Estimation Of Causal Treatment Effects With Interval-censored Data

In recent years,discussions on causal inference methods have increasingly appeared in various research fields,including economics,clinical medicine,sociology,etc.Naturally,by introducing causal inference into the research about survival analysis,people can scientifically evaluate the causal relationship between a variable that people are interested in,such as receiving breast cancer screening,and survival data.However,there are many difficulties in this process.On the one hand,how to correctly estimate causality,distinguish it from correlation,avoid error problems caused by the existence of endogenous bias,and deal with the noncompliance problem in randomized experiment,have always been the focus of causal analysis.On the other hand,the complexity of survival data undoubtedly increases the difficulty of research,such as the problem about interval-censored data,and even the occurrence of dependent censoring and missing covariates.In response to the above difficulties,this thesis provides an efficient method for causal effect estimation under independent interval-censored data,and also considers two other more complex situations.This thesis includes the following three parts.In Chapter 2,a causal inference method with independent interval-censored data under the additive hazards model is proposed.As we all know,the endogenous bias always occurs in causal inference,which is caused by an unobserved confounding factor correlated with both the variable of interest and failure time data.In order to solve the problem,this chapter introduces a binary instrumental variable into the model.As for the noncompliance problem that always appears in randomized experiment,the overall sample can be classified into several groups through the relationship between the instrumental variable and the variable of interest under the potential outcome framework.After that,the survival function of each group can be given,and finally the likelihood function of the overall sample can be established.After obtaining the maximum likelihood estimates of the parameters by using sieve method,this chapter further quantifies the causal relationship between the variable of interest and failure time clearly through two numerical indicators for causal analysis.This chapter discusses the asymptotic properties of model parameters and gives specific demonstrations with finite samples through simulation results.Finally,in order to verify whether the proposed method is effective,this chapter applies it to a a set of real data and demonstrates the advantages of the proposed method.In Chapter 3,we consider a more complex situation,that is,in the process of causal inference with interval-censored data,the failure time and the censoring time are no longer independent.In order to describe the relationship between the failure time and the censoring time,under the proportional hazards model,a fraility term is introduced into the hazard functions of failure time and censoring time,respectively.In the process of solving the likelihood function,when the fraility item follows some certain special forms,it can be integrated through mathematical derivation and we can obtain an explicit solution of the model parameters.By plugging them into two quantitative indicators for causal analysis,the causal effect of dependently censored data can be derived.Similarly,the asymptotic properties of the estimated covariate effects are given in this case and we verify the rationality of this estimation method under finite sample size through numerical simulation.Finally,this method is applied to a HIV data set in this chapter and we compare it with other causal analysis methods to show its effectiveness.In Chapter 4,we further consider the method for causal inference when covariates can be missing by design.Missing by design of covariates is likely to appear when researchers want to cut down the cost of carrying an experiment.Therefore,they may design some particular procedures before it starts.However,it may bring bias to estimations.In order to solve this problem,the idea of case-cohort design can be applied into causal effect estimation when the overall sample incidence rate is low.Under this design,it no longer extracts covariate information from the entire study population,but uses the subjects from a subcohort that is a random sample of the entire cohort and those who have experienced the failure event of interest as sources of covariate information.As for the estimation error problem that may be caused by biased sampling,the inverse probability weighting technique is intorduced into the likelihood function to solve the problem.We give the asymptotic properties of the estimated parameters and use numerical simulation to show its performance with finite samples.Finally,this method is valadated by actual data,and its effectiveness and advantages are verified.In conclusion,aiming at the problem of causal effect estimation for intervalcensored data when there is non-compliance in clinical trials,this paper introduces instrumental variables to provide effective methods in the case of independent interval censoring,dependent interval censoring and missing by design of covariates.