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.
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The probabilityofsuccess (POS) is a statistics concept commonly used in the pharmaceutical industry including by health authorities to support decision...
Boolean-valued outcome: success (with probability p) or failure (with probability q = 1 − p {\displaystyle q=1-p} ). A single success/failure experiment is also...
probability 1/2 and value −1 with probability 1/2. The binomial distribution, which describes the number ofsuccesses in a series of independent Yes/No experiments...
Predictive probabilityofsuccess (PPOS) is a statistics concept commonly used in the pharmaceutical industry including by health authorities to support...
2,3,\ldots \}} ; The probability distribution of the number Y = X − 1 {\displaystyle Y=X-1} of failures before the first success, supported on N 0 = {...
In statistics, the power of a binary hypothesis test is the probability that the test correctly rejects the null hypothesis ( H 0 {\displaystyle H_{0}}...
The posterior probability is a type of conditional probability that results from updating the prior probability with information summarized by the likelihood...
In probability theory and statistics, there are several relationships among probability distributions. These relations can be categorized in the following...
In probability theory and statistics, the beta distribution is a family of continuous probability distributions defined on the interval [0, 1] or (0, 1)...
interval is a confidence interval for the probabilityofsuccess calculated from the outcome of a series ofsuccess–failure experiments (Bernoulli trials)...
theory ofprobability and statistics, a Bernoulli trial (or binomial trial) is a random experiment with exactly two possible outcomes, "success" and "failure"...
odds in Wiktionary, the free dictionary. In probability theory, odds provide a measure of the likelihood of a particular outcome. When specific events...
Intervention: The Conditions for Success and Failure. Oxford University Press. ISBN 978-0-19-925243-5. "Just War Theory and the Last of Last Resort - Ethics & International...
In probability theory and statistics, the hypergeometric distribution is a discrete probability distribution that describes the probabilityof k {\displaystyle...
In probability theory and statistics, the negative binomial distribution is a discrete probability distribution that models the number of failures in a...
ofsuccesses seen, which we expect to converge to the underlying probabilityofsuccess. The third line writes out the probability mass function of the...
probability and statistics, a compound probability distribution (also known as a mixture distribution or contagious distribution) is the probability distribution...
binomial test is useful to test hypotheses about the probability ( π {\displaystyle \pi } ) ofsuccess: H 0 : π = π 0 {\displaystyle H_{0}\colon \pi =\pi...
In probability theory and statistics, the Poisson distribution is a discrete probability distribution that expresses the probabilityof a given number...
In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilitiesof occurrence of different possible...
technique for both success and failure that explores responses through a single initiating event and lays a path for assessing probabilitiesof the outcomes...
optimal stopping theory that is studied extensively in the fields of applied probability, statistics, and decision theory. It is also known as the marriage...
In probability theory and statistics, the cumulative distribution function (CDF) of a real-valued random variable X {\displaystyle X} , or just distribution...
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causing the probabilityofsuccess to change with each draw. Unlike the standard hypergeometric distribution, which describes the number ofsuccesses in a fixed...
mathematical problem in probability theory and combinatorics. In this problem, 100 numbered prisoners must find their own numbers in one of 100 drawers in order...
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