## Introduction

Lack of timely accrual presents a significant challenge to the performance of cardiovascular trials,1–3 generating resource-consuming underpowered trials that are unable to meet their intended objectives meaningfully. Unsuccessful recruitment poses ethical, economic and scientific problems for the clinical research enterprise.4

The ability to monitor and accurately predict clinical trial accrual allows for greater support for decisions to be made about the management and conduct of clinical trials.5 Measuring the likelihood of achieving the projected accrual within a reasonable time frame may prompt trial decisions in different directions. These range from adding further resources to implement interventions that may improve accrual performance to closing studies early to release resources for more promising trials.

Some authors4 5 suggest that mechanisms for terminating trials are not sensitive enough for recruitment futility and advocate the use of predictors of accrual performance to allow for better allocation of research resources and ensure that subjects enrolled in trials will actually play a role in advancing medical knowledge. With good monitoring tools, clearly identified and detailed in the planning phase of a trial, researchers would be able to define realistic targets for their sample sizes and gain an early warning when accrual rates are suffering.

From a technical standpoint, sophisticated statistical approaches6 7 and tools8 for accrual monitoring and prediction are available in the literature but are probably underused. As acknowledged by Barnard and colleagues,6 the ease of implementation of a model would also contribute to the choice of method to be used. In this trade-off between usability and accuracy, Bayesian models are probably at increased complexity of use compared with the relative simplicity of deterministic models (ie, the total accrual time is estimated by dividing the planned sample size by the number of subjects expected to enrol in the study during each time unit) or frequentist Poisson-based models (ie, number of participants recruited within a fixed time follows a Poisson distribution). However, accrual monitoring methods relying on the Bayesian approach are particularly attractive.9 10

We recall that any Bayesian analysis starts with a prior probability distribution for the value of interest, based on existing knowledge, and adds new evidence as data accumulate to produce a posterior predictive distribution, which is the distribution for future predicted data based on the data observed so far. The attractive key element of the Bayesian approach relies on this natural updating process. In fact, researchers’ experience from similar studies can be incorporated as prior knowledge, and when actual accrual data become available, the predictive distribution becomes the weighted average of the prior distribution and the actual observed data. As more data are collected, the weighting of the current observed data increases, while the weighting of prior information decreases.

Such an approach provides an effective assessment of the accrual process. In fact, one interesting feature of these models is that if the researcher’s a priori confidence in the subject accrual rate is strong, the posterior distribution will be weighted heavily towards the prior distribution, especially early in the trial. This prevents an undesirable alarm when the enrolment of the first few subjects is slower than expected. However, if the researcher has weak confidence, early evidence of slow accrual will be given greater weight, prompting a rapid response to address the slow accrual.

We present brief guidance on how to embed an accrual monitoring framework in a study protocol and how to assess patient accrual by retrospectively applying a Bayesian monitoring tool to Cost of Strategies After Myocardial Infarction (COSTAMI) trial11 12 and Biventricular Pacing After Cardiac Surgery (BiPACS)13 trial data.