Statistic Analysis Of Random Effect Models With Censored Data

The estimation and prediction are commonly needed in many fields, such as medical science, biology, insurance, reliability, population statistics and so on. The study of regularity of the time is called survival analysis. Survival analysis plays an important role in the forecast of the individual life. It has extensive applications in medical science, biology and so on. Researchers pay more and more attention to this problem. Meanwhile, the theory of systems analysis is continuously developed and improved. Many complex systems usually contain uncertainty, then probabilistic and statistical models are often used, and hence the methods of statistical inference become the important analysis methods in systems analysis. Many system analysis researchers and statisticians have paid great attention to the random effect models because of their wide application. Statistic diagnostics is a new branch which was developed in the middle 70s in the last century. A new field, in which theory and application have been mixed, have appeared in front of statistical researchers by its great application value, new idea, abundant content and practical achievement. The diagnostics of the parameter regression model includes the following contents: residual analysis, global influence analysis, data shift, local influence analysis and so on. Now it is very important for us to raise the more effective methods.In this paper, we systematically study the random effect models with censored data. The main ideas of the paper are as follows:In chapter 2, we discuss the nonlinear random effect models with censored data. Then we employ the Laplace methods to deal with these models. Based on this method, the fixed effect parameter estimates and Gauss-Newton formula are obtained. The results of Robinson(1991), Lee and Nelder(1996) are improved.In chapter 3, the diagnostics and influence analysis are systematically studied for the normal nonlinear models with random effect and censored data. Several diagnostic measures, such as Cook distance, generalized leverage, residuals, and likelihood ratio statistics et al. are obtained.In chapter 4, we systematically study the normal linear models with random effect and censored data. The fixed effect parameter estimates, variance estimates, several diagnostic measures are obtained. At last, a real example illustrates that our method is available.