A permutation test based on the restricted mean survival time for comparison of net survival distributions in non-proportional excess hazard settings

• Published in: Statistical methods in medical research 2020-06, Vol.29 (6), p.1612-1623
• Main Authors: Wolski, Anna, Grafféo, Nathalie, Giorgi, Roch
• Format: Article
• Language: English
• Subjects: Colorectal cancer; Hazards; Life Sciences; Mortality; Permutations; Rank tests; Santé publique et épidémiologie; Simulation; Survival; Survival analysis
• ISSN: 0962-2802; 1477-0334
• DOI: 10.1177/0962280219870217

Net survival is used in epidemiological studies to assess excess mortality due to a given disease when causes of death are unreliable. By correcting for the general population mortality, it allows comparisons between regions or periods and thus evaluation of health policies. The Pohar-Perme non-parametric estimator of net survival has been recently proposed, soon followed by an appropriate log-rank-type test. However, log-rank tests are known to be under-optimal in non-proportional settings (e.g. crossing of the hazard functions). In classical survival analysis, one solution is to compare the restricted mean survival times. A difference in restricted mean survival time represents a life benefit or loss over the studied period. In the present article the restricted mean net survival time was used to derive a specific test statistic to compare net survivals in proportional and non-proportional hazards settings. The new test was generalized to more than two groups and to stratified analysis. The test performance was assessed on simulation study, compared to the log-rank-type test, and its use illustrated on a population-based colorectal cancer registry. The new test for net survival comparisons proved robust to non-proportionality and well-performing in proportional hazards situations. Furthermore, it is also suited to the classical survival framework.