  Likelihood methods for measuring statistical evidence obey the likelihood
principle while maintaining bounded and well-controlled frequency properties.
These methods lend themselves to sequential study designs because they measure
the strength of statistical evidence in accumulating data without needing
adjustments for the number of planned or unplanned examinations of data.
However, sample size projections have, to date, only been developed for fixed
sample size designs. In this paper, we consider sequential study designs for
time-to-event outcomes assuming likelihood methods will be used to monitor the
strength of statistical evidence for efficacy and futility. We develop sample
size projections with the aim of controlling the probability of observing
misleading evidence under the null and alternative hypotheses, and we show how
efficacy and futility considerations are managed in this context. We also
consider relaxing the requirement of specifying the simple alternative
hypothesis in advance of the study. Finally, we end with a comparative
illustration of these methods in a phase II cancer clinical trial that
previously was designed within a Bayesian framework.
