AN APPROACH FOR FINDING A GENERAL APPROXIMATION TO THE GROUP SEQUENTIAL BOOTSTRAP TEST

Abstract: Randomized experiments are regarded as the gold standard for estimating causal effects. Commonly, a single test is performed using a fixed sample size. However, observations may also be observed sequentially and because of economical and ethical reasons, it may be desirable to terminate the trial early. The group sequential design allows for interim analyses and early stopping of a trial without the need for continuous monitoring of the accumulating data. The implementation of a group sequential procedure requires that the sampling distribution of the test statistic observed at each wave of testing to have a known or asymptotically known sampling distribution. This thesis investigates an approach for finding a general approximation to the group sequential bootstrap test for test statistics with unknown or analytically intractable sampling distributions. There is currently no bootstrap version of the group sequential test. The approach implies approximating the covariance structure of the test statistics over time, but not the marginal sampling distribution, with that of a normal test statistic. The evaluation is performed with a Monte Carlo simulation study where the achieved significance level is compared to the nominal. Evidence from the Monte Carlo simulations suggests that the approach performs well for test statistics with sampling distributions close to a normal distribution.