Proportional Hazards Models And Multiplicative Intensity Models With Measurement Error Data

In survival analysis, proportional hazards (PH) models are often employed to describe the relationship between the hazard function of the failure time and the co-variates. As an extension of proportional hazards model, the multiplicative intensity models are usually used to reveal the relationship between events and covariates in the context of recurrent events analysis. For the right censored data, the estimate of the regression coefficients in these methods can be performed easily, and the asymptotic properties of the estimators are pretty good. Thus these models are very popular in the analysis of survival data and recurrent event data. On the other hand, measure-ment error models research how to reduce the bias of the estimator when covariates are measured with error. This model can reflect the reality more accurately than common regression model, and it is another popular topic in statistics. Therefore,in this thesis, PH models or multiplicative intensity models are combined with the measurement error models to investigate some estimation problems when covariates are measured with error.For analyzing the measurement error data, the key point is to compute the con-ditional expectation of some function of the accurate covariates X conditional on its auxiliary variable W, that is E(g(X)|W). So, two different solutions are introduced in PH models and multiplicative intensity models, respectively. In PH models, a commonly used nonparametric smoothing procedure, kernel smoothing, is used to estimate the conditional expectation. While in multiplicative intensity models, some assumptions of distributions will be put forward to calculate the conditional expec-tation directly. At the end of this thesis, SIMEX method will make a supplement for situations in which the previous solutions does not work. And the property of SIMEX method will also be demonstrated briefly.The main contributions of this thesis are as follows: On the one hand, in PH models, AEPL function was proposed, which can improve the original EPL function in Zhou&Wang(2000). On the other hand, in multiplicative intensity models, the validation set is introduced to refine previous methods given in Yi&Lawless(2012).What's more, extensive simulation studies are conducted to demonstrate the valid-ity of the procedures proposed in this thesis. The simulation results show that the proposed procedures can improve the existing approaches and the estimators seem to satisfy the asymptotic properties quite well.