Alternative derivations of a rule for early stopping in favor of HO

It is often desirable to stop a large clinical trial before its planned end if a null result seems inevitable. This early stopping can save considerable resources. It is especially appealing when an experimental treatment is being compared to a standard treatment. Three procedures for early stopping, all with different interpretations and derivations, are described and shown to produce identical rules for normal data and certain parameters. In some cases, this is unexpected and informative. The procedures differ in which of their parameters are adjusted from the fixed sample values to maintain the desired Type I error in this setting of multiple looks at the data.