  The two-trials rule for drug approval requires "at least two adequate and
well-controlled studies, each convincing on its own, to establish
effectiveness". This is usually implemented by requiring two significant
pivotal trials and is the standard regulatory requirement to provide evidence
for a new drug's efficacy. However, there is need to develop suitable
alternatives to this rule for a number of reasons, including the possible
availability of data from more than two trials. I consider the case of up to 3
studies and stress the importance to control the partial Type-I error rate,
where only some studies have a true null effect, while maintaining the overall
Type-I error rate of the two-trials rule, where all studies have a null effect.
Some less-known $p$-value combination methods are useful to achieve this:
Pearson's method, Edgington's method and the recently proposed harmonic mean
$\chi^2$-test. I study their properties and discuss how they can be extended to
a sequential assessment of success while still ensuring overall Type-I error
control. I compare the different methods in terms of partial Type-I error rate,
project power and the expected number of studies required. Edgington's method
is eventually recommended as it is easy to implement and communicate, has only
moderate partial Type-I error rate inflation but substantially increased
project power.
