  Recently there has been much work on early phase cancer designs that
incorporate both toxicity and efficacy data, called Phase I-II designs because
they combine elements of both phases. However, they do not explicitly address
the Phase II hypothesis test of $H_0: p\le p_0$, where $p$ is the probability
of efficacy at the estimated maximum tolerated dose (MTD) $\widehat{\eta}$ from
Phase I and $p_0$ is the baseline efficacy rate. Standard practice for Phase II
remains to treat $p$ as a fixed, unknown parameter and to use Simon's 2-stage
design with all patients dosed at $\widehat{\eta}$. We propose a Phase I-II
design that addresses the uncertainty in the estimate $p=p(\widehat{\eta})$ in
$H_0$ by using sequential generalized likelihood theory. Combining this with a
Phase I design that incorporates efficacy data, the Phase I-II design provides
a common framework that can be used all the way from the first dose of Phase I
through the final accept/reject decision about $H_0$ at the end of Phase II,
utilizing both toxicity and efficacy data throughout. Efficient group
sequential testing is used in Phase II that allows for early stopping to show
treatment effect or futility. The proposed Phase I-II design thus removes the
artificial barrier between Phase I and Phase II, and fulfills the objectives of
searching for the MTD and testing if the treatment has an acceptable response
rate to enter into a Phase III trial.
