Modeling a Progressive Disease Process Under Panel Observation

Abstract

Longitudinal studies are a useful tool for investigating the course of chronic diseases. Many chronic diseases are progressive and can be characterized by a set of health states. We can improve our understanding of the natural history of the disease by modeling the sequence of visited health states and the duration in each state. However, in most applications, subjects are observed intermittently. This observation scheme creates a major modeling challenge: the transition times are not known exactly, and in some cases the path through the health states is not known. Existing methods for modeling this type of data either impose strong parametric assumptions on the sojourn times in each state, or model time discretely and carry out inference nonparametrically, but both approaches have drawbacks. We propose an alternative modeling approach that uses the principle of data augmentation. This method has several advantages: (1) it accommodates any parametric model for the sojourn times, including spline models; (2) it performs well under moderate sample sizes for suitable parametric choices for the sojourn time distributions; and (3) it does not require that subjects be observed in every health state. Using this approach it is possible to carry out inference about both the probability of taking a given path through the health states and the duration in each state. We evaluate the performance of our proposed approach via simulation study. We extend our basic approach to accommodate the presence of left-censored entry into the process. Further, we extend the approach to account for between-subject variability in the rate of progression through the process. We apply a basic version of our proposed approach first to a study of HIV infection and progression to AIDS in a cohort of patients with hemophilia who were infected via contaminated blood transfusions. Our findings reflect those of the original study, and illustrate the need for flexible modeling of the duration in each health state. We also apply our proposed approach to a more detailed study of HIV/AIDS staging among untreated patients in Senegal who were infected with different strains of HIV. Our results indicate that patients with HIV-2 tend to progress more slowly than those infected with HIV-1 or both viruses, corroborating existing knowledge of the natural history of the disease process in each case.