Sample size calculation in multi-centre clinical trials

Abstract

Background: Multi-centre randomized controlled clinical trials play an important role in modern evidence-based medicine. Advantages of collecting data from more than one site are numerous, including accelerated recruitment and increased generalisability of results. Mixed models can be applied to account for potential clustering in the data, in particular when many small centres contribute patients to the study. Previously proposed methods on sample size calculation for mixed models only considered balanced treatment allocations which is an unlikely outcome in practice if block randomisation with reasonable choices of block length is used.

Methods: We propose a sample size determination procedure for multi-centre trials comparing two treatment groups for a continuous outcome, modelling centre differences using random effects and allowing for arbitrary sample sizes. It is assumed that block randomisation with fixed block length is used at each study site for subject allocation. Simulations are used to assess operation characteristics such as power of the sample size approach. The proposed method is illustrated by an example in disease management systems.

Results: A sample size formula as well as a lower and upper boundary for the required overall sample size are given. We demonstrate the superiority of the new sample size formula over the conventional approach of ignoring the multi-centre structure and show the influence of parameters such as block length or centre heterogeneity. The application of the procedure on the example data shows that large blocks require larger sample sizes, if centre heterogeneity is present.

Conclusion: Unbalanced treatment allocation can result in substantial power loss when centre heterogeneity is present but not considered at the planning stage. When only few patients by centre will be recruited, one has to weigh the risk of imbalance between treatment groups due to large blocks and the risk of unblinding due to small blocks. The proposed approach should be considered when planning multi-centre trials.

Keywords: Block randomisation; Linear mixed model; Random effects.

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The authors declare that they have no competing interests.

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Figures

Fig. 1

Probability distribution. Conditional probability distributions of Δ2|r for varying numbers of randomized subjects r=1,…,b=6

Fig. 2

Expectation of Δ2|r. Conditional expected imbalance between treatment groups for allocation parameter k=1,2,3 and various numbers of subjects r=1…,b and block lengths b

Fig. 3

Example: Block randomisation. Number of final randomisation blocks by centre with block length b=6 based on the COMPETE II trial [17]

Fig. 4

Example: Sample size based on NMC,U1. Derived for μ=1, σ=4, varying block length b, number of centres c and intra-class correlation ρ. Dashed grey line represents the planned sample size of the trial (N=508)

Fig. 5

Example: Power simulations. Simulated power based on the planned sample sizes for μ=1, σ=4, ρ=0.5, varying numbers of centres and varying block lengths. Dashed black line represents the targeted power of 0.8