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Expected value of sample information (EVSI) measures the anticipated net benefit gained from conducting new research with a specific design to add to the evidence on which reimbursement decisions are made. Cluster randomized trials raise specific issues for EVSI calculations because 1) a hierarchical model is necessary to account for between-cluster variability when incorporating new evidence and 2) heterogeneity between clusters needs to be carefully characterized in the cost-effectiveness analysis model. Multi-arm trials provide parameter estimates that are correlated, which needs to be accounted for in EVSI calculations. Furthermore, EVSI is computationally intensive when the net benefit function is nonlinear, due to the need for an inner-simulation step. We develop a method for the computation of EVSI that avoids the inner simulation step for cluster randomized multi-arm trials with a binary outcome, where the net benefit function is linear in the probability of an event but nonlinear in the log-odds ratio parameters. We motivate and illustrate the method with an example of a cluster randomized 2 × 2 factorial trial for interventions to increase attendance at breast screening in the UK, using a previously reported cost-effectiveness model. We highlight assumptions made in our approach, extensions to individually randomized trials and inclusion of covariates, and areas for further developments. We discuss computation time, the research-design space, and the ethical implications of an EVSI approach. We suggest that EVSI is a practical and appropriate tool for the design of cluster randomized trials.