Causal Inference with a view towards Longitudinal Data Analysis
Authors
Term
4. term
Education
Publication year
2022
Submitted on
2022-06-02
Pages
66
Abstract
This master's thesis is a study of causal inference with a view towards longitudinal data analysis. The aim is to study the theory of causal inference and various methods to estimate causal effects. We present the TMLE, CV-TMLE and L-TMLE methods and properties of these methods. Moreover, we apply these methods to a subset of the Framingham Heart Study, which is a longitudinal study, to determine if smoking has a causal effect on stroke in both a non longitudinal study and a longitudinal study. In particular, we first define an (average) causal effect and present the identifiability conditions which are required in order to identify (average) causal effects for observational studies. Then we present the inverse probability weighting and standardisation methods. Furthermore, we describe how causal directed acyclic graphs can be used to illustrate relations between the covariates, treatment and outcome. Then we present structural causal models in order to specify the target parameter. Furthermore, we present the TMLE and CV-TMLE methods and show asymptotic linearity of the CV-TML estimator. Afterwards, we present a longitudinal extension of (average) causal effects, the identifiability conditions and the TMLE method. Finally, we apply the TMLE and CV-TMLE methods as well as the L-TMLE method in order to examine if smoking has a causal effect on stroke within $24$ years in a non longitudinal and longitudinal study, respectively.
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