Bayesian Semiparametric Cox Regression Analysis Of Interval-censored Data

The data we obtained about the time to the event of interest during survival analysis have a common characteristic that the results of surveying are either censored or truncated,especially call it interval-censored when we only know the event within an interval.Hitherto,the research of interval-censored data mainly focus on the estimation of survival function about this kind data,by contrast,there are less research on parametric estimation,therefore few methods on hand.The proportional hazards model is often used to express the relationship about the time to the event and the correlated variables.As to the model we mainly concerned two parts, one is the regression coefficient,the other is the baseline hazards function which reflects our common knowledge about the event of interest,so we can usually get some prior information about the baseline hazards function,as a result of the complicated prior information and the observed censoring intervals containing their survival times that frequently overlap with each other,we often face lots of computational difficulties about Bayesian analysis of the proportional hazards model,now available theory and computation are often formidable to practioners,it still remains a field for researchers.As to interval-censored data,we propose a semiparametric approach to the proportional hazards regression analysis of interval-censored data.first we assume that the regression coefficient and the baseline hazards function both follow a piecewise model on a fine grid of unit-width intervals and design a suitable semiparametric piror distribution respectively.An EM algorithm based on an approximate posterior likelihood applied leads to the estimators of the unknown parameters,the E-step takes a nonparametric method to approximate the conditional expectation which particularly simplified the computation,we use bootstrap method to yield the variance of the parameter to assess the stability of estimators.The method is illustrated on data from the breast cancer cosmetric trial,previously analyzed by several authors.