Nonproportional hazards in immunooncology: is an old perspective needed?
Abstract
A fundamental concept in twoarm nonparametric survival analysis is the comparison of observed versus expected numbers of events on one of the treatment arms (the choice of which arm is arbitrary), where the expectation is taken assuming that the true survival curves in the two arms are identical. This concept is at the heart of the countingprocess theory that provides a rigorous basis for methods such as the logrank test. It is natural, therefore, to maintain this perspective when extending the logrank test to deal with nonproportional hazards, for example by considering a weighted sum of the "observed  expected" terms, where larger weights are given to time periods where the hazard ratio is expected to favour the experimental treatment. In doing so, however, one may stumble across some rather subtle issues, related to the difficulty in ascribing a causal interpretation to hazard ratios, that may lead to strange conclusions. An alternative approach is to view nonparametric survival comparisons as permutation tests. With this perspective, one can easily improve on the efficiency of the logrank test, whilst thoroughly controlling the false positive rate. In particular, for the field of immunooncology, where researchers often anticipate a delayed treatment effect, sample sizes could be substantially reduced without loss of power.
 Publication:

arXiv eprints
 Pub Date:
 July 2020
 arXiv:
 arXiv:2007.04767
 Bibcode:
 2020arXiv200704767M
 Keywords:

 Statistics  Applications