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Multi-state models provide a statistical framework for studying longitudinal data on subjects when focus is on the occurrence of events that the subjects may experience over time. They find application particularly in biostatistics, medicine, and public health. The book includes mathematical detail which can be skipped by readers more interested in the practical examples. It is aimed at biostatisticians and at readers with an interest in the topic having a more applied background, such as epidemiology. This book builds on several courses the authors have taught on the subject. Key Features: • Intensity-based and marginal models • Survival data, competing risks, illness-death models, recurrent events • Includes a full chapter on pseudo-values • Intuitive introductions and mathematical details • Practical examples of event history data • Exercises Software code in R and SAS and the data used in the book can be found on the book’s webpage.

Analysis of recurrent events is becoming increasingly popular for understanding treatment effects in randomised controlled trials. The analysis of recurrent events can improve efficiency and capture disease burden compared to standard time-to-first event analyses. However, the added knowledge about the multi-state process comes at the cost of modelling complexity. High mortality rates can complicate matters even more. A case study using data from a randomised controlled trial, LEADER, is presented to highlight interpretation of common methods as well as potential pitfalls when analysing recurrent events in the presence of a competing risk. The presented methods either target features of the underlying intensity functions or marginal traits of a multi-state process which includes terminal events or not. In particular, approaches to handle death as a part of an event and as a competing risk are discussed. A new method targeting the marginal mean function for a composite endpoint, which includes both death as a component and as a competing risk, will be introduced. Finally, recommendations for how to capture meaningful treatment effects in randomised controlled trials when analysing recurrent and terminal events will be made.

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