Purpose: To develop methods to assess the value of further research into interventions to increase uptake to breast cancer screening in the UK: 1) before a cluster randomised trial reported in 2001 and 2) after that trial.

Methods: We analysed data from a cluster randomised 2x2 factorial trial on letter and flag interventions to increase attendance at breast cancer screening in the UK (Bankhead et al 2001). We use a random effects logistic regression model in a Bayesian decision analytic framework, which allows reasonable estimation of the interaction term, and is embedded directly into a cost-effectiveness model incorporating costs and life-years saved by screening and early treatment. We consider how to calculate the expected value of a trial of this design 1) before the trial and 2) after the trial. Prior to the 2001 study there was a substantial body of research into various types of intervention (mainly from Australia and the US). We use this evidence to inform a multivariate normal prior for our regression coefficients, including correlations. We then combine this prior information with the data to obtain a multivariate normal posterior that becomes the prior after the trial. We calculate, for both priors, the expected value of removing some uncertainty in intervention efficacy parameters by running a future cluster randomised factorial design trial of given cluster size - Expected Value of Sample Information (EVSI). EVSI is calculated by simulating future data from the prior and using weighted least-squares regression to obtain multivariate normal sufficient statistics for the regression coefficients, including correlations.

Results: Using a £30,000 valuation of a QALY, EVSI per woman invited to screening was £2.88 before and £1.58 after the trial, for the 2001 trial study design. Population EVSI over a 10-year horizon was £6.7m before and £3.6m after the trial.

Conclusions: By making multivariate normal approximations, we have calculated EVSI for cluster-randomised trials. There was considerable value in running the 2001 trial, and although the 2001 trial has reduced decision uncertainty, there is still value in running a similar trial in the future. We discuss methods for finding the optimal cluster sizes for a future study, allowing for the cost of the study and the opportunity cost of receiving a sub-optimal intervention during the trial.