Statistical Analysis Of Current Status Data With Informative Observation Times

Current status data arise when each study subject is observed only onceand the survival time of interest is known only to be either less or greater than the observation time. Such data often occur in, for example, crosssectional studies, demographical investigations and tumorigenicity experiments and several semi-parametric methods for their analysis have been proposed. However, most of the methods deal with the situation where observation time is independent of the underlying survival time completely or given covariates. This thesis discusses regression analysis of current status data when the observation time may be related to the underlying survival time and inference procedures are presented for estimation of regression parameters, for the situation where the hazard function of the survival times is the additive hazards regression model and the hazard function of the observation times is the proportional hazards model. To estimate the regression parameters, we divide the observation time into two cases: one is without the censoring time, other is with the censoring time, and employ the random effect to connect the survival time and the observation time. For the estimation of the parameters, we apply the methods similar to the maximum likelihood estimates which are the maximum partial likelihood estimates. This method is by solving a score function to get the estimated parameters. After the parameter estimates are proposed, we also propose the characters of the estimate. Similar tothe characters of maximum likelihood estimate, they are asymptotically normal and asymptotically effective. We apply existing statistical analysis software R to conduct a series of simulation studies without the censoring time and with the censoring time. For the case that the observation time is with the censoring time, according to the censoring percentage, we divide into the two cases: one is 20%, other is 60%. We apply the proposed methodology to the data given by the tumorigenicity experiments, and the result is similar to the fact that bladder tumours are usually more lethal than lung tumours. The innovation of the paper is that for the proposed methods we test the sensitivity of the model, according to changing the model used to generate the observation times.