Regression analysis for Dependent current status data

Abstract

In the current state data, each individual is observed only once, and the only available information is whether the failure event of interest occured during the observation time. In other words, the current state data cannot observe any individual's specific survival time or the failure time, therefore, it is significant different from the normal right-censored data. In this paper, we use the Cox model to construct the model of interested failure time and observation time, because the model contains not only regression coefficient of finite dimension, but also the unknown function of infinite dimension, and there are covariables which cannot be observed, so it is difficult to directly maximize the likelihood function. Therefore, the non-observable latent variable is introduced to describe the dependence of two kinds of time, the step function is used to approximate the unknown function to reduce the difficulty of non-parametric part, further the parameter estimation is given by the EM algorithm, the consistency and asymptotic of the estimators are also certified. Some data simulations are performed, whose results show that the method presented here performed well under a limited sample. In the following paper, a group of mouse experiments demonstrating that the sterile environment has no significant effect on tumor inhibition. This paper only considered the current state data and the Cox model, In the futher, the statistical inference problem under other more general and more complex models can be further considered.