Flexible testing of treatment equivalence in a survival setting

Equivalence testing is performed to assess whether or not there is a neglible difference, in terms of clinical relevance, between the effects of two treatments. This thesis will focus on equivalence tests carried out for time to event data as seen in survival analysis. The traditional approaches used for conducting equivalence tests for survival data utilizes properties of the Cox model. The advantage of the Cox model is that the treatment effect is summarized in an one-dimensional parameter, namely the hazard ratio. The tradional approaches directly use the asymptotic behaviour of the maximum partial likehood estimator of the regression coefficent derived from the Cox model. This regression coefficient has a direct link to the hazard ratio, through the exponential function. However, other summary measures derived from the distributions of the two treatment populations could be of relevance and perhaps be easier to interpret. This thesis will consider equivalence testing on alternative scales and with other measures to summarize time to event data. Examples include a restricted survival probability scale and a restricted mean scale. Moreover, it will not always be appropriate to assume an underlying Cox model, as the proportional hazards assumption can be violated. An example of this is when a treatment effect fades over time. This can be remedied by focusing on non-parametric approaches to modelling survival data instead. This thesis will develop more flexible equivalence tests based on the Aalen model. If equivalence tests are performed under a Cox model, where the model assumptions are violated, it will have grave consequences on the errors of testing. We avoid this by using tests derived under the flexible Aalen model. As an extension to the developed theory and methods, the thesis will consider how to adjust for potential confounders when performing equivalence tests in observatio