A test for the relationship between a time‐varying marker and both recovery and progression with missing data

For clinical studies of chronic diseases, patients are followed to determine whether treatment results in either improvement or decline in their clinical status. During periodic exams, laboratory specimens are collected that are believed to reflect both the progression and improvement in the disease status. Often patients miss visits and return with a changed disease status, resulting in interval-censored laboratory markers and indicators of disease status. The goal of this paper is to propose a single test that would evaluate the relationship between a longitudinal marker and clinical progression or recovery when missing visits result in interval-censored covariate and outcome data. We apply our test to evaluate the relationship between treatment compliance and progression and remission of renal disease in diabetic patients.