Joint Modeling Longitudinal Semi-continuous Data and Survival, with Application to Longitudinal Medical Cost Data

It has been increasingly common to analyze simultaneously repeated measures and time to failure data. In this paper we propose a joint model when the repeated measures are semi-continuous, characterized by the presence of a large portion of zero values, as well as right skewness of non zero (positive) values. Examples include monthly medical costs, car insurance annual claims, or annual number of hospitalization days. A random effects two-part model is used to describe respectively the odds of being positive and the level of positive values. The random effects from the two-part model are then incorporated in the hazard of the failure time to form the joint model. The estimation can be carried out by Gaussian quadrature techniques conveniently implemented in SAS Proc NLMIXED. Our model is applied to longitudinal (monthly) medical costs of 1455 chronic heart-failure patients from the clinical data repository at the University of Virginia.