Which test for crossing survival curves? A user’s guideline

Abstract

Background The exchange of knowledge between statisticians developing new methodology and clinicians, reviewers or authors applying them is fundamental. This is specifically true for clinical trials with time-to-event endpoints. Thereby, one of the most commonly arising questions is that of equal survival distributions in two-armed trial. The log-rank test is still the gold-standard to infer this question. However, in case of non-proportional hazards, its power can become poor and multiple extensions have been developed to overcome this issue. We aim to facilitate the choice of a test for the detection of survival differences in the case of crossing hazards. Methods We restricted the review to the most recent two-armed clinical oncology trials with crossing survival curves. Each data set was reconstructed using a state-of-the-art reconstruction algorithm. To ensure reproduction quality, only publications with published number at risk at multiple time points, sufficient printing quality and a non-informative censoring pattern were included. This article depicts the p-values of the log-rank and Peto-Peto test as references and compares them with nine different tests developed for detection of survival differences in the presence of non-proportional or crossing hazards. Results We reviewed 1400 recent phase III clinical oncology trials and selected fifteen studies that met our eligibility criteria for data reconstruction. After including further three individual patient data sets, for nine out of eighteen studies significant differences in survival were found using the investigated tests. An important point that reviewers should pay attention to is that 28% of the studies with published survival curves did not report the number at risk. This makes reconstruction and plausibility checks almost impossible. Conclusions The evaluation shows that inference methods constructed to detect differences in survival in presence of non-proportional hazards are beneficial and help to provide guidance in choosing a sensible alternative to the standard log-rank test.

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

“…For $$$ \tau =15 $$$ and $$$ \tau =18 $$$, the results confirm the findings of Hellmann et al 42 that the combination nivolumab plus ipilimumab improves the progression‐free time compared to the chemotherapy. The point estimates and confidence intervals in Table 4 help to quantify the improvement and can be interpreted easily.…”

“…Both tests lead to a $$$ P $$$‐value less than $$$ 0.1\% $$$. That is why the original analysis of Hellmann et al 42 using the hazard ratio (HR: 0.48 and $$$ 95\% $$$ CI $$$ \left[0.27,0.85\right] $$$) need to be considered carefully. The RMSTs offer the possibility to interpret the treatment effect easily beyond the Cox model.…”

“…To complement the previous simulation study, we additionally compared the proposed studentized permutation test for the RMST with recent novel two‐sample tests 42 which are robust against the assumption of proportional hazards. In particular, we included the omnibus permutation strategy of Gorfine et al 43 based on sample space partitioning, which is implemented in the R package KONPsurv .…”

“…To illustrate the presented permutation‐based methods, we reconsider the data analysis of Hellmann et al, 42 who compared the combination treatment of nivolumab plus ipilimumab with chemotherapy among 299 patients with nonsmall‐cell lung cancer. Their study focused on patients with a high tumor mutational burden, that is, at least 10 mutations per megabase.…”

“…Since the present methods are designed for small sample sizes, we conduct a relevant subgroup analysis, which was also done by Hellmann et al 42 In detail, we restrict to the patients having PD‐L1 (tumor programmed death ligand 1) expression of at least $$$ 1\% $$$. Based on the published Kaplan‐Meier curves in Hellmann et al 42 and some additional information therein, for example, the risk table, we reconstructed the individual patient data following the procedure of Guyot et al 45 The respective Kaplan‐Meier curves of the two treatment groups are displayed in Figure 3. Therein, we can observe a delayed treatment effect of nivolumab plus ipilimumab.…”