  An objective of phase I dose-finding trials is to find the maximum tolerated
dose; the dose with a particular risk of toxicity. Frequently, this risk is
assessed across the first cycle of therapy. However, in oncology, a course of
treatment frequently consists of multiple cycles of therapy. In many cases, the
overall risk of toxicity for a given treatment is not fully encapsulated by
observations from the first cycle, and hence it is advantageous to include
toxicity outcomes from later cycles in phase I trials. Extending the follow up
period in a trial naturally extends the total length of the trial which is
undesirable. We present a comparison of eight methods that incorporate late
onset toxicities whilst not extensively extending the trial length. We conduct
simulation studies over a number of scenarios and in two settings; the first
setting with minimal stopping rules and the second setting with a full set of
standard stopping rules expected in such a dose finding study. We find that the
model-based approaches in general outperform the model-assisted approaches,
with an Interval Censored approach and a modified version of the Time-to-Event
Continual Reassessment Method giving the most promising overall performance in
terms of correct selections and trial length. Further recommendations are made
for the implementation of such methods.
