Matching ratio and sample size for optimal sequential testing with binomial data

Statistical sequential analysis of binary data is an important tool in clinical trials such as placebo-controlled trials, where a total of $K$ individuals are randomly allocated into two groups, one of size ${\kappa }_1$ receiving the treatment/drug, and the other of size ${\kappa }_2$ for placebo. The ratio $z={\kappa }_2/{\kappa }_1$, namely "matching ratio," determines the expected proportion of adverse events from the treatment group among the ${\kappa }_1+{\kappa }_2$ individuals. Bernoulli-based designs are used for monitoring the safety of post-licensed drugs and vaccines as well. For instance, in a self-control design, $z$ is the ratio between the risk and the control time windows. Irrespective of the type of application, the choice of $z$ is a critical design criterion as it determines the sample size, the statistical power, the expected sample size, and the expected time to signal the sequential procedure. In this paper, we run exact calculations to offer a statistical rule of thumb for the choice of $z$. All the calculations and examples are performed using the R Sequential package.