# Sample Size Determination

## Sample size determination

What’s the importance of this? Sample size determination in clinical trials are required due to two reasons. One is ethical. As the name says, this is – designed by scientist, approved by authorities – “trial”. There are risks and we all would like to minimize the risk of causing any harm to any volunteer or patient. The real question is: how can we minimize  the risk with trying to reach the scitific goals? This is what sample size determination talks about. The calculations provice the reuqired sample size to confirm the research hypothesis (more preciously to decline the opposite one but this is a different story). Another view: we measure the “success” of a study – gennerally – in p-values. We say that we are quite certain in the efficacy of a treatment if the statement of “the treatment is not efficient enough” can be declined with a 95% probability. Due to the nature of the background mathematics, the probability of decline increases with the increase of the sample size. To simplify, you can prove any statement with increasing the sample size to infinity. Each design and eache background statistical tool has a sample size formula which is the minimally required to prove that specific statistical assumpation – if that is really valid. To avoid any potential bias – or freud – the clinical trials should be based on the calculated sample sizes.

### Sample size in closed formula

The statistical significance – generally – is defined as an outcome of a statistical test. A statistical test is not more or less than a formula of certain input data. If a statistical test can be derived by a closed formula, than the required sample size can also be determined as output of a mathematical function. These processes are well programmed and documented in SAS, R or PASS.

### Sample size by simulation

There are more complex designs, where the statistical evalution does not depend on a lonely statistical test, but rather a process of statistical testing. In those cases the required sample size cannot be determined with the help of closed formulas: it rather requires a kind of simulation. This procedured is much more complicated but not because of more programmic efforts, but due to the increased validation procedures.