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Title: Statistical causal inference and propensity analysis
Author: Guo, H.
Awarding Body: University of Cambridge
Current Institution: University of Cambridge
Date of Award: 2011
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Statistical causal inference from an observational study often requires adjustment for a possibly multi-dimensional covariate, where there is a need for dimension reduction. Propensity score analysis (Rosenbaum and Rubin 1983) is a popular approach to such reduction. This thesis addresses causal inference within Dawid’s decision-theoretic framework, where studies of “sufficient covariate” and its properties are essential. The role of a propensity variable, obtained from “treatment-sufficient reduction”, is illustrated and examined by a simple normal linear model. As propensity analysis is believed to reduce bias and improve precision, both population-based and sample-based linear regressions have been implemented, with adjustments for the multivariate covariate and for a scalar propensity variable. Theoretical illustrations are then verified by simulation results. In addition, propensity analysis in a non-linear model: logistic regression is also discussed, followed by the investigation of the augmented inverse probability weighted (AIPW) estimator, which is a combination of a response model and a propensity model. It is found that, in the linear regression with homoscedasticity, propensity variable analysis results in exactly the same estimated causal effect as that from multivariate linear regression, for both population and sample. It is claimed that adjusting for an estimated propensity variable yields better precision than the true propensity variable, which is proved to not be universally valid. The AIPW estimator has the property of “Double robustness” and it is possible to improve the precision given that the propensity model is correctly specified.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available