arXiv subjects

Andrew Copas

Publications and source records attributed to Andrew Copas.

4 recordsLinked to original sources

arXiv2025

Sample size calculations for multilevel factorial longitudinal cluster randomised trials

Typically, trials investigate the impact of either an individual-level intervention on participant outcomes, or the impact of a cluster-level intervention on participant outcomes. Factorial designs consider two (or more) treatments for each of two (or more) different factors. In factorial trial designs, trial units (individuals or clusters) are each randomised to a level of each of the treatments; these designs allow assessment of the interactions between different interventions. Recently, there has been growing interest in the design of trials that jointly assess the impact of individual- and cluster-level interventions (i.e. multi-level interventions); requiring the development of methodology that accommodates randomisation at multiple levels. While recent work has developed sample size methodology for variants combining standard cluster randomisation and individual randomisation, that work does not apply to longitudinal cluster randomised trial designs such as the stepped wedge design or cluster randomised crossover design. Here we present dedicated sample size methodology for "split-plot factorial longitudinal cluster randomised trials" with continuous outcomes: allowing for joint assessment of individual-level and cluster-level interventions that allows for the impact of the cluster-level intervention to be assessed using any longitudinal cluster randomised trial design. We show how the power to detect given effects of the individual-level intervention, the cluster-level intervention, and the interaction between the two depends on standard results for individually-randomised trials and longitudinal cluster randomised trials. We apply these results to the SharES trial, which considered the effects of a patient- and clinician-level interventions for patients with breast cancer on patient knowledge about the risks and benefits of treatment.

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arXiv2025

What is estimated in cluster randomized crossover trials with informative sizes? -- A survey of estimands and common estimators

In the analysis of cluster randomized trials (CRTs), previous work has defined two meaningful estimands: the individual-average treatment effect (iATE) and cluster-average treatment effect (cATE) estimand, to address individual and cluster-level hypotheses. In multi-period CRT designs, such as the cluster randomized crossover (CRXO) trial, additional weighted average treatment effect estimands help fully reflect the longitudinal nature of these trial designs, namely the cluster-period-average treatment effect (cpATE) and period-average treatment effect (pATE). We define different forms of informative sizes, where the treatment effects vary according to cluster, period, and/or cluster-period sizes, which subsequently cause these estimands to differ in magnitude. Under such conditions, we demonstrate which of the unweighted, inverse cluster-period size weighted, inverse cluster size weighted, and inverse period size weighted: (i.) independence estimating equation, (ii.) fixed effects model, (iii.) exchangeable mixed effects model, and (iv.) nested exchangeable mixed effects model treatment effect estimators are consistent for the aforementioned estimands in 2-period cross-sectional CRXO designs with continuous outcomes. We report a simulation study and conclude with a reanalysis of a CRXO trial testing different treatments on hospital length of stay among patients receiving invasive mechanical ventilation. Notably, with informative sizes, the unweighted and weighted nested exchangeable mixed effects model estimators are not consistent for any meaningful estimand and can yield biased results. In contrast, the unweighted and weighted independence estimating equation, and under specific scenarios, the fixed effects model and exchangeable mixed effects model, can yield consistent and empirically unbiased estimators for meaningful estimands in 2-period CRXO trials.

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arXiv2023

Demystifying estimands in cluster-randomised trials

Estimands can help clarify the interpretation of treatment effects and ensure that estimators are aligned to the study's objectives. Cluster randomised trials require additional attributes to be defined within the estimand compared to individually randomised trials, including whether treatment effects are marginal or cluster specific, and whether they are participant or cluster average. In this paper, we provide formal definitions of estimands encompassing both these attributes using potential outcomes notation and describe differences between them. We then provide an overview of estimators for each estimand, describe their assumptions, and show consistency (i.e. asymptotically unbiased estimation) for a series of analyses based on cluster level summaries. Then, through a reanalysis of a published cluster randomised trial, we demonstrate that the choice of both estimand and estimator can affect interpretation. For instance, the estimated odds ratio ranged from 1.38 (p=0.17) to 1.83 (p=0.03) depending on the target estimand, and for some estimands, the choice of estimator affected the conclusions by leading to smaller treatment effect estimates. We conclude that careful specification of the estimand, along with an appropriate choice of estimator, are essential to ensuring that cluster randomised trials address the right question.

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arXiv2019

Handling an uncertain control group event risk in non-inferiority trials: non-inferiority frontiers and the power-stabilising transformation

Background. Non-inferiority (NI) trials are increasingly used to evaluate new treatments expected to have secondary advantages over standard of care, but similar efficacy on the primary outcome. When designing a NI trial with a binary primary outcome, the choice of effect measure for the NI margin has an important effect on sample size calculations; furthermore, if the control event risk observed is markedly different from that assumed, the trial can quickly lose power or the results become difficult to interpret. Methods. We propose a new way of designing NI trials to overcome the issues raised by unexpected control event risks by specifying a NI frontier, i.e. a curve defining the most appropriate non-inferiority margin for each possible value of control event risk. We propose a fixed arcsine difference frontier, the power-stabilising transformation for binary outcomes. We propose and compare three ways of designing a trial using this frontier. Results. Testing and reporting on the arcsine scale leads to results which are challenging to interpret clinically. Working on the arcsine scale generally requires a larger sample size compared to the risk difference scale. Therefore, working on the risk difference scale, modifying the margin after observing the control event risk, might be preferable, as it requires a smaller sample size. However, this approach tends to slightly inflate type I error rate; a solution is to use a lower significance level for testing. When working on the risk ratio scale, the same approach leads to power levels above the nominal one, maintaining type I error under control. Conclusions. Our proposed methods of designing NI trials using power-stabilising frontiers make trial design more resilient to unexpected values of the control event risk, at the only cost of requiring larger sample sizes when the goal is to report results on the risk difference scale.

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