Estimation Of The Causal Effect Of Multinominal Exposure On The Marginal Mean Of The Data

Causal inference develops very fast recently in most epidemiologic, econometric, or social scientific areas, and it aims to study the causal relationship between variables which we are interested in. Causation is not association, and we need some special approaches to make inference, such as counterfactual (potential outcomes) models, graphical models, and structural equations models.My thesis's interest is that, when a patient receives a treatment, will he feel better or even worse? Some special papers have already focused on situation when treatment is binary datas. This thesis's main attribution is that, we estimate the causal effect of multinominal exposure on the marginal mean of a repeated outcome, when treatment and confounders are all time-varying. We achieve by MSM and its IPTW estimators.In chapter two, we provide a conceptual introduction to causal inference, including its origin and development. We illuminate the difference between causation and association; and also introduce new notation for expressing causal assumptions and causal claims. In Chapter three, we show former statistists' work about how to estimate the causal effect of binary exposure.In chapter four, which is our main work, we extend binary data to multinominal data. First of all, we specify a linear logistic MSM to model the mean of outcomes. Though confounders affect the outcomes and treatment, we adjust for the time-dependent confounders by using them to calculate the stabilized weights sω_i rather than by adding the confounders to the regression model as regressors. Stabilized weight can be viewed as a ratio of the probability of receiving treatment and the probability condition on the confounders, and that can be estimated with MLEs. At the last, we use weighted GEE to get corresponding estimators of the paramater, which reflect the causal effect of multinominal exposure in this area in the same way.In chapter five, we present augmented IPTW estimator of MSM's parameter and prove its consistency. Besides, in survival analysis, we view censoring as another time-varying treatment, and make causal inference.