Odds ratio-based group sequential analysis for joint binomial and inverse binomial sampling

We consider two treatment comparison in a clinical trial setup where the responses from one treatment are a priori known for a fixed number of individuals and patients are allocated in a groupsequential way for the other treatment using inverse sampling. We consider the odds ratio as the measure of treatment difference at the end of each group, where for the calculation of odds ratios we consider the full data on one treatment, which are a priori known, and the available data on the other treatment up to that point of time. We have calculated the optimal number of index subjects for inverse sampling and examine the effects of different type I and type II error spending functions on group sequential testing in this context. The methodology is illustrated by using a real data set.