In order to study the multivariate survival data

a unique random variable is applied to multiply each competing hazard to reveal the relation of different causes

and COX Proportional Hazard model is assumed for each competing hazard.This looks more difficult of estimating intensively in traditional view

but it is more coincident with the actual facts.Using hierarchical likelihood approach

the multidimensional integral is avoided

and the hierarchical likelihood function and the process of estimating model are derived.