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

Abstract

When comparing survival times of treatment and control groups under a more realistic nonproportional hazards scenario, the standard log‐rank (SLR) test may be replaced by a more efficient weighted log‐rank (WLR) test, such as the Fleming‐Harrington (FH) test. Designing a group‐sequential clinical trial with one or more interim looks during which a FH test will be performed, necessitates correctly quantifying the information fraction (IF). For SLR test, IF is defined simply as the ratio of interim to final numbers of events; but for FH test, it can deviate substantially from this ratio. In this article, we separate the effect of weight function (of FH test) alone on IF from the effect of censoring. We have shown that, without considering the effect of censoring, IF can be derived analytically for FH test using information available at the design stage and the additional effect due to censoring is relatively smaller. This article intends to serve two major purposes: first, to emphasize and rationalize the deviation of IF in weighted log‐rank test from that of SLR test which is often overlooked (Jiménez, Stalbovskaya, and Jones); second, although it is impossible to predict IF for a weighted log‐rank test at the design stage, our decomposition of effects on IF provides a reasonable and practically feasible range of IF to work with. We illustrate our approach with an example and provide simulation results to evaluate operating characteristics.

Group sequential design with maximin efficiency robust test for immunotherapy with generalized delayed treatment effect

“…This choice is due to the MERT weight functions changing with the analysis time, which makes the latter method inapplicable. 14,[16][17][18][19][20] Second, the positive values of α 1 , ÁÁÁ, α K can be specified arbitrarily as long as they satisfy the restriction of P K k¼1 α k ¼ α. This flexibility arises from the fact that the group sequential boundaries are determined mainly based on the previously derived covariance matrix (8) under the null hypothesis H Ã 0 in the maximum duration design.…”

“…First, we utilize the maximum duration method, 32 instead of the more commonly used maximum information method, 32,33 for group sequential monitoring. This choice is due to the MERT weight functions changing with the analysis time, which makes the latter method inapplicable 14,16–20 . Second, the positive values of can be specified arbitrarily as long as they satisfy the restriction of .…”

“…12 Consequently, if a null hypothesis of no difference is assumed, the covariances of group sequential MERT statistics do not align with the assumption of independent increments and the canonical joint distribution of traditional maximum information design. 14,[16][17][18] In other words, it would be inappropriate to determine the group sequential boundaries of MERT statistics using novel information fractions, as proposed for some weighted log-rank tests, [17][18][19][20] in conjunction with the specific traditional approaches of the maximum information design. [21][22][23] Additionally, several researchers have considered adopting the maximum duration design and deriving a multivariate joint distribution of group sequential weighted log-rank test statistics under the null hypothesis of no difference using the definite integral method, provided the calendar time of each analysis is used to obtain the group sequential boundaries.…”