The Analysis Of The Average Of Causal Effects Via The Propensity Score Under The Accelerated Failure Time Model

The propensity score is widely used to estimate causal effects in observational studies.The covariate balancing propensity score methodology recently proposed can obtain a more robust estimator by optimizing the covariate balance when estimating the propensity score.In some cases of medical and epidemiological studies,the outcome of interest is the survival time.When estimating the effect of the treatment assignment mechanism on the survival time,many approaches for complete data can't be used directly for the survival data with characters such as censoring,truncation mechanisms,etc.In this paper,the outcome is the right-censored survival time and we adopt a propensity score model and an accelerated failure time model(outcome model)which are based on methods of the adjusted covariate balancing propensity score and the weighted least squares.Then,we estimate the average of causal effects by four estimation methods including Horvitz-Thompson estimation,inverse propensity score weighting estimation,weighted least squares estimation,and doubly robust estimation.In the simulation study,we consider four scenarios as follows:(a)both the propensity score model and the outcome model are correctly specified;(b)the outcome model is correctly specified but the propensity score model is misspecified;(c)the propensity score model is correctly specified but the outcome model is misspecified;(d)both the propensity score model and the outcome model are misspecified.We compare the four estimations respectively under the four scenarios.Meanwhile,we assess the influence of censoring rate and sample size on estimators of the parameter and the average of causal effects.Finally,we apply the method in this paper to the primary biliary cirrhosis data and the breast cancer data.The contents of this paper are as follows.Section 1 expounds the research background and significance of this paper,analyzes the research status at home and abroad and proposes the main content of this paper.In Section 2,we introduce the related theoretical knowledge involved in this paper.Section 3 discusses the models and its parameter estimation methods in detail and gives the four estimations of the average of causal effects.In Section 4,the performance of the four estimations is compared by the numerical simulation in different situations.In Section 5,we apply the method in this paper to the primary biliary cirrhosis data and the breast cancer data.Finally,we summarize and give the conclusion.