In recent years increasing attention has been focused on violations of the proportional hazards assumption made in Cox’s famous proportional hazards model. This has occurred in particular due to trials of immuno-oncology treatments, where the mechanism of action may imply that any benefit of treatment would only occur some time after initiation of treatment. As a result, a large number of papers have been published recently looking at alternative methods of analysis (to Cox’s model), which I have written about before.
Recently a paper was published in the journal Statistics in Biopharmaceutical Research proposing methods of analysis for time to event data in randomised trials when it is anticipated that the proportional hazards assumption may be violated. The paper proposed an approach for hypothesis testing, the ‘max combo’ method, which is based on a series of weighted log rank tests. Weighted log rank tests are a generalisation of the standard log rank test for censored time to event data which weight the different follow-up periods differentially, ideally with highest weight in the period where one expects the largest treatment effect. Since one may not correctly anticipate when this will occur, the max combo test uses the weighted log rank test which is most statistically significant (among a small collection of weighted log rank tests), with an appropriate penalty incorporated for the fact that the particular weighted log rank test is being selected because it is the most significant. As well as hypothesis testing, effect estimation is obviously of crucial importance. In the presence of non-proportional hazards, the aforementioned paper advocated use of period specific hazard ratios (estimating separate hazard ratios in distinct portions of follow-up), and also a weighted hazard ratio that corresponds to the ‘winning’ weighted log rank test in order to characterise how the treatment effect changes over time.