Allocating the Sample Size in Phase II and III Trials to Optimize Success Probability

Abstract

{\bf Background} Clinical trials of phase II and III often fail due to poor experimental planning. Here, the problem of allocating available resources, in terms of sample size, to phase II and phase III is studied with the aim of increasing success rate. The overall success probability (OSP) is accounted for.

{\bf Methods} Focus is placed on the amount of resources that should be provided to phase II and III trials to attain a good level of OSP, and on how many of these resources should be allocated to phase II to optimize OSP. It is assumed that phase II data are not considered for confirmatory purposes and that are used for planning phase III through sample size estimation. Being $r$ the rate of resources allocated to phase II, $OSP(r)$ is a concave function and there exists an optimal allocation $r_{opt}$ giving $\max\{OSP\}$. If $M_I$ is the sample size giving the desired power to phase III, and $kM_I$ is the whole sample size that can be allocated to the two phases, it is indicated how large $k$ and $r$ should be in order to achieve levels of OSP of practical interest.

{\bf Results} For example, when 5 doses are evaluated in phase II and 2 parallel phase III confirmatory trials (one-tail type I error $=2.5\%$, power $=90\%$) are considered with 2 groups each, $k=24$ is needed to obtain $OSP\simeq 75\%$, with $r_{opt}\simeq 50\%$. The choice of $k$ depends mainly on how many phase II treatment groups are considered, not on the effect size of the selected dose. When $k$ is large enough, $r_{opt}$ is close to $50\%$. An $r\simeq25\%$, although not best, might give a good OSP and an invitingly small total sample size, provided that $k$ is large enough.

{\bf Conclusions} To improve the success rate of phase II and phase III trials, the drug development could be looked at in its entirety. Resources larger than those usually employed should be allocated to phase II to increase OSP. Phase II allocation rate may be increased to, at least, 25\%, provided that a sufficient global amount of resources is available.