Jul 2, 2015 1:33:01 PM
Clyde Haberman, a columnist for the New York Times, once commented on the remarkable consistency of train arrival times on the Tokyo subway: "Every station lists the scheduled arrival times: 9:01, 9:04, 9:08 and so on. I lived in that city for five years...I never saw a train arrive so much as a minute late, not once. A posting of 9:01 meant 9:01." . Such predictability is rarely observed in the messy world of clinical operations, yet many study plans are formulated like a Tokyo subway timetable. In a previous blog entry , we cited an example trial that targeted 1,800 patients across 50 sites over a 10-month period. Let us examine three underlying assumptions in this plan, with the help of a modeling and simulation tool.
(1) Will patients arrive at regular intervals or at random intervals?
In the example above, we required an enrollment rate of 3.6 patients per site per month. Of course, this does not mean that in every month, we will observe 3 or 4 patients at each site. Rather, many studies have shown [3, 4] that patient arrivals behave as a random process where the observed number of patients will vary from month to month according to a Poisson distribution . The figures above show the averaged planned enrollment in blue, and the 95% prediction intervals in red. The primary advantage of modeling enrollment as a random process is the ability to calculate a probability of success. Before doing so, we will consider other sources of random variation.
(2) Will enrollment rates across sites be identical or variable?
Just as we do not expect enrollment to be identical from month to month, we do not expect every site to recruit at exactly the same rate. Instead, enrollment rates will vary across sites according to some distribution. One flexible distribution used often in such applications is the gamma. In fact, Ansimov and Fedorov (2007) have shown in an analysis of several multi-center trials that, “a Poisson-gamma model is in good agreement with real data” . In the figures above, the updated prediction intervals incorporating this assumption are slightly wider, reflecting the greater uncertainty about exactly when the enrollment target will be achieved.
(3) Will sites open at the same time or with some delay?
Finally, not all sites in a study will come online at the same time. Site initiation involves a long sequence of complex procedures including: prestudy visits, regulatory documentation, as well as contract and budget negotiation. The time required for each of these steps will vary from country to country, and from site to site. In a comprehensive survey of study initiation practices, Lamberti et al (2012) found that a Phase III study can take around 10 months from prestudy visit to first patient in, and around 17 months from protocol approval to 100% approved sites initiated . Thus, enrollment will start more slowly when some sites take longer than others to initiate.
From this more realistic plan, our original hope of enrolling 1,800 patients within 10 months will not be feasible. Targeting an 80% probability of success, we predict the study duration will take up to 14 months. In this way, trial planners who use modeling and simulation tools will be able to maximize their chances of study completion. 
 Anisimov, V. V., & Fedorov, V. (2007). Modelling, prediction and adaptive adjustment of recruitment in multicentre trials. Statistics in Medicine, 26, 4958–4975.
 Barnard, K. D., Dent, L., & Cook, A. (2010). A systematic review of models to predict recruitment to multicentre clinical trials. BMC Medical Research Methodology, 10, 63.
 Lamberti, M. J., Brothers, C., Manak, D., & Getz, K. (2012). Benchmarking the study initiation process. Therapeutic Innovation & Regulatory Science, 47, 101–109.