Phase II Cancer Clinical Trial Design

For ease of exposition, our methodology will be developed in the context of phase II cancer clinical trials. In this setting, many drugs have been evaluated with tumor response, which has a specific definition that loosely translates into a reduction in the tumor size (or reduction in overall volume of disease).^{14 (link)} The probability of response will be designated with π_r. Another variable of interest in phase II oncology is the probability a patient survives without experiencing a progression of disease for a specified period of time (say 6 months or 2 years, depending on the aggressiveness of the disease). We will use 6 months as a matter of convenience and denote this binomial variable as “6-month progression-free survival (PFS)” or “at risk for PFS at 6 months.” The probability of this event will be designated with π_s. Tumor response is a variable that is capable of detecting agents that are effective at selectively killing tumor cells (cytotoxic) whereas 6-month PFS is capable of detecting agents that can stabilize disease but are not necessarily effective at cell kill (cytostatic).
The null hypothesis is formulated as follows: H₀ : π_r ≤ π_r0, and π_s ≤ π_s0, where π_r0 and π_s0 are specified values (obtained from historical data) that are believed to be uninteresting or comparable to the current standard of care. The alternative hypothesis is the complement of this null parameter space. Commonly the area of the parameter space where high statistical power is desired can be written as follows: H₁ : π_r ≥ π_r1 = π_r0 + Δ_r or π_s ≥ π_s1 = π_s0 + Δ_s where Δ_r and Δ_s are the (minimal) clinically significant improvements in the proportion responding and with 6-month PFS, respectively.