Intracluster correlation coefficients in cluster randomized trials: empirical insights into how should they be reported.
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ABSTRACT: Background
Increasingly, researchers are recognizing that there are many situations where the use of a cluster randomized trial may be more appropriate than an individually randomized trial. Similarly, the need for appropriate standards of reporting of cluster trials is more widely acknowledged.Methods
In this paper, we describe the results of a survey to inform the appropriate reporting of the intracluster correlation coefficient (ICC)--the statistical measure of the clustering effect associated with a cluster randomized trial.Results
We identified three dimensions that should be considered when reporting an ICC--a description of the dataset (including characteristics of the outcome and the intervention), information on how the ICC was calculated, and information on the precision of the ICC.Conclusions
This paper demonstrates the development of a framework for the reporting of ICCs. If adopted into routine practice, it has the potential to facilitate the interpretation of the cluster trial being reported and should help the development of new trials in the area.
SUBMITTER: Campbell MK
PROVIDER: S-EPMC415547 | biostudies-literature | 2004 Apr
REPOSITORIES: biostudies-literature
Publications
Intracluster correlation coefficients in cluster randomized trials: empirical insights into how should they be reported.
Campbell Marion K MK Grimshaw Jeremy M JM Elbourne Diana R DR
BMC medical research methodology 20040428
<h4>Background</h4>Increasingly, researchers are recognizing that there are many situations where the use of a cluster randomized trial may be more appropriate than an individually randomized trial. Similarly, the need for appropriate standards of reporting of cluster trials is more widely acknowledged.<h4>Methods</h4>In this paper, we describe the results of a survey to inform the appropriate reporting of the intracluster correlation coefficient (ICC)--the statistical measure of the clustering ...[more]
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Project description:BackgroundSample size calculations for cluster randomized trials are a recognized methodological challenge for malaria research in pre-elimination settings. Positively correlated responses from the participants in the same cluster are a key feature in the estimated sample size required for a cluster randomized trial. The degree of correlation is measured by the intracluster correlation coefficient (ICC) where a higher coefficient suggests a closer correlation hence less heterogeneity within clusters but more heterogeneity between clusters.MethodsData on uPCR-detected Plasmodium falciparum and Plasmodium vivax infections from a recent cluster randomized trial which aimed at interrupting malaria transmission through mass drug administrations were used to calculate the ICCs for prevalence and incidence of Plasmodium infections. The trial was conducted in four countries in the Greater Mekong Subregion, Laos, Myanmar, Vietnam and Cambodia. Exact and simulation approaches were used to estimate ICC values for both the prevalence and the incidence of parasitaemia. In addition, the latent variable approach to estimate ICCs for the prevalence was utilized.ResultsThe ICCs for prevalence ranged between 0.001 and 0.082 for all countries. The ICC from the combined 16 villages in the Greater Mekong Subregion were 0.26 and 0.21 for P. falciparum and P. vivax respectively. The ICCs for incidence of parasitaemia ranged between 0.002 and 0.075 for Myanmar, Cambodia and Vietnam. There were very high ICCs for incidence in the range of 0.701 to 0.806 in Laos during follow-up.ConclusionICC estimates can help researchers when designing malaria cluster randomized trials. A high variability in ICCs and hence sample size requirements between study sites was observed. Realistic sample size estimates for cluster randomized malaria trials in the Greater Mekong Subregion have to assume high between cluster heterogeneity and ICCs. This work focused on uPCR-detected infections; there remains a need to develop more ICC references for trials designed around prevalence and incidence of clinical outcomes. Adequately powered trials are critical to estimate the benefit of interventions to malaria in a reliable and reproducible fashion.Trial registrationClinicalTrials.govNCT01872702. Registered 7 June 2013. Retrospectively registered. https://clinicaltrials.gov/ct2/show/NCT01872702.
| S-EPMC6921387 | biostudies-literature
Project description:Background/aimsGeneralized estimating equations are commonly used to fit logistic regression models to clustered binary data from cluster randomized trials. A commonly used correlation structure assumes that the intracluster correlation coefficient does not vary by treatment arm or other covariates, but the consequences of this assumption are understudied. We aim to evaluate the effect of allowing variation of the intracluster correlation coefficient by treatment or other covariates on the efficiency of analysis and show how to account for such variation in sample size calculations.MethodsWe develop formulae for the asymptotic variance of the estimated difference in outcome between treatment arms obtained when the true exchangeable correlation structure depends on the treatment arm and the working correlation structure used in the generalized estimating equations analysis is: (i) correctly specified, (ii) independent, or (iii) exchangeable with no dependence on treatment arm. These formulae require a known distribution of cluster sizes; we also develop simplifications for the case when cluster sizes do not vary and approximations that can be used when the first two moments of the cluster size distribution are known. We then extend the results to settings with adjustment for a second binary cluster-level covariate. We provide formulae to calculate the required sample size for cluster randomized trials using these variances.ResultsWe show that the asymptotic variance of the estimated difference in outcome between treatment arms using these three working correlation structures is the same if all clusters have the same size, and this asymptotic variance is approximately the same when intracluster correlation coefficient values are small. We illustrate these results using data from a recent cluster randomized trial for infectious disease prevention in which the clusters are groups of households and modest in size (mean 9.6 individuals), with intracluster correlation coefficient values of 0.078 in the control arm and 0.057 in an intervention arm. In this application, we found a negligible difference between the variances calculated using structures (i) and (iii) and only a small increase (typically <5%) for the independent correlation structure (ii), and hence minimal effect on power or sample size requirements. The impact may be larger in other applications if there is greater variation in the ICC between treatment arms or with an additional covariate.ConclusionThe common approach of fitting generalized estimating equations with an exchangeable working correlation structure with a common intracluster correlation coefficient across arms likely does not substantially reduce the power or efficiency of the analysis in the setting of a large number of small or modest-sized clusters, even if the intracluster correlation coefficient varies by treatment arm. Our formulae, however, allow formal evaluation of this and may identify situations in which variation in intracluster correlation coefficient by treatment arm or another binary covariate may have a more substantial impact on power and hence sample size requirements.
| S-EPMC8883478 | biostudies-literature
Project description:Cluster randomized trials (cRCT) to assess vaccine effectiveness incorporate indirect effects of vaccination, helping to inform vaccination policy. To calculate the sample size for a cRCT, an estimate of the intracluster correlation coefficient (ICC) is required. For infectious diseases, shared characteristics and social mixing behaviours may increase susceptibility and exposure, promote transmission and be a source of clustering. We present ICCs from a school-based cRCT assessing the effectiveness of a meningococcal B vaccine (Bexsero, GlaxoSmithKline) on reducing oropharyngeal carriage of Neisseria meningitidis (Nm) in 34,489 adolescents from 237 schools in South Australia in 2017/2018. We also explore the contribution of shared behaviours and characteristics to these ICCs. The ICC for carriage of disease-causing Nm genogroups (primary outcome) pre-vaccination was 0.004 (95% CI: 0.002, 0.007) and for all Nm was 0.007 (95%CI: 0.004, 0.011). Adjustment for social behaviours and personal characteristics reduced the ICC for carriage of disease-causing and all Nm genogroups by 25% (to 0.003) and 43% (to 0.004), respectively. ICCs are also reported for risk factors here, which may be outcomes in future research. Higher ICCs were observed for susceptibility and/or exposure variables related to Nm carriage (having a cold, spending ≥1 night out socializing or kissing ≥1 person in the previous week). In metropolitan areas, nights out socializing was a highly correlated behaviour. By contrast, smoking was a highly correlated behaviour in rural areas. A practical example to inform future cRCT sample size estimates is provided.
| S-EPMC8516260 | biostudies-literature
Project description:Objectives: With the emerging trends, more cluster randomized trials will be conducted in older adults, where facilities are randomized rather than individuals. Similarity of individuals from a facility (intraclass correlation coefficient/ICC) plays a critical role, but not readily available. We document ICCs for measures commonly used in community-dwelling older adults and discuss implications. Method: Secondary analysis of a range of baseline measures from the On the Move cluster randomized trial, whose ICCs were computed using a linear mixed model. Results: Self-reported disability measures related to facility characteristics and sense of community had the greatest ICCs (>0.10), while mobility performance measures had 0.05 to 0.10, and cognitive measure 0.11. Discussion: The ICCs for measures commonly used in older adults are of a sufficient magnitude to have a substantial impact on planned sample size of a study and credibility of results, and should be taken into consideration in study planning and data analysis.
| S-EPMC8012005 | biostudies-literature
Project description:The aim of this study was to compute intra-class correlations (ICCs) for weight-related and patient-reported outcomes in a cluster randomized clinical trial (cRCT) for weight loss. Baseline and follow-up data from the Promoting Successful Weight Loss in Primary Care in Louisiana (PROPEL) cRCT were used in this analysis. ICCs were computed for baseline and follow-up measures, and changes in body weight, cardiometabolic risk factors and health-related and weight-related quality of life at 6, 12, 18 and 24 months. Baseline ICCs ranged from 0 for PROMIS measures of anxiety and fatigue to 0.055 for total cholesterol (median = 0.019). The ICCs were higher for changes and decreased over time during follow-up. The ICCs for changes were highest in the pooled sample (intervention and usual care combined) followed by the intervention and usual care groups, respectively. The results demonstrated significant ICCs for several outcomes in a weight loss cRCT. The ICCs differed in magnitude depending on whether baseline versus longitudinal data were used, whether data were combined across treatment arms or were considered separately, and varied across the follow-up period. All these factors must be considered when choosing an ICC to inform sample size estimates for future weight loss cRCTs conducted in primary care settings.
| S-EPMC9283264 | biostudies-literature
Project description:BackgroundThe effectiveness of malaria vector control interventions is often evaluated using cluster randomized trials (CRT) with outcomes assessed using repeated cross-sectional surveys. A key requirement for appropriate design and analysis of longitudinal CRTs is accounting for the intra-cluster correlation coefficient (ICC). In addition to exchangeable correlation (constant ICC over time), correlation structures proposed for longitudinal CRT are block exchangeable (allows a different within- and between-period ICC) and exponential decay (allows between-period ICC to decay exponentially). More flexible correlation structures are available in statistical software packages and, although not formally proposed for longitudinal CRTs, may offer some advantages. Our objectives were to empirically explore the impact of these correlation structures on treatment effect inferences, identify gaps in the methodological literature, and make practical recommendations.MethodsWe obtained data from a parallel-arm CRT conducted in Tanzania to compare four different types of insecticide-treated bed-nets. Malaria prevalence was assessed in cross-sectional surveys of 45 households in each of 84 villages at baseline, 12-, 18- and 24-months post-randomization. We re-analyzed the data using mixed-effects logistic regression according to a prespecified analysis plan but under five different correlation structures as well as a robust variance estimator under exchangeable correlation and compared the estimated correlations and treatment effects. A proof-of-concept simulation was conducted to explore general conclusions.ResultsThe estimated correlation structures varied substantially across different models. The unstructured model was the best-fitting model based on information criteria. Although point estimates and confidence intervals for the treatment effect were similar, allowing for more flexible correlation structures led to different conclusions based on statistical significance. Use of robust variance estimators generally led to wider confidence intervals. Simulation results showed that under-specification can lead to coverage probabilities much lower than nominal levels, but over-specification is more likely to maintain nominal coverage.ConclusionMore flexible correlation structures should not be ruled out in longitudinal CRTs. This may be particularly important in malaria trials where outcomes may fluctuate over time. In the absence of robust methods for selecting the best-fitting correlation structure, researchers should examine sensitivity of results to different assumptions about the ICC and consider robust variance estimators.
| S-EPMC10021932 | biostudies-literature
Project description:PurposeCluster randomized controlled trials (cRCTs) are popular in school-based research designs where schools are randomized to different trial arms. To help guide future study planning, we provide information on anticipated effect sizes and intra-cluster correlation coefficients (ICCs), as well as school sizes, for dating violence (DV) and interpersonal violence outcomes based on data from a cRCT which evaluated the bystander-based violence intervention 'Green Dot'.MethodsWe utilized data from 25 schools from the Green Dot High School study. Effect size and ICC values corresponding to dating and interpersonal violence outcomes are obtained from linear mixed effect models. We also calculated the required number of schools needed for future studies utilizing available methods that do and do not consider variation in school size.ResultsObserved effect sizes for DV outcomes range from 0.06 to 0.11. Observed ICC values for DV outcomes range from 0.0006 to 0.0032. The upper limit of 95% CIs for the true ICCs range from 0.0023 to 0.0070.ConclusionSchool-based evaluations with violence outcomes are expected to have small effect sizes. Observed ICCs are less than 0.005 and upper limit of of 95% CIs for the true ICCs are less than 0.01. Designing school-based cRCTs should account for the ICC, even if its value is assumed to be negligible. Furthermore, variation in school sizes should also be accounted for to avoid having too few schools to achieve the desired power.
| S-EPMC8367849 | biostudies-literature
Project description:Within cluster randomized trials no algorithms exist to generate a full enumeration of a block randomization, balancing for covariates across treatment arms. Furthermore, often for practical reasons multiple blocks are required to fully randomize a study, which may not have been well balanced within blocks.We present a convenient and easy to use randomization tool to undertake allocation concealed block randomization. Our algorithm highlights allocations that minimize imbalance between treatment groups across multiple baseline covariates. We demonstrate the algorithm using a cluster randomized trial in primary care (the PRE-EMPT Study) and show that the software incorporates a trade off between independent random allocations that were likely to be imbalanced, and predictable deterministic approaches that would minimise imbalance. We extend the methodology of single block randomization to allocate to multiple blocks conditioning on previous allocations.The algorithm is included as Additional file 1 and we advocate its use for robust randomization within cluster randomized trials.
| S-EPMC2588445 | biostudies-other
Project description:The assessment of the sensitivity of statistical methods has received little attention in cluster randomized trials (CRTs), especially for stratified CRT when the outcome of interest is continuous. We empirically examined the sensitivity of five methods for analyzing the continuous outcome from a stratified CRT - aimed to investigate the efficacy of the Classroom Communication Resource (CCR) compared to usual care to improve the peer attitude towards children who stutter among grade 7 students. Schools - the clusters, were divided into quintile based on their socio-political resources, and then stratified by quintile. The schools were then randomized to CCR and usual care groups in each stratum. The primary outcome was Stuttering Resource Outcomes Measure. Five methods, including the primary method, were used in this study to examine the effect of CCR. The individual-level methods were: (i) linear regression; (ii) mixed-effects method; (iii) GEE with exchangeable correlation structure (primary method of analysis). And the cluster-level methods were: (iv) cluster-level linear regression; and (v) meta-regression. These methods were also compared with or without adjustment for stratification. Ten schools were stratified by quintile, and then randomized to CCR (223 students) and usual care (231 students) groups. The direction of the estimated differences was same for all the methods except meta-regression. The widths of the 95% confidence intervals were narrower when adjusted for stratification. The overall conclusion from all the methods was similar but slightly differed in terms of effect estimate and widths of confidence intervals.TrialregistrationClinicaltrials.gov, NCT03111524. Registered on 9 March 2017.
| S-EPMC6627034 | biostudies-literature
Project description:BackgroundThe intracluster correlation coefficient is a key input parameter for sample size determination in cluster-randomised trials. Sample size is very sensitive to small differences in the intracluster correlation coefficient, so it is vital to have a robust intracluster correlation coefficient estimate. This is often problematic because either a relevant intracluster correlation coefficient estimate is not available or the available estimate is imprecise due to being based on small-scale studies with low numbers of clusters. Misspecification may lead to an underpowered or inefficiently large and potentially unethical trial.MethodsWe apply a Bayesian approach to produce an intracluster correlation coefficient estimate and hence propose sample size for a planned cluster-randomised trial of the effectiveness of a systematic voiding programme for post-stroke incontinence. A Bayesian hierarchical model is used to combine intracluster correlation coefficient estimates from other relevant trials making use of the wealth of intracluster correlation coefficient information available in published research. We employ knowledge elicitation process to assess the relevance of each intracluster correlation coefficient estimate to the planned trial setting. The team of expert reviewers assigned relevance weights to each study, and each outcome within the study, hence informing parameters of Bayesian modelling. To measure the performance of experts, agreement and reliability methods were applied.ResultsThe 34 intracluster correlation coefficient estimates extracted from 16 previously published trials were combined in the Bayesian hierarchical model using aggregated relevance weights elicited from the experts. The intracluster correlation coefficients available from external sources were used to construct a posterior distribution of the targeted intracluster correlation coefficient which was summarised as a posterior median with a 95% credible interval informing researchers about the range of plausible sample size values. The estimated intracluster correlation coefficient determined a sample size of between 450 (25 clusters) and 480 (20 clusters), compared to 500-600 from a classical approach. The use of quantiles, and other parameters, from the estimated posterior distribution is illustrated and the impact on sample size described.ConclusionAccounting for uncertainty in an unknown intracluster correlation coefficient, trials can be designed with a more robust sample size. The approach presented provides the possibility of incorporating intracluster correlation coefficients from various cluster-randomised trial settings which can differ from the planned study, with the difference being accounted for in the modelling. By using expert knowledge to elicit relevance weights and synthesising the externally available intracluster correlation coefficient estimates, information is used more efficiently than in a classical approach, where the intracluster correlation coefficient estimates tend to be less robust and overly conservative. The intracluster correlation coefficient estimate constructed is likely to produce a smaller sample size on average than the conventional strategy of choosing a conservative intracluster correlation coefficient estimate. This may therefore result in substantial time and resources savings.
| S-EPMC10262340 | biostudies-literature