assumed asymptotic normality to evaluate their uncertainty. @martens2018 relied on asymptotic normality for evaluating regression coefficients under the Fine–Gray model in GSD settings. @Asendorf2018 evaluated asymptotic properties with SSR under a fixed alternative for negative binomial random variables. @gao2013 is a rare exception in not making a normality assumption; these authors mostly dealt with set operations and probabilities and, using stage-wise ordering of events, they calculated P-values, confidence intervals, and a median unbiased estimate of the parameter of interest.

Asymptotic normality holds when a sequential study is powered against a fixed (not local) alternative. The problem is that all consistent tests asymptotically reject the null in favor of *any* fixed alternative hypothesis with $100\%$ statistical power. As the sample size increases, with a proportional increase of all stage-specific sample sizes, the probability to reject the converges to $1$ at stage 1 and tests statistics degenerate to a point mass, see Section 7.4 in @Fleming1991. Thus, for large samples at fixed alternatives, the need for a power concept and the need for an interim analysis disappears.

To mitigate the limited applicability of multivariate normality to GSD trials with possibility of early stopping, many researchers rely on a sequential recursive formula suggested 