| Model checking for statistical models is an important part of any statistical analysis. In this dissertation, the model checking techniques for two types of models in survival analysis are developed.; In Part I, we discuss the marginal proportional hazards frailty model for multivariate failure time data. We suggest a two-stage method for checking the adequacy of the marginal proportional hazards frailty model. In the first stage, the goodness of fit test from Spiekerman and Lin (1996) can be applied for checking the marginal proportional hazards model. Our work is focused on the second stage. We develop a graphical as well as a numerical method for checking the adequacy of the gamma frailty distribution. The test process is derived from the posterior expectation of the frailty given the observable data. Its distributions under the assumed model can be approximated through simulation.; In Part II, we study the problem of checking the adequacy of a parametric model for the distribution function based on several possibly censored biased samples. The identifiability problems related to the original distribution and the distributions of the biased samples are discussed. The test statistic proposed is based on the supremum of the weighted martingale residual processes from K biased samples. A Monte Carlo method is used to approximate the critical values of the proposed test. Simulations are conducted to assess the finite sample performance of the test. |
