Inference For Cox Proportional Hazards Model Under A Missing Not At Random Mechanism

This dissertation considers likelihood-based estimation under the Cox proportional hazards model and the Cox proportional hazards cure rate model in the situations where some covariate entries are missing not at random.Firstly,we present the semiparametric maximum likelihood esti-mator under the Cox proportional hazards model with some covariate entries are missing not at random.Assuming the conditional distribu-tion of the missing entries is known,we demonstrate the existence of the semiparametric maximum likelihood estimator of the model pa-rameters,establish the consistency and weak convergence under some appropriate conditions.By simulation,we examine the finite sample performance of the estimation procedure,and compare the SPMLE with the one resulted from using an estimated conditional distribu-tion of the missing entries.We analyze the data from a tuberculosis(TB)study applying the proposed approach for illustration.Secondly,we consider a semiparametric logistic/proportional-hazards mixture model,or the proportional-hazards cure model in which the proportional hazards regression models the survival times while the logistic regression models the cure fraction.Under this mix-ture modelling approach,we proposed the semiparametric maximum likelihood estimation with some covariate entries are missing not at random.We derive the asymptotic theory property of the estima-tor for both the model parameter and the unknown baseline hazard function.We use the complete but unobserved likelihood function to construct estimating functions,and apply the EM algorithm to re-solve them.Simulation studies and the real data analysis show that our proposed approach performs well.