# Confidence intervals in group sequential trials for a binomial parameter

**Rufibach, K.** (2006, revised 2011).

Group sequential procedures are widely employed in phase II clinial trials. Often, only an uncorrected point estimate and/or confidence intervals for the true response rate are given at the end of the trial, irrespective of its multistage nature. Such estimates are generally biased.

The R code below enables one to calculate a (unbiased) point estimate (Jung & Kim, 2004) and confidence intervals (Jennison & Turnbull, 2000) which are corrected for the Stage 1 and Stage 2 decisions (the code is applicable to trials with at most 3 stages).

Examples of phase II trials, taken from the respective publications

For comparisons of the corrected interval to the ordinary Clopper-Pearson intervals check out this plot which applies the code to the first example above.

# References

Jennison, C., Turnbull, B. W. (2000). *Group sequential methods with applications to clinical trials*. Chapman & Hall, Boca Raton.

Jung, S. H., Kim, K. M. (2004). *On the estimation of the binomial probability in multistage clinical trials*. Statist. Med., 23, 881-896.