Rejoinder to Letter to the Editor "The Hazards of Period Specific and Weighted Hazard Ratios"

A dietary commensal microbe enhances antitumor immunity by activating tumor macrophages to sequester iron

Innate immune cells generate a multifaceted antitumor immune response, including the conservation of essential nutrients such as iron. These cells can be modulated by commensal bacteria; however, identifying and understanding how this occurs is a challenge. Here we show that the food commensal Lactiplantibacillus plantarum IMB19 augments antitumor immunity in syngeneic and xenograft mouse tumor models. Its capsular heteropolysaccharide is the major effector molecule, functioning as a ligand for TLR2. In a two-pronged manner, it skews tumor-associated macrophages to a classically active phenotype, leading to generation of a sustained CD8+ T cell response, and triggers macrophage 'nutritional immunity' to deploy the high-affinity iron transporter lipocalin-2 for capturing and sequestering iron in the tumor microenvironment. This process induces a cycle of tumor cell death, epitope expansion and subsequent tumor clearance. Together these data indicate that food commensals might be identified and developed into 'oncobiotics' for a multi-layered approach to cancer therapy.

Two-sample inference procedures under nonproportional hazards

We introduce a new two-sample inference procedure to assess the relative performance of two groups over time. Our model-free method does not assume proportional hazards, making it suitable for scenarios where nonproportional hazards may exist. Our procedure includes a diagnostic tau plot to identify changes in hazard timing and a formal inference procedure. The tau-based measures we develop are clinically meaningful and provide interpretable estimands to summarize the treatment effect over time. Our proposed statistic is a U-statistic and exhibits a martingale structure, allowing us to construct confidence intervals and perform hypothesis testing. Our approach is robust with respect to the censoring distribution. We also demonstrate how our method can be applied for sensitivity analysis in scenarios with missing tail information due to insufficient follow-up. Without censoring, Kendall's tau estimator we propose reduces to the Wilcoxon-Mann-Whitney statistic. We evaluate our method using simulations to compare its performance with the restricted mean survival time and log-rank statistics. We also apply our approach to data from several published oncology clinical trials where nonproportional hazards may exist.

A MCP-Mod approach to designing and analyzing survival trials with potential non-proportional hazards

Non-proportional hazards have been observed in many studies especially in immuno-oncology clinical trials. Traditional analysis using the combined approach with log-rank test as the significance test and Cox model for treatment effect estimation becomes questionable as this approach relies heavily on the proportional hazards assumption. Inspired by the MCP-Mod (multiple comparisons and modeling approach) that has been widely used in dose-finding studies, we propose a similar approach to handle non-proportional hazards. Using this approach, efficacy signal is first established by a max-combo test, after which hazard ratios across time will be estimated using a logically nested splines model. Simulations studies and real-data examples are used to illustrate the use of this approach.

Design and analysis of group-sequential clinical trials based on a modestly weighted log-rank test in anticipation of a delayed separation of survival curves: A practical guidance

BACKGROUND

A common feature of many recent trials evaluating the effects of immunotherapy on survival is that non-proportional hazards can be anticipated at the design stage. This raises the possibility to use a statistical method tailored towards testing the purported long-term benefit, rather than applying the more standard log-rank test and/or Cox model. Many such proposals have been made in recent years, but there remains a lack of practical guidance on implementation, particularly in the context of group-sequential designs. In this article, we aim to fill this gap.

METHODS

We illustrate how the POPLAR trial, which compared immunotherapy versus chemotherapy in non-small-cell lung cancer, might have been re-designed to be more robust to the presence of a delayed effect using the modestly-weighted log-rank test in a group-sequential setting.

CONCLUSION

We provide step-by-step instructions on how to analyse a hypothetical realization of the trial, based on this new design. Basic theory on weighted log-rank tests and group-sequential methods is covered, and an accompanying R package (including vignette) is provided.

Critical review of oncology clinical trial design under non-proportional hazards

In trials of novel immuno-oncology drugs, the proportional hazards (PH) assumption often does not hold for the primary time-to-event (TTE) efficacy endpoint, likely due to the unique mechanism of action of these drugs. In practice, when it is anticipated that PH may not hold for the TTE endpoint with respect to treatment, the sample size is often still calculated under the PH assumption, and the hazard ratio (HR) from the Cox model is still reported as the primary measure of the treatment effect. Sensitivity analyses of the TTE data using methods that are suitable under non-proportional hazards (non-PH) are commonly pre-planned. In cases where a substantial deviation from the PH assumption is likely, we suggest designing the trial, calculating the sample size and analyzing the data, using a suitable method that accounts for non-PH, after gaining alignment with regulatory authorities. In this comprehensive review article, we describe methods to design a randomized oncology trial, calculate the sample size, analyze the trial data and obtain summary measures of the treatment effect in the presence of non-PH. For each method, we provide examples of its use from the recent oncology trials literature. We also summarize in the Appendix some methods to conduct sensitivity analyses for overall survival (OS) when patients in a randomized trial switch or cross-over to the other treatment arm after disease progression on the initial treatment arm, and obtain an adjusted or weighted HR for OS in the presence of cross-over. This is an example of the treatment itself changing at a specific point in time - this cross-over may lead to a non-PH pattern of diminishing treatment effect.