Flexibly Monitoring Group Sequential Survival Trials When Testing is Based Upon a Weighted Log-Rank Statistic

Abstract

We consider the repeated group sequential testing of a survival endpoint with a time-varying treatment effect using a weighted logrank statistic. The emphasis of this paper is on the monitoring of this statistic where information growth is non-linear. We propose using a constrained boundaries approach to maintain the planned operating characteristics of a group sequential design. A simulation study is presented to demonstrate the operating characteristics of the method together with a case study to illustrate the procedure. We show that when monitoring a weighted logrank statistic, the entry and survival distribution needs to be estimated at interim analyses.

Group sequential monitoring based on the weighted log‐rank test statistic with the Fleming–Harrington class of weights in cancer vaccine studies

“…In this case, the surrogate information fraction based on the number of events provides a conservative procedure, because the PPPW statistic emphasizes the early events. More generally, Brummel and Gillen proposed a prediction algorithm of information fraction in the G ρ , γ family. Although Tsiatis showed that the G ρ , γ statistic has an independent increments structure, the information fraction depends not only on the number of events but also on the event timing and size of the risk set at the event times .…”

“…More generally, Brummel and Gillen proposed a prediction algorithm of information fraction in the G ρ , γ family. Although Tsiatis showed that the G ρ , γ statistic has an independent increments structure, the information fraction depends not only on the number of events but also on the event timing and size of the risk set at the event times . Therefore, Brummel and Gillen's algorithm requires parametric assumptions regarding the entry, survival, and censoring distributions.…”

On information fraction for Fleming‐Harrington type weighted log‐rank tests in a group‐sequential clinical trial design

“…The realization of a censoring pattern in a study is a convolution of three distinct distributions—enrollment, LTFU, and TTE distributions. Since censoring affects IF, a precise knowledge of these three distributions is necessary to calculate IF 18‐21 . However, since these distributions cannot be predicted precisely at the design stage, an obvious strategy would be to evaluate all possible censoring scenarios and then to choose the minimum IF to preserve the overall size.…”

“…However, estimation of IF, which determines the rejection boundaries for testing at the interim analysis, remains a challenging problem: For the SLR test, the IF is proportional to the number of interim events; but in general, this relationship is not guaranteed to hold for the WLR test 18 . As Brummel and Gillen 19 pointed out, if IFs accrued at the interim analyses are not correctly estimated at the design stage, then power and type I error will differ from the originally targeted value: If IF is underestimated, then the overall size of the test may be inflated; on the contrary, if IF is overestimated, then the overall power of the test may be compromised. The focus of this article is to correctly estimate IF for test in a group‐sequential trial.…”

“…Previous works 18‐20 observed that for the test, information growth depends on the underlying pooled survival and censoring distributions across treatment arms along with the number of events at interim and final analyses. Consequently, all previous works on estimating IF are primarily based on parametric assumptions on TTE, enrollment, and lost‐to‐follow‐up (LTFU) distributions 18‐21 . In practice, these distributions cannot be predicted upfront at the design stage.…”