Modeling a Marker of Disease Progression and Onset of Disease

We consider the problem of developing joint models for a periodically observed marker of underlying disease progression and its relationship to either onset of disease or occurrence of a disease-related endpoint. We use the framework of relative risk regression models with time-dependent covariates to specify the relationship between marker and disease onset and use a mixed linear model to describe the evolution of the marker process. The construction of partial likelihood is discussed and a two step procedure is described for estimation of parameters in the model. For a special case a heuristic development of a large sample distribution theory for the proposed estimators is presented which suggests variance estimators. The method is illustrated by applying it to an analysis of periodic measurements of T4 and T8 cells and time from seroconversion to AIDS diagnosis.