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

Abstract

BackgroundClustered 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.MethodsThis 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.ResultsData 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.ConclusionsThese 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 materialThe online version of this article (doi:10.1186/s13063-016-1532-9) contains supplementary material, which is available to authorized users.

Sample Size Determination for GEE Analyses of Stepped Wedge Cluster Randomized Trials

“…The within‐period correlation is usually estimated by the intraclass correlation reported in previous trials with a similar endpoint. However, the inter‐period correlation is less commonly reported, although such reporting practice is advocated (Preisser et al., ; Martin et al., ). This type of correlation was also discussed in designing crossover CRTs, and a default value of half the within‐period correlation has been recommended in the absence of external information (Giraudeau et al., ).…”

“…In particular, the values of are representative of small correlations commonly reported in parallel CRTs (Murray, ), and the inter‐period correlation was assumed smaller than , as observed in Martin et al. (). The values of were chosen to reflect small to moderate within‐individual correlations in longitudinal studies, and were assumed to be larger than and .…”

“…For both types of responses, we chose α = (α 0 , α 1 , α 2 ) = {(0.03, 0.015, 0.2), (0.1, 0.05, 0.2), (0.01, 0.005, 0.4)} to represent a range of different correlation values. In particular, the values of α 0 are representative of small correlations commonly reported in parallel CRTs (Murray, 1998), and the inter-period correlation α 1 was assumed smaller than α 0 , as observed in Martin et al (2016). The values of α 2 were chosen to reflect small to moderate within-individual correlations in longitudinal studies, and were assumed to be larger than α 0 and α 1 .…”

Analysis of cluster randomised trials with an assessment of outcome at baseline

“…In a study using the Health Improvement Network general practice database, the health outcomes of glycated haemoglobin, systolic and diastolic blood pressure, body mass index, total cholesterol, and high density lipoprotein cholesterol were investigated. Researchers found that correlations between individuals from the same practice were between 12% and 51% smaller when those individuals were sampled from different 15 month periods,17 motivating the use of the second, more flexible model. A constrained baseline analysis that lacks this flexibility in the correlation structure is known to overstate the precision of the treatment effect, potentially leading to false positive findings 15…”

Accounting for a decaying correlation structure in cluster randomized trials with continuous recruitment

“…We will compare designs and models in the context of the following example: a potential four‐period trial over 30 months of the effect of a weight management intervention on body mass index (BMI) among people with diagnosed type‐2 diabetes in general practices in the UK. Administratively collected data on patients with type‐2 diabetes across 430 primary care facilities in the UK were used to obtain plausible correlation parameter estimates . The data were sourced from The Health Improvement Network (THIN) database and cover patients' measurements over a 30‐month interval from October 1, 2007 to March 31, 2010.…”