## Basic considerations

In determining sample size, it is helpful to consider the problem in terms of hypothesis testing, even though the aim of the trial should be to provide an estimate of the treatment effect and not just to enable us to state whether the effect is 'statistically significant' or not.

If we consider a clinical trial comparing treatment A with treatment B with respect to survival, then the 'null hypothesis' (often referred to as Ho) is first defined. Typically,

 True effect Conclusion from trial A = B A = B A = B ✓ Type I error A = B Type II error ✓

this states that there is no difference in the main outcome measure (OM) between A and B (OMA = OMB, that is the result you hope not to see).

The 'alternative' hypothesis (Hi) defines the result you hope to see which might be: There is a difference (OMA — OMB = d, where d = 0).

Here d, which is a measure of treatment effect, is often known as the effect size. The aim of careful sample size calculation is to ensure that the impact of random error is small in relation to the effect size you wish to detect. Random error itself can act to mask or enhance the true treatment effect, as illustrated in Table 5.1. It is, however, possible to control both type I and type II errors, and the setting of acceptable limits for these is part of the process of calculating the sample size for a given trial.

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