Regression Analysis Of Case ? Interval-Censored Failure Time Data Under The Additive Hazards Model With Auxiliary Covariates

In the fields of economics,insurance mathematics,biology,medicine,demography,criminology,reliability engineering and other subjects,people are always interested in estimating and predicting the time when a given event would have happened.Survival Analysis is the method of using statistical theories to solve problems about occurrence time related to certain events.The data sets those we can get have a common feature which is that the observed results are either censored or truncated.In particular,when individual has only two observations,then we can only determine the event's occurrence period but not sure of the exact occurrence time point,we call it case II interval-censored data.In survival analysis,we usually can use proportional hazards model and additive hazards model to describe the relationship between survival time and covariates those influencing survival status.The two models describe the relationship between failure time and covariates from different perspectives,respectively.However,additive hazards model is more applicable when risk difference is emphasized.In practice,there may be missing covariates,or covariates cannot be measured exactly but there may be some related information such as auxiliary covariates.Estimation efficiency will be improved if we take into account available auxiliary covariates.Based on Feng et al.(2015),we solve the problems about regression analysis of case II interval-censored data under the additive hazards model with auxiliary covariates.This article first reviews some relevant theoretical background then puts forward to an estimated partial likelihood method based on traditional partial likelihood function,which using estimating equations with intensity process.Furthermore,we also put forwards to a two-stage method,which can improve the estimation results' efficiency.These two methods can be easily implemented,and the asymptotic properties of the resulting estimators are established.Then in some generalized cases,estimation process is briefly discussed.Finally,the application value of the two methods proposed in this paper is illustrated by numerical simulation and an illustrative example.