A score test for association of a longitudinal marker and an event with missing data

Often clinical studies periodically record information on disease progression as well as results from laboratory studies that are believed to reflect the progressing stages of the disease. A primary aim of such a study is to determine the relationship between the lab measurements and a disease progression. If there were no missing or censored data, these analyses would be straightforward. However, often patients miss visits, and return after their disease has progressed. In this case, not only is their progression time interval censored, but their lab test series is also incomplete. In this article, we propose a simple test for the association between a longitudinal marker and an event time from incomplete data. We derive the test using a very intuitive technique of calculating the expected complete data score conditional on the observed incomplete data (conditional expected score test, CEST). The problem was motivated by data from an observational study of patients with diabetes.