Probability of success
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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.
- Conditional probability of success (CPOS): It is the probability of observing success (in terms of the observed result) in the future given the observed data and the treatment effect equaling a specific value. CPOS is an extension of conditional power. Its success criteria are not restricted to statistical significance. However when the success is defined as statistical significance, it becomes conditional power.
- Predictive probability of success (PPOS): It is the probability of observing success in the future given the observed data. PPOS is an extension of predictive power. Its success criteria are not restricted to statistical significance. However when the success is defined as statistical significance, it becomes predictive power. Note that PPOS is a conditional probability conditioned on randomly observed data. Hence it is a random variable.
- Posterior probability of success (OPOS): It is the probability of success (in terms of the treatment effect parameter) calculated using posterior probability. Note that OPOS is a conditional probability conditioned on randomly observed data. Hence it is a random variable.