Dr. Gen Li is president of Phesi. He can be reached at gen.li@phesi.com.

Dr. Gen Li

	On the surface, every veteran in clinical trials can tell you a lot about different factors impacting patient enrollment cycle times. A specifically defined patient population in a particular disease, for example, can impact the ability of sites to identify and recruit patients in a defined period of time, therefore, impacting enrollment cycle time. An experienced and successful investigator/site has better ability to enroll qualified patients compared to an inexperienced investigator/site. The higher proportion of experienced sites in a pool of sites deployed in a clinical trial can result in shorter enrollment cycle times.

	Instinctively, when there are more investigators/sites being deployed for a trial with a defined number of patients needed, we should expect shortened enrollment cycle time. This sounds right, but is it really?

	Here are two different scenarios:                                    

	As clinical development organizations are under pressure to deliver new products faster, senior management seems happy to apply “unlimited” resources behind pivotal clinical trials evaluating promising drug candidates. The simple logic is to add more sites to the pool for enrollment, aiming to proportionately shorten enrollment cycle time. But realistically, how often does this shorten enrollment cycle time? The simple answer is: rarely, if at all.

	In another common scenario, when we are transitioning to a Phase III program after a successful Phase II program, we often “extrapolate” the operational results from Phase II trials(s) to Phase III trial(s); we use the enrollment rate from the Phase II trial(s) to calculate the number of sites needed for Phase III trials, hoping to achieve similar enrollment cycle times as we did in Phase II trial(s). That is all fine, except that the enrollment cycle time(s) will unlikely to be close to the calculation. The enrollment cycle times are generally substantially longer in this situation.

	We have long noted that adding extra sites to a clinical trial has only limited impact to enrollment cycle time.

 We naturally want a better, in-depth understanding of the issue-is there a pattern between the number of sites deployed and enrollment cycle time? If the answer is yes, is it possible to define that pattern in a simple and universally applicable mathematical relationship?

	Interestingly, similar phenomena exist in other areas. When we track the growth of a school of fish, we find the average size of the fishes grows rapidly in the earliest days since their hatch. The incremental increase of their size diminishes at the same time segment was added. Eventually, the average size of these fishes will hit a ceiling; they will no long grow in size.

	Similarly, when we charge a battery, we can relatively quickly get to, for example, the first 50% of the battery being charged. The charge speed slows down, until it hits a ceiling at some point.

	We know that the fish growth pattern has been thoroughly studied by ecologists, and the pattern to charge a battery has also been thoroughly studied by physicists. Could we possibly borrow what they have learned and apply it to understand the relationship between investigator sites and enrollment rates?

	We know it is never easy to find any pattern in clinical trial planning and execution, for a simple reason: each clinical trial is distinctly different, and there is no such thing as two identical clinical studies.

	This article is a part of the author’s integrated effort to build a conceptual structure for managing study operations in clinical development by focusing on forecasting enrollment rate at the clinical trial level (clinical trial enrollment rate, CTER) and site level (gross site enrollment rate, GSER). We are able to establish a relationship between the site activation process and site enrollment performance.

	This article will also establish the relationships between these concepts. They are truly integrated components of an increasingly comprehensive conceptual framework.

	Clinical trial enrollment rate (CTER, number of patients per trial per month)

	Using a clinical development database created by the author-a sub-database meeting-the following inclusion criteria was established:

		Completed enrollment at the time of analysis

	The sub-database of relatively “homogeneous” clinical trials for a single metabolic disease condition looked like this:

	We took the following steps to derive this chart:

		Focus on trials with a single disease condition as primary condition

		Put the clinical trial into baskets according to number of sites:					

		Build a data table to pair median number of sites and median of trial level enrollment rate (CTER, clinical trial enrollment rate, number of patients enrolled per month):

	Going through the same steps, we can draw a similar chart for trials in a single respiratory disease conditions:

	Or for trials in a single neurology disease condition:

	As a matter of fact, we can draw similar charts for a group of clinical trials in every single disease condition, when the sample size is big enough, and the disease condition is “pure” enough.

	In each of the charts, we see a generalizable pattern: as more sites are added to a clinical trial in the same disease condition, the CTER increases. However, for every equal number of sites (N) added, the benefit to CTER diminishes. Eventually, the CTER will hit some sort of ceiling: the benefit from adding more sites becomes negligible.

	The mathematics relationship is exactly the same relationship used to describe the growth rate for a school of fish in the ocean.

	Each and every one of these charts seems to have distinct sizes and shapes. For the trained eyes of a mathematician, there is a simple equation to include all the charts:

	We can do the same for the other two charts:

	Going through the same steps, we can draw similar chart for trials in a single respiratory disease conditions:

	From what we know now, there is no “proportionate” relationship between number of sites and CTER. That is to say, the relationship between sites and enrollment rate are not linear. With all factors equal, adding sites to a clinical trial can increase CTER, but at a diminished incremental benefit. Moreover, the benefit diminishes as more and more sites are being added.

	In another words, there is an operational boundary where we have to plan and execute clinical trials within. When we keep adding sites to a study, we will hit the ceiling at some point, where there will be no measurable benefit in gaining enrollment rate. It is safe to say that there is a limitation in terms of how far we can go to shorten enrollment cycle time by adding investigator sites. (The details of the operational boundaries are discussed in mathematical terms in the appendix).

	But why? If we were adding more sites to a trial relatively homogenously, and assuming each of the sites behave in the same pattern as the others and do their job in recruiting patients for the trial, why can’t their contributions be added up to give a “proportional” (linear) relationship to increase CTER?

	The fact is, as we add more sites to a trial, participating sites can no longer behave in the same pattern as before. Simply put, the ability for individual sites to recruit and contribute patients to the trial is suppressed continuously as more sites are added to a clinical study, when other factors are equal.

	Using the same approach as we just used to understand CTER, we can learn more about site level enrollment rate (GSER, gross site enrollment rate or number of patients per site per month).

	Starting from the same sub-database being used to understand CTER, we took the following step to build the chart showing the relationship between number of sites (N) and GSER:

	Going through the same steps, we can draw similar charts for trials in a single respiratory disease condition (left), and trials in a single neurology disease condition (right):

Articles

Instinctively, when there are more investigators/sites being deployed for a trial with a defined number of patients needed, we should expect shortened enrollment cycle time. This sounds right, but is it really?

Dr. Gen Li

Articles

Forecast Enrollment Rate in Clinical Trials