Tobit, fixed effects, and cohort analyses of the relationship between severity and duration of rheumatoid arthritis

Three methodological problems are commonly faced by researchers investigating relationships between severity and duration of illness among patients with rheumatoid arthritis (RA). (1) Linear regression techniques yield biased estimates when measures of severity are continous but range between and include limiting values such as 0 and 3. (2) Data from the same patient over time are typically pooled together with data from different patients at the same time and over time. Models are then used that do not account for the statistical problems that can result from pooling. (3) Persons with varying years of duration of disease are typically combined and analyzed without any special attention to cohort effects. Changes in severity over time for cohorts of patients with fewer than 10 years of duration may be different from changes in severity of patients with more than 20 years of duration from the onset of the disease. In this study, severity is measured by the 0-3 disability scale in the Stanford Health Assessment Questionnaire (HAQ). Duration is measured by self-report of the onset of symptoms by subjects. Popular techniques are borrowed from econometrics--Tobit, Fixed Effects, and dummy variables for Cohort Models--that were developed to address three analogous problems in economic data. The three economic techniques are applied separately and together using data collected by Arthritis, Rheumatism, and Aging Medical Information System (ARAMIS) on 330 RA patients in 1981 who were followed until 1989. Although the Tobit technique does not appear to be especially useful with these data, Fixed Effects and Cohort Models do appear to be useful. This study illustrates how methods used in economics to address three problems of censoring, panel data, and cohort effects can be applied to medical data. These three problems are often ignored in medical studies.