# Sample size for clinical trials

Ensure optimal power or sample size using power analysis. Power for clinical trials available in Excel using the XLSTAT statistical software.

## Power and sample size analysis in clinical trials

XLSTAT-Power enables you to compute the necessary sample size for a clinical trial.

Three types of trials can be studied:

**Equivalence trials:**An equivalence trial is where you want to demonstrate that a new treatment is no better or worse than an existing treatment.**Superiority trials:**A superiority trial is one where you want to demonstrate that one treatment is better than another.**Non-inferiority trials:**A non-inferiority trial is one where you want to show that a new treatment is not worse than an existing treatment.

These tests can be applied to a binary outcome or a continuous outcome.

When testing a hypothesis using a statistical test, there are several decisions to take:

- The null hypothesis H0 and the alternative hypothesis Ha.
- The statistical test to use.
- The type I error also known as alpha. It occurs when one rejects the null hypothesis when it is true. It is set a priori for each test and is 5%.

The type II error or beta is less studied but is of great importance. In fact, it represents the probability that one does not reject the null hypothesis when it is false. We can not fix it upfront, but based on other parameters of the model we can try to minimize it. The power of a test is calculated as 1-beta and represents the probability that we reject the null hypothesis when it is false.

We therefore wish to maximize the power of the test. The XLSTAT-Power module calculates the power (and beta) when other parameters are known. For a given power, it also allows to calculate the sample size that is necessary to reach that power. The usual power used in 0.9, however, it can differ depending on the trial.

The sample size requirements or the statistical power calculations are usually done before the experiment is conducted. The main application of power calculations is to estimate the number of observations necessary to properly conduct an experiment.

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