  The use of `backfilling', assigning additional patients to doses deemed safe,
in phase I dose-escalation studies has been used in practice to collect
additional information on the safety profile, pharmacokinetics and activity of
a drug. These additional patients help ensure that the Maximum Tolerated Dose
(MTD) is reliably estimated and give additional information in order to
determine the recommended phase II dose (RP2D). In this paper, we study the
effect of employing backfilling in a phase I trial on the estimation of the MTD
and the duration of the study. We consider the situation where only one cycle
of follow-up is used for escalation as well as the case where there may be
delayed onset toxicities. We find that, over a range of scenarios, there is an
increase in the proportion of correct selections and a notable reduction in the
trial duration at the cost of more patients required in the study.
