Causal Inference for Observational Longitudinal Survival Data
Specialeforsvar: Mark Bech Knudsen
Titel: Causal Inference for Observational Longitudinal Survival Data
Abstract: This thesis concerns causal inference for observational longitudinal survival data. In particular, estimation of the effect a treatment has on survival, when the treatment varies over time and is subject to time-varying confounding. First, we define causal effects in terms of potential outcomes, and for the discrete-time case show how the distribution of potential outcomes can be related to observational data through the g-formula. We explain why hazard ratios cannot be interpreted causally, and show how the parameter in a Cox proportional hazards model might instead be interpreted causally as a log-survival ratio, assuming the Markov property for the hazard, and that survival status does not affect future exposure. We continue with a
deeper look at the Markov assumption, and show that in the presence of unobserved frailty, it implies that the underlying distribution is not faithful to its causal change-of-measure framework is used to redefine causal effects, giving a definition that extends quite naturally to the continuous-time case. It is then shown how these effects can be estimated using a continuous-time version of the classic inverse probability weights, with a particularly easy special case being the effect of always treating compared to never treating. The methods are illustrated on real data from patients suffering from esophageal cancer.
Vejledere: Susanne Ditlevsen
Torben Martinussen, Helene Charlotte Wiese Rytgaard, SUND
Censor: Klaus Kähler Holst, Mærsk