Stochastically curtailed tests in long–term clinical trials

In data monitoring of long-term clinical trials one frequently faces the question of whether the trial should be terminated early either to reject or "accept" the null hypothesis (H0). To help answer this question, this paper suggests that, in the context of a particular proposed analysis at the end of the trial, one might stop early and reject (accept) H0 when the Conditional probability under H0 (the alternative hypothesis, Ha)