Torsten Hothorn, University of Zurich (CH):
A Transformation Perspective on Survival Analysis (Tutorial)
It is well known that many prominent models in survival analysis can be understood as transformation models. Cox' proportional hazards model is maybe the most prominent case, but also other models, such as the Weibull or the reverse time proportional hazards model, belong to this class.
Survival analysts have always been forced to work with models for conditional distributions (usually looking at conditional survivor functions) because a simple mean regression is neither interesting nor appropriate for describing the impact of patient characteristics on some time-to-event outcome. Thus, the field has much to offer in the recent development of distributional regression models, ie models for a conditional distribution and not just a conditional mean. For this discussion to be fruitful in practice, however, one has to address some old-fashioned habits, such as application of the partial likelihood for semiparametric inference in Cox models.
We will discuss connections between many well-known and some less well-known and even some novel members in the family of transformation models. Once we understood the conceptual simplicity of this model family, we'll introduce a generic estimation approach based on simple maximum likelihood estimators for fully parameterised transformation models. These estimators are also the key ingredient to machine-learning-flavoured approaches, such as transformation trees, transformation forests, and transformation boosting machines.
Torben Martinussen, University of Copenhagen (DK):
Subtleties in the interpretation of hazard ratios
The hazard ratio is one of the most commonly reported measures of treatment effect in randomised trials, yet the source of much misinterpretation. This point was made clear by Hernán (2010) in a commentary, which emphasised that the hazard ratio contrasts populations of treated and untreated individuals who survived a given period of time, populations that will typically fail to be comparable - even in a randomised trial - as a result of different pressures or intensities acting on both populations. The commentary has been very influential, but also a source of surprise and confusion. In this talk, I aim to provide more insight into the subtle interpretation of hazard ratios and differences, by investigating in particular what can be learned about a treatment effect from the hazard ratio becoming 1 after a certain period of time. We further define a hazard ratio that has a causal interpretation and study its relationship to the Cox hazard ratio. I will first give a brief introduction to causal inference.
Jan Beyersmann, Ulm University:
Censoring and causality
These are a layman's views on causality and (perhaps a little less layman) on censoring. Censoring makes survival and event history analysis special. One important consequence is that less customized statistical techniques will be biased when applied to censored data. Another important consequence is that hazards remain identifiable under rather general censoring mechanisms. In this talk, I will demonstrate that there is a Babylonian confusion on "independent censoring" in the textbook literature, which is a worry in its own right. It is a small step from this mess to misinterpretations of hazards, a challenge not diminished when the aim is a causal interpretation.
In philosophy, causality has pretty much been destroyed by David Hume. This does not imply that statisticians should avoid causal reasoning, but it might suggest some modesty. In fact, statistical causality is mostly about interventions, and a causal survival analysis often aims at statements about the intervention "do(no censoring)", which, however, is not what identifiability of hazards is about. The current debate about estimands (in time-to-event trials) is an example where these issues are hopelessly mixed up.
The aim of this talk is to mix it up a bit further or, perhaps, even shed some light. Time permitting, I will illustrate matters with a causal g-computation-type/Aalen-Johansen-type analysis of clinical hold in a randomized clinical trial.