To provide brief guidance on how to design accrual monitoring activities in a clinical trial protocol.

Two completed clinical trials that did not achieve the planned sample size, the Cost of Strategies After Myocardial Infarction (COSTAMI) trial and the Biventricular Pacing After Cardiac Surgery (BiPACS) trial.

A Bayesian monitoring tool, the constant accrual model, is applied retrospectively to accrual data from each case study to illustrate how the tool could be used to identify problems with accrual early in the trial period and to frame the conditions in which the approach can be used in practice.

After 312 days and 155 patients enrolled in the COSTAMI trial, accrual could be classified as ‘off target’ on the basis of statistical criteria outlined in the protocol. As for the BiPACS trial, after 2 years, it was already evident that the accrual was ‘considerably off target’.

Prompt awareness of a high risk of accrual failure could trigger different interventions to overcome protocol-related, patient-related or investigator-related barriers to recruitment or ultimately contribute to an early stopping decision due to recruitment futility.

Accrual prediction models should be included as standard tools for routine monitoring activities in cardiovascular research. Among them, methods relying on the Bayesian approach are particularly attractive, as they can naturally update past evidence when actual accrual data becomes available.

Slow patient accrual in clinical trials can have significant negative impact on their success. Careful monitoring and prediction of accrual success (or failure) is crucial for improving enrolment in clinical trials and thus increasing the likelihood of their overall success.

This study showcases the several different Bayesian options for accrual monitoring available to investigators and frames the conditions in which the different approaches can be used in practice.

Proposing a standard operating procedure for the application of Bayesian monitoring tools will hopefully encourage their use in general clinical trial monitoring.

Lack of timely accrual presents a significant challenge to the performance of cardiovascular trials,

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.

Some authors

From a technical standpoint, sophisticated statistical approaches

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) trial

In line with the policy of major research institutions such as the National Heart, Lung and Blood Institute (NHLBI) (

Before initiating any study, the investigators, in collaboration with the monitoring entity, if applicable, and the biostatistics advisors shall agree on the best practices for quality assurance. This requires them to outline plans and benchmarks for monitoring recruitment, including the statistical model, projected recruitment time duration and final recruitment target. Although there is no obvious choice,

Contingency table between choice of prior for Bayesian constant accrual model

Prior choice | |||

Inverse gamma prior depending on constant P | Accelerated prior | Hedging prior | |

Sceptical prior built around the position that the planned enrolment target is unlikely to be achieved in the given time | ‘small’ P | Performs much like the sceptical prior when the accrual is extremely off target | |

Optimistic prior built around the position that the planned enrolment target is likely to be achieved in the given time | ‘large’ P | Performs similar to an optimistic prior | Performs much like the optimistic prior when the accrual is on target or only slightly off target |

Small sample size at interim | Use different priors and conduct sensitivity analyses to assess the influence of the prior specification on the conclusions | ||

Large sample size at interim | Designed to transition rapidly from an optimistic to a sceptical prior when more accrual data are available |

Formal reviews may occur at given time points of the projected recruitment period or continuously, depending on the characteristics of the study, including such factors as the total length of time for recruitment and the level of risk. Ideally, these formal reviews serve as the minimum number of time points at which action will be taken.

On the basis of statistical decision rules, recruitment is classified as falling into one of four categories: ‘on target’, ‘slightly off target’, ‘considerably off target’ and ‘off target’. Evidence of inadequate accrual requires that a corrective plan come into play.

Notwithstanding the availability of statistical models for evaluating accrual, their implementation into an easily accessible, user-friendly software program is not well established. To the best of our knowledge, the only software widely accessible is the R package ‘accrual’,

The COSTAMI trial

The trial terminated after a 3-year accrual with 686 patients recruited. Only some of the planned comparisons were addressed with satisfactory power. Individual data were accessible to authors.

The following is a proposal of how key elements pertaining to accrual monitoring could have been presented in the trial protocol. Recruitment targets and duration are taken from the original protocol.

The trial is expected to accrue 1506 patients (753 per arm) in a 3-year period. Accrual monitoring will be performed using the Bayesian constant accrual model.

The Bayesian constant accrual model

Let us define the upper and lower limits of the credibility interval around the point estimate of the mean predicted total duration time (_{upper}
_{lower}

‘On target’ if _{upper}

‘Slightly off target’ if _{upper}

‘Considerably off target’ if _{upper}

‘Off target’ if _{lower}

The results of the retrospective application of the chosen Bayesian monitoring model are shown in

Results of Bayesian models for accrual prediction for COSTAMI trial. Ninety-five per cent credibility intervals and point estimates of predicted total accrual duration. In green ‘on-target’ accrual, in yellow ‘slightly off-target’ accrual, in orange ‘considerably off-target’ accrual and in red ‘off-target’ accrual.

An early alert on the slow accrual could have noted the clinical trial’s failure to include enough patients to achieve the declared study power.

After 196 days, the predicted sample size at the end of the trial ranged from 799 to 945 patients, meaning a reduction in the power of the study from a minimum of 20 percentage points to a maximum of 27 percentage points. At 312 days, things worsened as the power, based on the predicted sample size achieved at the end of trial, was far below 60% (ranging from 51% to 57%).

Within the first year of the clinical trial, a monitoring procedure could have promptly posed questions about early study termination for futility due to lack of power.

The BiPACS

The following is a proposal of how key elements pertaining to accrual monitoring could have been presented in the trial protocol. Recruitment targets and duration are taken from the original protocol.

The trial is expected to accrue 196 patients (treatment allocation ratio of 1:1) in a 5-year period. Accrual monitoring will be performed using the Bayesian constant accrual model.

The Bayesian constant accrual model

Let us define (for each prior choice) the upper and lower limits of the credibility interval around the point estimate of the mean predicted total duration time (_{upper}
_{lower}

‘On target’ if _{upper}

‘Slightly off target’ if _{upper}

‘Considerably off target’ if _{upper}

‘Off target’ if _{lower}

Up to the second evaluation point (30/196), two out of three prior choices consistently indicate that the accrual is ‘considerably off target’ and therefore that it was very unlikely to reach the target sample size in a reasonable time frame, even tolerating a delay of 25%. After 40 patients enrolled, accrual was markedly ‘off target’, with a mean predicted total accrual duration of 3835 days (95% credibility interval 3410–4329) for the accelerated prior. Of note, the choice of prior does not affect this conclusion (

Results of Bayesian models for accrual prediction for BiPACS trial. Ninety-five per cent credibility intervals and point estimates of predicted total accrual duration. In green ‘on-target’ accrual, in yellow ‘slightly off-target’ accrual, in orange ‘considerably off-target’ accrual and in red ‘off-target’ accrual. From left to right: P=0.5, P=1 and accelerated prior. BiPACS, Biventricular Pacing After Cardiac Surgery.

At the first interim evaluation (20 patients in approximately 400 days), the predicted sample size at the end of the second year, computed using the accrual model, provides a potential early alert on trial accrual. On the basis of the constant accrual model with a sceptical prior (which was considered as the interim evaluations are based on small numbers), 41–65 patients are expected.

The number of patients actually enrolled at the end of the second year is slightly inferior (30 patients), implying an expected power for the study ranging from 49% to 66%. While a study with a power of approximately 70% can still be considered acceptable, an early alert would have triggered some interventions such as incentives or recruitment programmes, if feasible.

At the end of the third year, the number of patients is again under the minimum sample size predicted by the model (40 patients), showing an inherently slow accrual process. Projecting these data to the end of the study indicates a study power ranging from 44% to 58%.

Patient recruitment difficulties are caused by a number of factors, including high financial costs, competing demands on clinicians, regulatory barriers, narrow eligibility criteria and cultural attitudes towards research.

This paper provides a formal framework for accrual monitoring that should be envisaged in a clinical trial protocol and illustrates the use of some statistical monitoring tools. This is in line with the requirements of major health institutions, such as the NHLBI, which are increasingly encouraging investigators to use operational performance measures, such as enrolment rates, to regularly track progress and enhance trial efficiency.

Study investigators and ethical oversight bodies should have the needed and appropriate tools for monitoring accrual to either fix poorly accruing trials or terminate trials that cannot accrue a reasonable number of patients in a reasonable time frame to best reallocate human and economic resources to more promising studies. In the latter case, complete follow-up of subjects already enrolled for endpoints assessment and ancillary information should be guaranteed.

The use of simplistic and unsatisfactory monitoring tools should not be justified by a lack of statistical expertise. Alternatively, recruitment prediction services should be offered by local clinical trials units or research design services, which may allow models to be better tailored to the clinical trial needs.

The allocation of sufficient time for participant recruitment is a fundamental aspect of planning a clinical trial. We agree with Carlisle and colleagues

The recruitment needs for clinical trials, often conducted simultaneously and involving patients with similar conditions, results in competition for eligible subjects.

As acknowledged by others,

As our examples illustrate, problems with patient accrual can become evident early, during the first years of the clinical trial. A prompt alert on this issue could trigger different interventions to overcome protocol-related, patient-related or investigator-related barriers to recruitment, such as amending the inclusion criteria or implementing recruitment incentives and effective communications, just to mention a few.

We do not advocate making decisions solely on accrual performance; rather, we advise using accrual-monitoring metrics to complement scientific judgement when making decisions about the management of trials. Specifically, we advocate applying this tool into a continuous and integrated decision-making process to optimise the utilisation of resources throughout the trial.

IB and PB designed the study, wrote the manuscript and performed the statistical analysis. All authors read and approved the final manuscript.

None declared.

Not commissioned; externally peer reviewed.

No additional data are available.