Inferring median survival differences in general factorial designs via permutation tests

Abstract

Factorial survival designs with right-censored observations are commonly inferred by Cox regression and explained by means of hazard ratios. However, in case of non-proportional hazards, their interpretation can become cumbersome; especially for clinicians. We therefore offer an alternative: median survival times are used to estimate treatment and interaction effects and null hypotheses are formulated in contrasts of their population versions. Permutation-based tests and confidence regions are proposed and shown to be asymptotically valid. Their type-1 error control and power behavior are investigated in extensive simulations, showing the new methods’ wide applicability. The latter is complemented by an illustrative data analysis.

Studentized Permutation Method for Comparing Restricted Mean Survival Times with Small Sample from Randomized Trials

“…More general study designs may be part of future research. For that purpose, we can follow Dobler and Pauly (2020) and Ditzhaus et al (2020a), who recently discussed permutationbased inference for the concordance measure and median survival times, respectively, in the general context of factorial designs. Sample size determination can also be developed, in parallel to the asymptotic test based results (Ye and Yu, 2018)…”

“…Especially in immunotherapy trials, a delayed treatment effect often lead to a violation of the proportional hazard assumption (Mick and Chen, 2015;Alexander et al, 2018) and suchlike could also be observed when comparing bone marrow transplant and chemotherapy for hematologic malignancies (Zittoun et al, 1995;Scott et al, 2017). More classical and known effect sizes as landmark survival (Taori et al, 2009) and the median survival time (Brookmeyer and Crowley, 1982;Chen and Zhang, 2016;Ditzhaus et al, 2020a) provide rather a snapshot for a time point than information about the complete Kaplan-Meier curves.…”

CASANOVA: Permutation inference in factorial survival designs

“…In the context of survival data, just a few nonparametric methods account for factorial designs: the approaches of Akritas and Brunner (1997), which require a strong assumption on the underlying censoring distribution that is often too strict from a practical point of view, and the procedures of Dobler and Pauly (2020) and Ditzhaus et al. (2021) formulating null hypotheses in terms of certain concordance effects, that restricts their analysis to a pre‐specified time range [0, τ], and medians, respectively. All three approaches are not flexibly adaptable to detect certain crossing structures.…”

“…These were mainly explored for testing means and other functionals in the two‐sample case (Janssen and Pauls, 2003; Ditzhaus et al., 2021). Later, the concept of studentization was extended to one‐way layouts by Chung and Romano (2013), and finally, reached its full potential under general factorial designs (Pauly et al., 2015; Ditzhaus et al., 2021). Thereof, only Ditzhaus et al.…”

“…Thereof, only Ditzhaus et al. (2021) treated factorial survival models, but with a less flexible median‐based approach. Therefore, the aims of the present paper are to derive a permutation procedure: (a)without any restrictive assumption on the censoring distribution or the time range, (b)with reasonable power under proportional hazards and crossing curve scenarios, (c)for general factorial designs allowing the study of main and interaction effects, and (d)being asymptotically valid with satisfactory small sample size performance. This will be achieved by combining a weighted combination approach with the studentized permutation strategy.…”