‐effects models with fixed time and random subject and cluster effects (including interactions with time), and explore the optimal choice of uptake times. The results apply both to cross‐sectional studies where new subjects are observed at each time‐point, and longitudinal studies with repeat observations on the same subjects. The efficiency of the design is expressed in terms of a ‘cluster‐mean correlation’ which carries information about the dependency‐structure of the data, and two design coefficients which reflect the pattern of uptake‐times. In cross‐sectional studies the cluster‐mean correlation combines information about the cluster‐size and the intra‐cluster correlation coefficient. A formula is given for the ‘design effect’ in both cross‐sectional and longitudinal studies. An algorithm for optimising the choice of uptake times is described and specific results obtained for the best balanced stepped designs. In large studies we show that the best design is a hybrid mixture of parallel and stepped‐wedge components, with the proportion of stepped wedge clusters equal to the cluster‐mean correlation. The impact of prior uncertainty in the cluster‐mean correlation is considered by simulation. Some specific hybrid designs are proposed for consideration when the cluster‐mean correlation cannot be reliably estimated, using a minimax principle to ensure acceptable performance across the whole range of unknown values. © 2016 The Authors. Statistics in Medicine published by John Wiley & Sons Ltd

BAYESIAN META-ANALYSIS ON MEDICAL DEVICES: APPLICATION TO IMPLANTABLE CARDIOVERTER DEFIBRILLATORS

Objectives: The aim of this study is to describe and illustrate a method to obtain early estimates of the effectiveness of a new version of a medical device

Intra-cluster and inter-period correlation coefficients for cross-sectional cluster randomised controlled trials for type-2 diabetes in UK primary care

BACKGROUND: Clustered randomised controlled trials (CRCTs) are increasingly common in primary care. Outcomes within the same cluster tend to be correlated with one another. In sample size calculations, estimates of the intra-cluster correlation coefficient (ICC) are needed to allow for this nonindependence. In studies with observations over more than one time period, estimates of the inter-period correlation (IPC) and the within-period correlation (WPC) are also needed. METHODS: This is a retrospective cross-sectional study of all patients aged 18 or over with a diagnosis of type-2 diabetes, from The Health Improvement Network (THIN) database, between 1 October 2007 and 31 March 2010. We report estimates of the ICC, IPC, and WPC for typical outcomes using unadjusted and adjusted generalised linear mixed models with cluster and cluster by period random effects. For binary outcomes we report on the proportions scale, which is the appropriate scale for trial design. Estimated ICCs were compared to those reported from a systematic search of CRCTs undertaken in primary care in the UK in type-2 diabetes. RESULTS: Data from 430 general practices, with a median [IQR] number of diabetics per practice of 241 [150–351], were analysed. The ICC for HbA1c was 0.032 (95 % CI 0.026–0.038). For a two-period (each of 12 months) design, the WPC for HbA1c was 0.035 (95 % CI 0.030–0.040) and the IPC was 0.019 (95 % CI 0.014–0.026). The difference between the WPC and the IPC indicates a decay of correlation over time. Following dichotomisation at 7.5 %, the ICC for HbA1c was 0.026 (95 % CI 0.022–0.030). ICCs for other clinical measurements and clinical outcomes are presented. A systematic search of ICCs used in the design of CRCTs involving type-2 diabetes with HbA1c (undichotomised) as the outcome found that published trials tended to use more conservative ICC values (median 0.047, IQR 0.047–0.050) than those reported here. CONCLUSIONS: These estimates of ICCs, IPCs, and WPCs for a variety of outcomes commonly used in diabetes trials can be useful for the design of CRCTs. In studies with observations taken at different time-points, the correlation of observations may decay over time, as reflected in lower values for the IPC than for the ICC. The IPC and WPC estimates are the first reported for UK primary care data. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/s13063-016-1532-9) contains supplementary material, which is available to authorized users

Comparison of intra subject repeatability of quantitative fluoroscopy and static radiography in the measurement of lumbar intervertebral flexion translation

Low back pain patients are sometimes offered fusion surgery if intervertebral translation, measured from static, end of range radiographs exceeds 3mm. However, it is essential to know the measurement error of such methods, if selection for back surgery is going to be informed by them. Fifty-five healthy male (34) and female (21) pain free participants aged 21-80 years received quantitative fluoroscopic (QF) imaging both actively during standing and passively in the lateral decubitus position. The following five imaging protocols were extracted from 2 motion examinations, which were repeated 6 weeks apart: 1. Static during upright free bending. 2. Maximum during controlled upright bending, 3. At the end of controlled upright bending, 4. Maximum during controlled recumbent bending, 5. At the end of controlled recumbent bending. Intervertebral flexion translations from L2-S1 were determined for each protocol and their measurement errors (intra subject repeatability) calculated. Estimations using static, free bending radiographic images gave measurement errors of up to 4mm, which was approximately twice that of the QF protocols. Significantly higher ranges at L4-5 and L5-S1 were obtained from the static protocol compared with the QF protocols. Weight bearing ranges at these levels were also significantly higher in males regardless of the protocol. Clinical decisions based on sagittal translations of less than 4mm would therefore require QF imaging

Sample size calculations for cluster randomised controlled trials with a fixed number of clusters

Background\ud Cluster randomised controlled trials (CRCTs) are frequently used in health service evaluation. Assuming an average cluster size, required sample sizes are readily computed for both binary and continuous outcomes, by estimating a design effect or inflation factor. However, where the number of clusters are fixed in advance, but where it is possible to increase the number of individuals within each cluster, as is frequently the case in health service evaluation, sample size formulae have been less well studied. \ud \ud Methods\ud We systematically outline sample size formulae (including required number of randomisation units, detectable difference and power) for CRCTs with a fixed number of clusters, to provide a concise summary for both binary and continuous outcomes. Extensions to the case of unequal cluster sizes are provided. \ud \ud Results\ud For trials with a fixed number of equal sized clusters (k), the trial will be feasible provided the number of clusters is greater than the product of the number of individuals required under individual randomisation ($n_i$) and the estimated intra-cluster correlation ($\rho$). So, a simple rule is that the number of clusters ($\kappa$) will be sufficient provided: \ud \ud $\kappa$ > $n_i$ x $\rho$\ud \ud Where this is not the case, investigators can determine the maximum available power to detect the pre-specified difference, or the minimum detectable difference under the pre-specified value for power. \ud \ud Conclusions\ud Designing a CRCT with a fixed number of clusters might mean that the study will not be feasible, leading to the notion of a minimum detectable difference (or a maximum achievable power), irrespective of how many individuals are included within each cluster. \ud \u