Determining the late effect parameter in the Fleming-Harrington test using asymptotic relative efficiency in cancer immunotherapy clinical trials.

The delayed treatment effect, which manifests as a separation of survival curves after a change point, has often been observed in immunotherapy clinical trials. A late effect of this kind may violate the proportional hazards assumption, resulting in the non-negligible loss of statistical power of an ordinary log-rank test when comparing survival curves. The Fleming-Harrington (FH) test, a weighted log-rank test, is configured to mitigate the loss of power by incorporating a weight function with two parameters, one each for early and late treatment effects. The two parameters need to be appropriately determined, but no helpful guides have been fully established. Since the late effect is expected in immunotherapy trials, we focus on the late effect parameter in this study. We consider parameterizing the late effect in a readily interpretable fashion and determining the optimal late effect parameter in the FH test to maintain statistical power in reference to the asymptotic relative efficiency (ARE). The optimization is carried out under three lag models (i.e. linear, threshold, and generalized linear lag), where the optimal weights are proportional to the lag functions characterized by the change points. Extensive simulation studies showed that the FH test with the selected late parameter reliably provided sufficient power even when the change points in the lag models were misspecified. This finding suggests that the FH test with the ARE-guided late parameter may be a reasonable and practical choice for the primary analysis in immunotherapy clinical trials.

Robust group sequential designs for trials with survival endpoints and delayed response.

Randomized clinical trials in oncology typically utilize time-to-event endpoints such as progression-free survival or overall survival as their primary efficacy endpoints, and the most commonly used statistical test to analyze these endpoints is the log-rank test. The power of the log-rank test depends on the behavior of the hazard ratio of the treatment arm to the control arm. Under the assumption of proportional hazards, the log-rank test is asymptotically fully efficient. However, this proportionality assumption does not hold true if there is a delayed treatment effect. Cancer immunology has evolved over time and several cancer vaccines are available in the market for treating existing cancers. This includes sipuleucel-T for metastatic hormone-refractory prostate cancer, nivolumab for metastatic melanoma, and pembrolizumab for advanced nonsmall-cell lung cancer. As cancer vaccines require some time to elicit an immune response, a delayed treatment effect is observed, resulting in a violation of the proportional hazards assumption. Thus, the traditional log-rank test may not be optimal for testing immuno-oncology drugs in randomized clinical trials. Moreover, the new immuno-oncology compounds have been shown to be very effective in prolonging overall survival. Therefore, it is desirable to implement a group sequential design with the possibility of early stopping for overwhelming efficacy. In this paper, we investigate the max-combo test, which utilizes the maximum of two weighted log-rank statistics, as a robust alternative to the log-rank test. The new test is implemented for two-stage designs with possible early stopping at the interim analysis time point. Two classes of weights are investigated for the max-combo test: the Fleming and Harrington (1981) Gρ,γ$G^{\rho , \gamma }$ weights and the Magirr and Burman (2019) modest (τ∗)$ (\tau ^{*})$  weights.

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

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.