Profit Evaluations When Adaptation by Design Is Applied

Background: Adaptation by design consists in conservatively estimating the phase III sample size on the basis of phase II data; it is also called conservative sample size estimation (CSSE). The usual assumptions are that the effect size is the same in both phases and that phase II data are not used for phase III confirmatory analysis. CSSE has been introduced to increase the rate of successful trials, and it can be applied in most clinical areas. CSSE reduces the probability of underpowered experiments and can improve the overall success probability of phase II and III, but it also increases phase III sample size, increasing the time and cost of experiments. Thus, the balance between higher revenue and greater cost is the issue. Methods: A profit model was built assuming that CSSE was applied and considering income per patient, annual incidence, time on market, market share, phase III success probability, fixed cost of the 2 phases, and cost per patient under treatment. Results: Profit turns out to be a random variable depending on phase II sample size and conservativeness. Profit moments are obtained in a closed formula. Profit utility, which is a linear function of profit expectation and volatility, is evaluated in accordance with the modern theory of investment performances. Indications regarding phase II sample size and conservativeness can be derived on the basis of utility, for example, through utility optimization. Conclusions: CSSE can be adopted in many different statistical problems, and consequently the profit evaluations proposed here can be widely applied.