Due to logistical and ethical concerns, the use of group sequential methods for monitoring clinical trials has become commonplace. When monitoring a group sequential trial, it is of utmost importance to maintain prespecified operating characteristics such as type one error, power, maximal sample size, and/or average sample number. Maintaining these design operating characteristics necessitates correctly estimating information growth. In this dissertation we consider how deviations in estimated information growth impact planned statistical operating characteristics and develop methods for maintaining design operating characteristics under flexible testing schedules.

We first consider a general paradigm for how to update information when using a constrained boundaries monitoring approach. The use of constrained boundaries necessitates that information be specified, and possibly updated, at each analysis. For normally distributed outcomes, we contrast updating information estimates with a common variance estimate and compare this approach to an algorithm that reestimates group variances at each analysis using the most current available data. We show that, depending on the scale used for monitoring, one can obtain contrary trial results if variance estimates are continually updated.

Next we consider monitoring a survival endpoint using a common class of weighted logrank statistics. In this case, we show that the relationship between statistical information growth and the portion of observed events is highly non-linear, requiring careful estimation to maintain desired trial operating characteristics. We develop a general constrained boundaries algorithm for monitoring these weighted statistics and consider the use of both Bayesian and frequentist probability models for predicting future information accrual.

Lastly we consider the utility of missing data models for the estimation of information growth in the setting of adjudicated trial endpoints where, at the time of an interim analysis, local assessment is available on all subjects but independent assessment is only available on a subset of patients. This commonly encountered scenario results in a missing data problem wherein a surrogate measure of response may provide useful information for interim decisions and future monitoring strategies. We present imputation models that are helpful for monitoring a group sequential clinical trial in these cases and evaluate the proposed strategies via simulation.