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# Practical considerations for estimating clinical trial accrual periods: application to a multi-center effectiveness study

- Rickey E Carter
^{1}Email author, - Susan C Sonne
^{2}and - Kathleen T Brady
^{2}

**5**:11

https://doi.org/10.1186/1471-2288-5-11

© Carter et al; licensee BioMed Central Ltd. 2005

**Received: **23 November 2004

**Accepted: **30 March 2005

**Published: **30 March 2005

## Abstract

### Background

Adequate participant recruitment is vital to the conduct of a clinical trial. Projected recruitment rates are often over-estimated, and the time to recruit the target population (accrual period) is often under-estimated.

### Methods

This report illustrates three approaches to estimating the accrual period and applies the methods to a multi-center, randomized, placebo controlled trial undergoing development.

### Results

Incorporating known sources of accrual variation can yield a more justified estimate of the accrual period. Simulation studies can be incorporated into a clinical trial's planning phase to provide estimates for key accrual summaries including the mean and standard deviation of the accrual period.

### Conclusion

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.

## Keywords

- Poisson Model
- Clinical Center
- Conditional Model
- Conditional Approach
- Accrual Rate

## Background

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.

## Methods

### Unconditional approach

A common approach to estimating the accrual period in a clinical trial is to divide the sample size by the expected rate. Often, the expected rate for the clinical trial is estimated by summing the historical trends at each participating research site to create a study-wide estimate of the accrual rate. For example, if subjects are to be recruited from 5 sites at the expected rate of 5 participants per month per site, then one could estimate that it would take 8 months to enroll 200 participants using the combined rate of 25 participants per month. However, since the rate of 25 participants per month is assumed to be fixed in value, it is best to consider that "on average" it may take 8 months to enroll 200 participants. The obvious limitation of this approach is that there is no mechanism to account for known sources of variation in the rate. For example, if the 5 sites were to begin enrolling at different times, then a study-wide estimate of 25 participants per month is no longer tenable. The following approach directly addresses this limitation.

### Conditional rates

A more accurate estimate of the accrual period is possible when additional prior information is incorporated into the model. Two important sources of variation in the overall accrual period are the rates at which individual sites accrue and the length of time in which sites actively recruit participants. For example, suppose that a large research institution (Site A) may be capable of recruiting 15 participants per month and that four additional sites are only capable of recruiting a combined 10 participants per month. Then, the point in time in which the Site A begins enrollment will greatly affect the trial's overall accrual rate. Moreover, the timing of Site A's initiation and subsequent accrual should be critically evaluated by the sponsor.

For example, if it is known in advance that Site A will take 4 to 8 weeks longer to initiate recruitment than the other four sites, an estimate of 8 months to enroll 200 participants would seem overly optimistic. The sponsor might be interested in determining the effect of including Site A on key trial markers (e.g., feasibility, cost, and total clinical trial duration) by allowing for up to an 8-week delay in Site A's initiation. However, the calculation of a more refined accrual period, which would drive many of the cost estimates, would require the adjustment for time dependent changes in the overall accrual rate. Fortunately, computational tools such as a spreadsheet aid in the necessary calculations.

### Poisson process

The methodology presented by Carter [1] allows for a more sophisticated model that can incorporate a variety of sources of variations. In this paper, the exploration of mean accrual time will be examined. As the two previous approaches illustrate, the mean number of participants per month per site was assumed to be fixed, yet the overall accrual time varied. The source of variation introduced was a delay in the initiation of the protocol at a site. There is another source of variation. Just as is well established in economics, historical trends may not adequately reflect future trends especially when short periods of time are considered.

One approach to incorporating variation into mean number of participants per month is to assume that participants arrive into the study according to a known probability distribution. Carter [1] proposed the Poisson distribution since it has widespread applications that often include the statistical modeling of the number of arrivals or observations [4, 5]. Essentially, this method simulates the accrual into a trial using a random number generator. At the end of each simulation iteration, the number of days (or months) required for the program to reach the sample size is recorded. When the simulations are repeated many times, an empirical distribution of the accrual period is obtained. Using this empirical distribution, one can answer questions related to the probability of completing accrual within a specified time as well as observe how much variance in accrual time can be expected given the model assumptions. This probabilistic approach is most beneficial when a finite amount of time has been granted for the clinical trial. Thus by conditioning on the predetermined time, one could estimate the number of clinical centers and the rate per month needed to ensure with high probability, such as 80%, that the clinical trial will complete enrollment before the allocated time expires.

## Results

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.

Estimated accrual periods for a 360-participant, 10-center clinical trial.

Unconditional Approach | Conditional Rates | Poisson Process | Poisson Process Variable Rates | |
---|---|---|---|---|

Estimated Accrual Period (in months) | ||||

Mean | 18 | 23 | 23.2 | 42.6 |

Standard Deviation | NA | NA | 1.0 | 8.0 |

Range | NA | NA | [20.1, 25.8] | [28.0, 84.0] |

75th Percentile | NA | NA | 24.0 | 46.0 |

## Discussion

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.

## Conclusion

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.

## Declarations

### Acknowledgements

This work is partially supported by the National Institutes of Health Grants DA013727 and HS10871.

## Authors’ Affiliations

## References

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- The pre-publication history for this paper can be accessed here:http://www.biomedcentral.com/1471-2288/5/11/prepub

### Pre-publication history

## Copyright

This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.