RESUMEN
Many clinical trials involve partially clustered data, where some observations belong to a cluster and others can be considered independent. For example, neonatal trials may include infants from single or multiple births. Sample size and analysis methods for these trials have received limited attention. A simulation study was conducted to (1) assess whether existing power formulas based on generalized estimating equations (GEEs) provide an adequate approximation to the power achieved by mixed effects models, and (2) compare the performance of mixed models vs GEEs in estimating the effect of treatment on a continuous outcome. We considered clusters that exist prior to randomization with a maximum cluster size of 2, three methods of randomizing the clustered observations, and simulated datasets with uninformative cluster size and the sample size required to achieve 80% power according to GEE-based formulas with an independence or exchangeable working correlation structure. The empirical power of the mixed model approach was close to the nominal level when sample size was calculated using the exchangeable GEE formula, but was often too high when the sample size was based on the independence GEE formula. The independence GEE always converged and performed well in all scenarios. Performance of the exchangeable GEE and mixed model was also acceptable under cluster randomization, though under-coverage and inflated type I error rates could occur with other methods of randomization. Analysis of partially clustered trials using GEEs with an independence working correlation structure may be preferred to avoid the limitations of mixed models and exchangeable GEEs.
RESUMEN
INTRODUCTION: Clinical trial designs based on the assumption of independent observations are well established. Clustered clinical trial designs, where all observational units belong to a cluster and outcomes within clusters are expected to be correlated, have also received considerable attention. However, many clinical trials involve partially clustered data, where only some observational units belong to a cluster. Examples of such trials occur in neonatology, where participants include infants from both singleton and multiple births, and ophthalmology, where one or two eyes per participant may need treatment. Partial clustering can also arise in trials of group-based treatments (e.g. group education or counselling sessions) or treatments administered individually by a discrete number of health care professionals (e.g. surgeons or physical therapists), when this is compared to an unclustered control arm. Trials involving partially clustered data have received limited attention in the literature and the current lack of standardised terminology may be hampering the development and dissemination of methods for designing and analysing these trials. METHODS AND EXAMPLES: In this article, we present an overarching definition of partially clustered trials, bringing together several existing trial designs including those for group-based treatments, clustering due to facilitator effects and the re-randomisation design. We define and describe four types of partially clustered trial designs, characterised by whether the clustering occurs pre-randomisation or post-randomisation and, in the case of pre-randomisation clustering, by the method of randomisation that is used for the clustered observations (individual randomisation, cluster randomisation or balanced randomisation within clusters). Real life examples are provided to highlight the occurrence of partially clustered trials across a variety of fields. To assess how partially clustered trials are currently reported, we review published reports of partially clustered trials. DISCUSSION: Our findings demonstrate that the description of these trials is often incomplete and the terminology used to describe the trial designs is inconsistent, restricting the ability to identify these trials in the literature. By adopting the definitions and terminology presented in this article, the reporting of partially clustered trials can be substantially improved, and we present several recommendations for reporting these trial designs in practice. Greater awareness of partially clustered trials will facilitate more methodological research into their design and analysis, ultimately improving the quality of these trials.