The Cox proportional hazards model has long been the standard method for the analysis of time-to-event endpoints in pharmaceutical clinical trials. Recent development of new classes of therapeutics with delayed onset of effect has sparked interest in statistical methods that do not rely on the proportional hazards assumption. Of particular interest is the situation in which early harm is outweighed by later benefit. Evaluation of the validity of methods for this situation clearly depends on the definition of the null hypothesis. In this presentation, we discuss two fundamentally different null hypotheses that can be defined, one in which the time scale is of interest and one in which it is not, and the dependence of the choice of the null hypothesis on the scientific question of interest. By defining a flexible piecewise exponential model, we demonstrate that alternative analysis methods cannot be valid for both null hypotheses, and we provide recommendations for researchers facing this issue.