  We describe group sequential tests which efficiently incorporate information
from multiple endpoints allowing for early stopping at pre-planned interim
analyses. We formulate a testing procedure where several outcomes are examined,
and interim decisions are based on a global summary statistic. An error
spending approach to this problem is defined which allows for unpredictable
group sizes and nuisance parameters such as the correlation between endpoints.
We present and compare three methods for implementation of the testing
procedure including numerical integration, the Delta approximation and Monte
Carlo simulation. In our evaluation, numerical integration techniques performed
best for implementation with error rate calculations accurate to five decimal
places. Our proposed testing method is flexible and accommodates summary
statistics derived from general, non-linear functions of endpoints informed by
the statistical model. Type 1 error rates are controlled, and sample size
calculations can easily be performed to satisfy power requirements.
