The Joint Modeling For Item Response And Survival Process

In modern clinical trials and medical research,the researchers collected the longitudinal data over some extended time frame for different subject and the corresponding survival data.They analyzed the longitudinal data and survival data respectively.Therefore the relationship between longitudinal process and survival process is ignored.However the relationship is considerably important for clinical medical research.So the joint modeling of longitudinal and timeto-event data has received a lot of attention in recent years.This paper discuss item response and Cox's proportional hazard model.For the joint modeling,the main difficulty arises from the requirement of integration which does not have closed expression.Numerical method Gaussianquadrature is applied to solve the problem.However the computational complexity increases exponentially with the dimension the random effect-vector.Based on adaptive Gauss-Hermite quadrature rule,a solution to overcome this problem is proposed using pseudo-adaptive GaussHermite quadrature rule.As the simulation shows,pseudo-adaptive Gauss-Hermite quadrature rule performs well,the computational speed and the precision are better than standard GaussHermite quadrature rule.