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Abstract
Survival analysis plays an important role in biomedical research studies such as clinical trials and clinical research, of which the typical primary outcome of interest is time-to-event. Among the large number of methods for investigating the association between covariates and time-to-event, the Cox proportional hazards model is the most widely used. However, in survival data, covariates are often subject to substantial measurement error that the true values of these error-prone covariates are unavailable. A naive analysis that uses the mismeasured covariates and ignores measurement error may lead to substantial bias in estimations of the parameters of survival models. Frequently used statistical approaches which adjust for measurement error in survival analysis usually have some common parametric assumptions. In this dissertation research, we focus on relaxing several widely used parametric assumptions in survival analysis with covariate measurement error.
The first topic considers a Bayesian semi-parametric partly linear Cox model that allows the log hazard to depend on an unspecified function of a continuous error-prone covariate and a linear error-free covariate with time-varying coefficient. Our method relaxes the assumption on the functional form of the error-prone covariate and is robust to non-constant covariate effect. Simulation studies are conducted to assess the performance of the proposed method. The results demonstrate that our proposed method has favorable statistical performance. The proposed method is also illustrated by an application to data from a clinical trial study.
The second topic is a generalization of the first topic. We consider the linear component with time-varying coefficient in the survival model to be a continuous or binary error-prone covariate subject to measurement error or misclassification. Extensive simulation studies are performed to evaluate the proposed method and the results show that our method is superior.
In the first and the second topics, the measurement error is assumed to be normally distributed. In the third topic, we consider a similar Cox model as in the first topic, but the measurement error distribution is unspecified and the linear error-free covariate effect is constant. We relax the distributional assumption on the measurement error by a Dirichlet process. We evaluate the performance of our proposed method via extensive numerical studies and it shows that the proposed method is robust to non-normally distributed measurement error.
The first topic considers a Bayesian semi-parametric partly linear Cox model that allows the log hazard to depend on an unspecified function of a continuous error-prone covariate and a linear error-free covariate with time-varying coefficient. Our method relaxes the assumption on the functional form of the error-prone covariate and is robust to non-constant covariate effect. Simulation studies are conducted to assess the performance of the proposed method. The results demonstrate that our proposed method has favorable statistical performance. The proposed method is also illustrated by an application to data from a clinical trial study.
The second topic is a generalization of the first topic. We consider the linear component with time-varying coefficient in the survival model to be a continuous or binary error-prone covariate subject to measurement error or misclassification. Extensive simulation studies are performed to evaluate the proposed method and the results show that our method is superior.
In the first and the second topics, the measurement error is assumed to be normally distributed. In the third topic, we consider a similar Cox model as in the first topic, but the measurement error distribution is unspecified and the linear error-free covariate effect is constant. We relax the distributional assumption on the measurement error by a Dirichlet process. We evaluate the performance of our proposed method via extensive numerical studies and it shows that the proposed method is robust to non-normally distributed measurement error.