Survival analysis is a statistical framework for studying the time to the occurrence of an event. In practice, data subjected to survival analysis are often observational, which implies that the causal effect of a treatment or exposure of interest cannot be directly inferred due to the presence of confounding variables. Classical survival analysis methods, such as the Kaplan–Meier estimator and the Cox proportional hazards model, generally do not support valid causal inference in such settings. This limitation represents a significant challenge and has motivated the development of causal inference methods specifically adapted to survival analysis.
In the theoretical introduction, we presented the fundamental concepts of causal inference, including Simpson’s paradox, representations of dependencies between variables, standard notation, and key assumptions underlying causal analysis. This was followed by a review of survival analysis theory, in which we described the basic quantities of interest as well as the classical Kaplan–Meier estimator and the Cox proportional hazards model. The final part of the theoretical chapter focused on causal inference methods applied in survival analysis, namely the G-formula, inverse probability of treatment weighting (IPTW), and augmented inverse probability of treatment weighting (AIPTW). These methods enable adjustment for confounding variables and facilitate the estimation of causal effects in observational data.
In the empirical part, we conducted an extensive simulation study in which we compared the aforementioned methods with the classical nonparametric Kaplan–Meier estimator. First, we replicated a simulation study from the selected literature and subsequently designed additional scenarios in which we systematically varied the data-generating process, the strength of covariate effects, the treatment assignment distribution, and the correctness of model specification for both the outcome and treatment mechanisms. The results demonstrated that methods which appropriately account for confounding yield less biased estimates than classical approaches. The G-formula was shown to be sensitive to misspecification of the outcome model, and IPTW to misspecification of the treatment model, whereas AIPTW performed well provided that at least one of the two models was correctly specified. When both models were misspecified, however, its performance deteriorated. Further simulations indicated that failure to adjust for relevant covariates (i.e., violation of the assumption of no unmeasured confounding) leads to biased estimates across all considered methods, with relatively small differences between them. In addition, weighting-based methods (IPTW and AIPTW) were found to be more sensitive to imbalance in treatment proportions, resulting in increased variability of the estimates, particularly in settings with rare treatments.
The results of this master’s thesis contribute to a deeper understanding of the application and comparison of causal inference methods in survival analysis and suggest that careful and judicious use of these methods can substantially improve the quality of conclusions drawn from observational data.
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