CASANOVA: Permutation inference in factorial survival designs

Abstract

We propose inference procedures for general factorial designs with time-to-event endpoints. Similar to additive Aalen models, null hypotheses are formulated in terms of cumulative hazards. Deviations are measured in terms of quadratic forms in Nelson-Aalen-type integrals. Different from existing approaches, this allows to work without restrictive model assumptions as proportional hazards.In particular, crossing survival or hazard curves can be detected without a significant loss of power. For a distribution-free application of the method, a permutation strategy is suggested. The resulting procedures' asymptotic validity is proven and small sample performances are analyzed in extensive simulations. The analysis of a data set on asthma illustrates the applicability.

Studentized permutation method for comparing two restricted mean survival times with small sample from randomized trials

“…For other right‐censoring survival problems, in particular, in testing $$$ {\tilde{\mathscr{H}}}_0:{S}_1(t)={S}_2(t),0\le t<\tau $$$, an imputation strategy was used to tackle the issue of different censoring between treatment arms, for instance, by Wang et al 18,31,55,56 Therein, censored observations are imputed according to the group‐specific estimated censoring distribution whenever their group memberships are changed by the permutation process. This permutation strategy was also recently used by Gorfine et al 43 to derive a powerful $$$ k $$$‐sample test.…”

“…However, the censoring distributions may differ between comparison groups. In addition, confidence intervals for the quantity of interest, here the difference or ratio of the RMSTs, cannot be derived as Horiguchi and Uno 18 mentioned: “Further research to develop methods for constructing confidence intervals for RMST difference with a small sample data is warranted.” Therefore we propose another strategy known as studentized permutation which was already successfully applied to different two‐sample survival and nonsurvival settings, 21–25 one‐way layouts 8,26 and, more recently, even to factorial designs 9,27–32 . Using the studentized permutation strategy we are able to solve the existing issues and, moreover, preserve the finite exactness under exchangeability.…”

“…Therefore we propose another strategy known as studentized permutation which was already successfully applied to different two-sample survival and nonsurvival settings, [21][22][23][24][25] one-way layouts 8,26 and, more recently, even to factorial designs. 9,[27][28][29][30][31][32] Using the studentized permutation strategy we are able to solve the existing issues and, moreover, preserve the finite exactness under exchangeability. This is justified in the present paper on a theoretical level employing the empirical process theory 33 as well as by an extensive simulation study.…”

Inference for all variants of the multivariate coefficient of variation in factorial designs

“…Brunner et al, 1997;Friedrich and Pauly, 2018;Sattler et al, 2022) and Wald-type statistics (e.g. Pauly et al, 2015;Smaga, 2015Smaga, , 2017Ditzhaus et al, 2021b). In particular, the latter is usually an asymptotically pivotal statistic which is beneficial for the resampling procedures proposed later.…”

“…For this purpose, we will adopt the results of Ditzhaus and Smaga (2022) and, in particular, derive permutation versions with a better performance under small sample sizes, see Section 5. In this way, we add a further chapter to the success story of studentized permutation tests in complex factorial designs (Pauly et al, 2015;Friedrich et al, 2017;Harrar et al, 2019;Ditzhaus et al, 2021b). While classical permutation tests for exchangeable data settings are well-known, it is less known that the studentized permutation versions are also valid beyond exchangeability.…”