The hazard ratio based on Cox’s proportional hazards model is the most popular measure used to quantify the magnitude of the treatment effect on time-to-event outcomes in clinical research. However, the limitations of using the traditional Cox’s hazard ratio as a summary of the magnitude of the treatment effect on time-to-event outcomes have been widely discussed, and alternative measures that do not have such limitations (e.g., difference or ratio of restricted mean survival time) are gaining attention. One of the alternative methods recently proposed in a simple two-sample comparison setting uses the average hazard with survival weight (AH), which can be interpreted as the general censoring-free person-time incidence rate in a given time window. The difference in AH or ratio of AH does not have the limitations of Cox’s hazard ratio as a summary measure of the between-group difference. In this paper, we review the main limitations of Cox’s hazard ratio and the definition and interpretation of the AH proposed by Uno and Horiguchi (2023), along with the nonparametric inference procedure and a data example.

Ridge regression was originally proposed as an alternative to ordinary least-squares regression to mitigate the multicollinearity problem in linear regression; it was later extended to logistic and Cox regressions. When the regression coefficients follow multivariate normal priors, the ridge regression estimators can be interpreted as a Bayesian posterior mean or median in the Bayesian framework. However, in the presence of interaction terms, multivariate normal priors may not provide efficient posterior estimates for regression coefficients. Consequently, novel priors that can appropriately model the relationships among regression coefficients are required. Therefore, in this article, classical (e.g., multivariate normal) and recently proposed (e.g., vine copula-based joint) priors are reviewed for Bayesian ridge estimators under the Cox proportional hazards models. The settings and composition of the priors on the regression coefficients, composition of likelihood functions, and derivation of Bayesian posteriors are illustrated. Subsequently, the performance of the priors are compared based on simulations and a real dataset, and the comparative advantages and disadvantages of the vine copula-based joint priors are considered. Finally, to conclude, suggestions regarding new research directions are provided.

Survival analysis is usually necessary in the analysis of endpoints in oncology clinical trials. When the main interest lies in events other than death, death should be adequately handled statistically. Analysis where death events are censored has been shown to lead to erroneous conclusions; however, deaths are still censored in many oncology trials. Competing risks models where death is treated as a competing event is not widely used. In this paper, we discuss why death events should not be censored and provide an accessible introduction to competing risks analysis. Moreover, we explain multistate models, which can be viewed as an extension of competing risks models. By using multistate models, more clinical questions can be tackled, as shown in this paper.

Cancer clinical trials often evaluate overall survival (OS) as the primary endpoint for measuring clinically important effects for treatments. However, observing OS may require considerable time and cost for patient follow-up. Thus, surrogate endpoints were widely employed for OS to accelerate trials, facilitating the introduction of potentially beneficial treatments. For any surrogate endpoint to be valid, it must be tightly correlated to OS, and the treatments effects on OS must be predictable by those on the surrogate. This article reviews meta-analytic approaches (based on a set of randomized controlled trials) for statistically validating a surrogate endpoint for OS based on two criteria (individual-level surrogacy and trial-level surrogacy). We review the traditional two-step approach via copula models, one-step approaches via frailty models, and approaches with frailty-copula models. We illustrate these approaches using the gastric cancer dataset from the GASTRIC group.

A variety of statistical methods for interval-censored data have been actively researched and developed in various disease areas since 1970s, when research on the new infectious disease HIV/AIDS attracted attention. In oncology, the data are obtained as partially interval-censored, such as progression free survival time, where the application of the usual survival data analysis method is often performed after imputing right-point of the censoring interval. However, other single point imputation methods such as left-point or midpoint also could be candidates, and a lot of research has been done on the statistical properties of single/multiple imputations, but it was limited to only simulation studies. In our study, we examine the characteristics of deterministic (left-, mid, and right-point) imputations from a theoretical aspect, and show that midpoint imputation is the most preferable if the true distribution is the exponential distribution. In our simulation, we compared the performance of these three deterministic single-point imputation methods and Finkelstein’s proportional hazards model without imputation in the setting of the selection design, so called a pick-the-winner design, in which the most promising treatment is identified based on the point estimate. The correct selection probability and performance measures of a regression coefficient were used for evaluation criteria. Midpoint imputation or left-point imputation was shown to be the best depending on the simulation condition.

In meta-analyses, Individual Participant Data (IPD) is considered the gold standard for summarizing results from individual studies. However, in studies focusing on survival outcomes, the IPD is often unavailable, and researchers typically present Kaplan-Meier curves alongside summary statistics like hazard ratios. Recently, methods have been developed to reconstruct IPD from Kaplan-Meier curves, enabling meta-analyses without relying on summary statistics alone. Nonetheless, the accuracy of meta-analyses based on reconstructed IPD compared to those using true IPD has not been well-examined. This paper assesses the utility of reconstructed IPD in meta-analyses through simulation studies and real-data re-analysis. Our findings suggest that meta-analyses using reconstructed IPD yield results comparable to those obtained with true IPD, provided that a sufficient number of data points are available from the Kaplan-Meier curves for IPD reconstruction. Therefore, meta-analyses based on reconstructed IPD can offer sufficient precision when true IPD is unavailable, presenting a viable alternative approach.