Clinical trials often plan to enroll hundreds to thousands of human subjects, and careful and regulated planning is employed to ensure that the trial's scientific objectives are fulfilled. However, the importance of the feasibility and timeliness of participant accrual is often minimized during the planning stage. This is unfortunate since the recruitment of human subjects into a clinical trial must be timely and is vital to the success of the trial [1, 2]. In addition, a slowly progressing trial may expose the human subjects to ineffective treatments for a longer period of time than necessary, and as such, human subject protection may be compromised [2, 3]. Therefore, a clinical trial must be planned with an adequate understanding of the potential accrual rate so that the clinical trial's scientific objectives can be evaluated in a timely manner.

The first step in estimating the clinical trial's accrual period is to estimate the accrual rate. In the context of a multi-center trial, each clinical center's rate will need to be estimated. One approach for evaluating each clinical center is to solicit information via a questionnaire. Content of the questionnaire could include measurements of the total number of cases currently or recently seen for the targeted condition, a listing of other clinical trials that might compete for the same patients, and a summary of the investigator's (or clinical center's) experience meeting prior accrual expectations. The completed questionnaires can be used to formulate an initial estimate of the accrual rate for each participating clinical center.

However, experience has shown the accrual period is longer than planned even when such tangible efforts are made to estimate the accrual rate. Carter [1] presented a methodological examination of this issue and developed a statistical model to estimate the accrual period of a clinical trial. It was argued that utilizing only the historical mean for the projected accrual period fails to account for the variation in the rate that may occur as the study progresses. In this brief report, we illustrate three approaches to estimating the accrual period of a clinical trial and offer discussion on potential best practices.

To illustrate these three approaches, a multi-center protocol undergoing development is presented. The primary objective of the study is to measure the effectiveness of a selective serotonin reuptake inhibitor (SSRI) in the treatment of depression in a patient population with comorbid substance dependence. A sample size of 360 participants, enrolled from 10–12 research sites, has been estimated to test the primary hypothesis with 90% power. While the protocol is still being finalized, an initial estimate of the accrual period is of practical interest to the protocol investigators.

To account for the delay, the conditional model could be utilized. Suppose the initial rate of accrual is two participants per month for the first two months while the protocol is active at only one site. At the start of month three, one additional site will be released for enrollment to bring the estimated accrual rate to four participants per month. Figure 1 illustrates the expected accrual as additional sites are added to the study and that full accrual potential is not reached until approximately 1/3 of the trial duration has passed. The estimate of 23 months seems much more reasonable given the staggered initiation process; however, additional models could be implemented to examine the effects of fluctuations in the accrual rates. Two separate Poisson models are presented in Table 1. Both models use the initiation pattern of the conditional model; however, the daily rate, which is the monthly rate divided by the standard number of days in the month, has been adjusted to reflect anticipated enrollment dynamics. Specifically, while the clinical sites treat potential participants every day of the week, research staff are expected to be available only five days per week. Thus, the estimated rate per month is discounted effectively by 5/7 to reflect this anticipated pattern. The second Poisson model further adjusts the estimate of 2 participants per month downward to be uniformly distributed between zero and two. Such an adjustment might be necessary to account for the difference in the number of participants eligible for the trial and the number that will actually consent to participate in the research. In addition, this reduction in the overall rate also adjusts the rate downward for other competing demands that could affect the participant accrual rate but would be difficult to quantify directly. As Table 1 illustrates, a dramatic difference in the expected accrual period is obtained if the rate is allowed to fluctuate uniformly on the interval 0 to 2; however, the conditional approach and the fixed-rate Poisson model provide similar results with the exception that the Poisson-based approach provides additional summary statistics that may be of interest during the planning phase.

The estimation of the accrual period of a clinical trial has dramatic practical, scientific and economic consequences and warrants greater attention in practice. As our example illustrates, the unconditional approach, while simple to implement, can yield results not consistent with trial assumptions, and may endanger the successful completion of the trial. It is acknowledged that the most complicated aspect pertaining to the estimation of accrual periods is the determination of the expected rate. As our example illustrates, sometimes dramatically different results occur with what are apparently minor modifications to model assumptions. When the potential impact of a poorly accruing clinical trial is considered, spending additional time examining the effects of model assumptions is well justified. In the end, accounting for variation and planning are essential components of good clinical research.

For the research study under consideration in this example, an estimate of 24 months to complete study recruitment seems reasonable. An accrual rate of at least two participants per month is the minimum requirement, so the expected rate after adjustment for screening to enrollment dropout percentages should still yield an accrual rate of approximately two per month. However, a more refined estimate of the accrual period can be obtained once final selection of the research sites has been made and all historical information has been analyzed. These models can also be applied after study enrollment has begun, and in the case of the Poisson model, estimating the probability of meeting the established accrual deadline has several practical implications. Although the methods have been presented in the context of a multi-center clinical trial, they are valid in the planning of a single-center clinical trial.

To facilitate implementation of the models in practice, a spreadsheet template for the calculation of the conditional model and SAS programs for the Poisson process are posted on the first author's website http://people.musc.edu/~carterre/manuscripts. Each may be freely downloaded and implemented with very little training. The posted conditional model allows for individual sites to enroll at site-specific rates as well as provides means to quickly adjust model assumptions so that sensitivity analyses can be performed. A more detailed discussion of the Poisson method is available elsewhere [1]. In summary, the conditional and Poisson accrual estimation methods may be useful to researchers designing a complex, multi-center clinical trial.

The accrual period of a clinical trial should be carefully considered, and the allocation of sufficient time for participant recruitment is a fundamental aspect of planning a clinical trial. For most multi-center clinical trials, the conditional approach should be implemented. Simulation studies using the Poisson model are recommended if there is uncertainty in the accrual rate or if the accrual rate is expected to change over time.