Abstract:
Current status data arise in many fields including epidemiological surveys and animal carcinogenicity experiments. By current status data we mean each subject in a study is observed only once at a certain time to ascertain whether or not the event of interest has occurred. This means that for current status data, the event (failure) time is not exactly observed but only known to be smaller or greater than the observation (censoring) time. The standard assumption in survival data analysis is that the observation time is non-informative, that is, the observation time is unrelated to the failure time. However, this assumption may not be valid in some circumstances, especially if the subject is lost-to-follow-up before the study ends. The examination time for such a subject can potentially be linked to the failure time and hence the examination time will be said to be informatively censored. To avoid severely misleading inferences that can result from failing to account for informative censoring, shared frailty models have been proposed in literature to account for informative censoring with current status data. The most commonly used estimation procedure is the Expectation-Maximization (EM) algorithm, but this approach yield discrete estimation of the distribution and possibly a negative hazard estimate. Thus the EM algorithm might not only be able to provide an accurate trend of how the baseline hazard estimates are changing over time, but also affect the accuracy of the estimated parameters. The goal of this thesis therefore, is to develop Maximum Penalized Likelihood (MPL) methods for current status data with informative censoring based on gamma-shared frailty assumption. We intend to show how the MPL procedure can be employed to simultaneously estimate the regression parameters and the smooth baseline continuous hazard functions for Proportional Hazards Model, Semiparametric transformation Model and Clustered data under the proportional hazards model. The variances and the asymptotic properties of these MPL estimators will be studied. Simulations studies will also be conducted to ascertain the performance of our proposed MPL methods. Comparisons will also be made with some of the existing EM methods. For illustrative purposes, we will apply our methods to the data set on rodent tumorigenicity experiment example provided by National Toxicology Program (1998)