Probability of success

The probability of success (POS) is a statistics concept commonly used in the pharmaceutical industry including by health authorities to support decision making.

The probability of success is a concept closely related to conditional power and predictive power. Conditional power is the probability of observing statistical significance given the observed data assuming the treatment effect parameter equals a specific value. Conditional power is often criticized for this assumption. If we know the exact value of the treatment effect, there is no need to do the experiment. To address this issue, we can consider conditional power in a Bayesian setting by considering the treatment effect parameter to be a random variable. Taking the expected value of the conditional power with respect to the posterior distribution of the parameter gives the predictive power. Predictive power can also be calculated in a frequentist setting. No matter how it is calculated, predictive power is a random variable since it is a conditional probability conditioned on randomly observed data. Both conditional power and predictive power use statistical significance as the success criterion. However, statistical significance is often not sufficient to define success. For example, a health authority often requires the magnitude of the treatment effect to be bigger than an effect which is merely statistically significant in order to support successful registration. In order to address this issue, we can extend conditional power and predictive power to the concept of probability of success. For probability of success, the success criterion is not restricted to statistical significance. It can be something else such as a clinical meaningful result.

Traditional pilot trial design is typically done by controlling type I error rate and power for detecting a specific parameter value. The goal of a pilot trial such as a phase II trial is usually not to support registration. Therefore it doesn't make sense to control type I error rate, especially a big type I error, as typically done in a phase II trial. A pilot trial usually provides evidence to support a Go/No Go decision for a confirmatory trial. Therefore it makes more sense to design a trial based on PPOS. To support a No/Go decision, traditional methods require the PPOS to be small. However the PPOS can be small just due to chance. To solve this issue, we can require the PPOS credible interval to be tight such that the PPOS calculation is supported by sufficient information and hence PPOS is not small just due to chance. Finding an optimal design is equivalent to find the solution to the following 2 equations.

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