How to deal with the Poisson-gamma model to forecast patients' recruitment in clinical trials when there are pauses in recruitment dynamic?

Recruiting patients is a crucial step of a clinical trial. Estimation of the trial duration is a question of paramount interest. Most techniques are based on deterministic models and various methods neglecting the variability in the recruitment process. To overpass this difficulty the so-called Poisson-gamma model has been introduced involving, for each centre, a recruitment process modelled by a Poisson process whose rate is assumed constant in time and gamma-distributed. The relevancy of this model has been widely investigated. In practice, rates are rarely constant in time, there are breaks in recruitment (for instance week-ends or holidays). Such information can be collected and included in a model considering piecewise constant rate functions yielding to an inhomogeneous Cox model. The estimation of the trial duration is much more difficult. Three strategies of computation of the expected trial duration are proposed considering all the breaks, considering only large breaks and without considering breaks. The bias of these estimations procedure are assessed by means of simulation studies considering three scenarios of breaks simulation. These strategies yield to estimations with a very small bias. Moreover, the strategy with the best performances in terms of prediction and with the smallest bias is the one which does not take into account of breaks. This result is important as, in practice, collecting breaks data is pretty hard to manage.