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The Australian and New Zealand Intensive Care Society Adult Patient Database (ANZICS APD) is one of the largest databases of its kind in the world and collects individual admissions' data from intensive care units (ICUs) around Australia and New Zealand. Use of this database for monitoring and comparing the performance of ICUs, quantified by the standardised mortality ratio, poses several theoretical and computational challenges, which are addressed in this paper. In particular, the expected number of deaths must be appropriately estimated, the ICU casemix adjustment must be adequate, statistical variation must be fully accounted for, and appropriate adjustment for multiple comparisons must be made. Typically, one or more of these issues have been neglected in ICU comparison studies. Our approach to the analysis proceeds by fitting a random coefficient hierarchical logistic regression model for the inhospital death of each patient, with patients clustered within ICUs. We anticipate the majority of ICUs will be estimated as performing 'usually' after adjusting for important clinical covariates. We take as a starting point the ideas in Ohlssen et al and estimate an appropriate null model that we expect these ICUs to follow, taking a frequentist rather than a Bayesian approach. This methodology allows us to rigorously account for the aforementioned statistical issues and to determine if there are any ICUs contributing to the Australian and New Zealand Intensive Care Society database that have comparatively unusual performance. In addition to investigating the yearly performance of the ICUs, we also estimate changes in individual ICU performance between 2009 and 2010 by adjusting for regression-to-the-mean. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

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., (© 2024 The Author(s). Statistics in Medicine published by John Wiley & Sons Ltd.)

In a randomized controlled trial, outcomes of different subjects may be independent at baseline, but correlated at a follow-up measurement due to treatment. This treatment-related clustering at follow-up can arise for instance because the treatment is given in a group or because subjects are treated individually but by the same therapist (therapist effect). There is substantial literature on the design and analysis of such trials when estimation of the intervention effect is based on a follow-up measurement (eg, directly after treatment or at a later time point). However, often the baseline measurement of the outcome is highly correlated with the follow-up measurement, and this information can be used in the analysis. For a randomized design with a baseline and a follow-up measurement, we compare sample size requirements for analyses with and without adjustment for this baseline measure. We show that adjusting for baseline reduces required sample size. This reduction depends on the variance of the difference between arms at baseline, the variance of this difference at follow-up, and the correlation between the two. From this, we derive sample size formulas for partially or fully nested designs, and cluster randomized trials with treatment as a partially or fully cross-classified factor. Also, we discuss situations where clusters are already present at baseline or where treatment by cluster interaction is present. For the partially nested design, we work out practical design considerations (eg, use of content-matter input, design factors and optimal allocation ratio) and investigate small sample properties of the sample size formula., (© 2023 The Authors. Statistics in Medicine published by John Wiley & Sons Ltd.)

Stepped wedge designs are an increasingly popular variant of longitudinal cluster randomized trial designs, and roll out interventions across clusters in a randomized, but step-wise fashion. In the standard stepped wedge design, assumptions regarding the effect of time on outcomes may require that all clusters start and end trial participation at the same time. This would require ethics approvals and data collection procedures to be in place in all clusters before a stepped wedge trial can start in any cluster. Hence, although stepped wedge designs are useful for testing the impacts of many cluster-based interventions on outcomes, there can be lengthy delays before a trial can commence. In this article, we introduce "batched" stepped wedge designs. Batched stepped wedge designs allow clusters to commence the study in batches, instead of all at once, allowing for staggered cluster recruitment. Like the stepped wedge, the batched stepped wedge rolls out the intervention to all clusters in a randomized and step-wise fashion: a series of self-contained stepped wedge designs. Provided that separate period effects are included for each batch, software for standard stepped wedge sample size calculations can be used. With this time parameterization, in many situations including when linear models are assumed, sample size calculations reduce to the setting of a single stepped wedge design with multiple clusters per sequence. In these situations, sample size calculations will not depend on the delays between the commencement of batches. Hence, the power of batched stepped wedge designs is robust to unexpected delays between batches., (© 2022 The Authors. Statistics in Medicine published by John Wiley & Sons Ltd.)

In practice, stepped wedge trials frequently include clusters of differing sizes. However, investigations into the theoretical aspects of stepped wedge designs have, until recently, typically assumed equal numbers of subjects in each cluster and in each period. The information content of the cluster-period cells, clusters, and periods of stepped wedge designs has previously been investigated assuming equal cluster-period sizes, and has shown that incomplete stepped wedge designs may be efficient alternatives to the full stepped wedge. How this changes when cluster-period sizes are not equal is unknown, and we investigate this here. Working within the linear mixed model framework, we show that the information contributed by design components (clusters, sequences, and periods) does depend on the sizes of each cluster-period. Using a particular trial that assessed the impact of an individual education intervention on log-length of stay in rehabilitation units, we demonstrate how strongly the efficiency of incomplete designs depends on which cells are excluded: smaller incomplete designs may be more powerful than alternative incomplete designs that include a greater total number of participants. This also serves to demonstrate how the pattern of information content can be used to inform a set of incomplete designs to be considered as alternatives to the complete stepped wedge design. Our theoretical results for the information content can be extended to a broad class of longitudinal (ie, multiple period) cluster randomized trial designs., (© 2021 John Wiley & Sons, Ltd.)

When calculating sample size or power for stepped wedge or other types of longitudinal cluster randomized trials, it is critical that the planned sampling structure be accurately specified. One common assumption is that participants will provide measurements in each trial period, that is, a closed cohort, and another is that each participant provides only one measurement during the course of the trial. However some studies have an "open cohort" sampling structure, where participants may provide measurements in variable numbers of periods. To date, sample size calculations for longitudinal cluster randomized trials have not accommodated open cohorts. Feldman and McKinlay (1994) provided some guidance, stating that the participant-level autocorrelation could be varied to account for the degree of overlap in different periods of the study, but did not indicate precisely how to do so. We present sample size and power formulas that allow for open cohorts and discuss the impact of the degree of "openness" on sample size and power. We consider designs where the number of participants in each cluster will be maintained throughout the trial, but individual participants may provide differing numbers of measurements. Our results are a unification of closed cohort and repeated cross-sectional sample results of Hooper et al (2016), and indicate precisely how participant autocorrelation of Feldman and McKinlay should be varied to account for an open cohort sampling structure. We discuss different types of open cohort sampling schemes and how open cohort sampling structure impacts on power in the presence of decaying within-cluster correlations and autoregressive participant-level errors., (© 2020 The Authors. Statistics in Medicine published by John Wiley & Sons, Ltd.)

Trial planning requires making efficient yet practical design choices. In a cluster randomized crossover trial, clusters of subjects cross back and forth between implementing the control and intervention conditions over the course of the trial, with each crossover marking the start of a new period. If it is possible to set up such a trial with more crossovers, a pertinent question is whether there are efficiency gains from clusters crossing over more frequently, and if these gains are substantial enough to justify the added complexity and cost of implementing more crossovers. We seek to determine the optimal number of crossovers for a fixed trial duration, and then identify other highly efficient designs by allowing the total number of clusters to vary and imposing thresholds on maximum cost and minimum statistical power. Our results pertain to trials with continuous recruitment and a continuous primary outcome, with the treatment effect estimated using a linear mixed model. To account for the similarity between subjects' outcomes within a cluster, we assume a correlation structure in which the correlation decays gradually in a continuous manner as the time between subjects' measurements increases. The optimal design is characterized by crossovers between the control and intervention conditions with each successive subject. However, this design is neither practical nor cost-efficient to implement, nor is it necessary: the gains in efficiency increase sharply in moving from a two-period to a four-period trial design, but approach an asymptote for the scenarios considered as the number of crossovers continues to increase., (© 2019 John Wiley & Sons, Ltd.)

Stepped-wedge cluster randomized trials, which randomize clusters of subjects to treatment sequences in which clusters switch from control to intervention conditions, are being conducted with increasing frequency. Due to the real-world nature of this design, methodological and implementation challenges are ubiquitous. To account for such challenges, more complex statistical models to plan studies and analyze data are required. In this paper, we consider stepped-wedge trials that accommodate treatment effect heterogeneity across clusters, implementation periods during which no data are collected, or both treatment effect heterogeneity and implementation periods. Previous work has shown that the sequence-period cells of a stepped-wedge design contribute unequal amounts of information to the estimation of the treatment effect. In this paper, we extend that work by considering the amount of information available for the estimation of the treatment effect in each sequence-period cell, sequence, and period of stepped-wedge trials with more complex designs and outcome models. When either treatment effect heterogeneity and/or implementation periods are present, the pattern of information content of sequence-period cells tends to be clustered around the times of the switch from control to intervention condition, similarly to when these complexities are absent. However, the presence and degree of treatment effect heterogeneity and the number of implementation periods can influence the information content of periods and sequences markedly., (© 2019 John Wiley & Sons, Ltd.)

A requirement for calculating sample sizes for cluster randomized trials (CRTs) conducted over multiple periods of time is the specification of a form for the correlation between outcomes of subjects within the same cluster, encoded via the within-cluster correlation structure. Previously proposed within-cluster correlation structures have made strong assumptions; for example, the usual assumption is that correlations between the outcomes of all pairs of subjects are identical ("uniform correlation"). More recently, structures that allow for a decay in correlation between pairs of outcomes measured in different periods have been suggested. However, these structures are overly simple in settings with continuous recruitment and measurement. We propose a more realistic "continuous-time correlation decay" structure whereby correlations between subjects' outcomes decay as the time between these subjects' measurement times increases. We investigate the use of this structure on trial planning in the context of a primary care diabetes trial, where there is evidence of decaying correlation between pairs of patients' outcomes over time. In particular, for a range of different trial designs, we derive the variance of the treatment effect estimator under continuous-time correlation decay and compare this to the variance obtained under uniform correlation. For stepped wedge and cluster randomized crossover designs, incorrectly assuming uniform correlation will underestimate the required sample size under most trial configurations likely to occur in practice. Planning of CRTs requires consideration of the most appropriate within-cluster correlation structure to obtain a suitable sample size., (© 2019 John Wiley & Sons, Ltd.)