7. All Mixed Up

Possible relationships between the probability of early response and expected survival time with a given treatment are at the heart of the conventional paradigm for using phase II response data to plan phase III trials. These relationships often are misunderstood, however, which can lead to very bad decisions. To illustrate this, I will present a simple probability computation which gives numerical results that may seem surprising. I then will give an example of how a trial effect can be mistaken for a treatment effect if one compares data from different trials rather than randomizing. A method will be described for computing the predictive probability that a future phase III trial will be successful given observed phase II data, and this will be illustrated by a numerical example. An example will be given of a randomized trial in which between-arm comparisons of the 90-day response probabilities and the 12-month progression-free survival probabilities gave opposite conclusions regarding which treatment was superior. These examples illustrate the facts that probability often can be counterintuitive, and that basing treatment comparisons on early outcomes can be very misleading.