LAUSR

We read with great interest the excellent article, “Design and monitoring of survival trials in complex scenarios”, by Xiaodong Luo and colleagues.1 We thank the authors for citing our work in this important area of flexible design of trials with a time-to-event outcome. The authors' approach is not limited to initial design but also covers interim monitoring, which is a welcome addition. However, we would like to note the following points. Regarding our ART package, in the Introduction, the authors state “As compared with the methods in existing commercial softwares (ART in Stata,18,19, nQuery, EAST, etc) that base on simulations, our approach is calculation-based so it is more efficient and provides less ambiguous results.” ART is not itself commercial software; it is a community-contributed program freely available to all users of the commercially available statistics package Stata. The authors are incorrect in their statement that ART results are based on simulation. In fact, almost all of the sample size and power estimates in ART are based on a mathematical framework (piecewise exponential distributions for time to event, loss to follow-up, and cross-over) and exact calculations that are very similar to what the authors present. Moreover, ART is not limited to comparisons of two treatment arms but deals with a global test of comparison between an arbitrary number K of arms. The only situation where simulation is used is in the derivation of the distribution of the (weighted) logrank statistic, which is a quadratic form Q of dimension K-1, under the alternative hypothesis. This is because, in general, there is no known closed analytical expression for the PDF and CDF of Q when K > 2. In our paper,2 we also provided a well-known approximation3,4 as an alternative to simulation in this case. Of course, in the case when K = 2, as considered by the authors, neither the approximation nor simulations are necessary as the distribution of Q is a constant multiple of a noncentral chi-square distribution.