Maximum Duration and Information Trials
In clinical trials in which a response variable is observed more or less instantaneously, the statistical information of the test statistic is proportional to the number of study subjects, which is directly related to the duration of the study in calendar time and the rate by which subjects are enrolled and randomized into the study. However, in clinical trials in which a response variable is observed over follow-up as time to event, the statistical information is not directly related to the number of subjects but rather to the number of events of interest.
Regardless of the type of response variable, the efficient score is
where is Fisher’s information and θ is the canonical parameter representing treatment, effect according to the likelihood theory under the assumption of a relative large sample and a small effect size of treatment. A one-sided fixed-sample test of the null hypothesis H0: θ = 0 indicating no treatment difference with a significance level α to detect the alternative hypothesis H1: θ = θ1 > 0 with power 1 − β requires
This determines the information content or the information horizon ...