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).

R-functions

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.