# Bioequivalence and Bioavailability Forum

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Ben
Regular

2016-12-29 14:15

Posting: # 16905
Views: 958

## Expected Power [Power / Sample Size]

Dear All,

You may have noticed that the latest `PowerTOST` update (1.4-3) now includes an updated functionality regarding the so-called expected power.

I would like to briefly introduce this concept here because (i) there already were several discussions on incorporating previous information into the sample size calculations (see e.g. here or here) and (ii) I believe this can be a valuable tool to assess the probability of trial success. The idea is that the usual power (`power.TOST()`) is conditional on the unknown (true) values for gCV and gMean ratio and therefore the specified values are assumed to be known. That means it reflects the probability of trial success only if gCV and gMean ratio are known with absolute certainty. Since this may not be a realistic assumption we usually perform power sensitivity analyses to tackle the uncertainty here. The expected power (sometimes also known as assurance) aims at defining the power without conditioning on gCV and/or gMean ratio: it is a weighted average power over all possible values of gCV and/or gMean ratio, where the weights are chosen according to the likelihood of the respective outcome to occur. It is therefore a power that directly deals with uncertainty of the input parameters and can be seen as probability of trial success. A more detailed view on the underlying theory may be found for example here: https://github.com/Detlew/PowerTOST/tree/master/inst/doc. Example calls and a detailed description of the arguments are given in the PowerTOST manual.

I should make some additional comments as this function should not be used without carefully thinking what is behind it. The expected power is sometimes bounded above by a value which is less than one! This often happens when the previous information is simply too unreliable. As a consequence, there is a systematic chance of not achieving the goal/success at all. This is in my opinion important information for the further development of a compound and the decision process. Depending on the importance this may mean that the sample size should be rather (very) high (as compared to the classical power approach) or that a reasonable target power is lower than what is usually considered (a sufficiently high target power may already be for example 70%). In order for the whole team to make an informed decision here, I would always compare the expected power to the classical power (i.e. with `power.TOST()`), but also highlight that the expected power provides a state of the art method to cope with uncertainty (whereas power.TOST does not directly take this into account).

I hope you find this tool valuable in assessing trial success chances. We would highly appreciate any feedback on it!

Best regards,
Ben.
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