A Bayesian Model to Analyze the Association of Rheumatoid Arthritis With Risk Factors and Their Interactions

Rheumatoid arthritis (RA) is a chronic autoimmune disorder that commonly manifests as destructive joint inflammation but also affects multiple other organ systems. The pathogenesis of RA is complex where a variety of factors including comorbidities, demographic, and socioeconomic variables are known to associate with RA and influence the progress of the disease. In this work, we used a Bayesian logistic regression model to quantitatively assess how these factors influence the risk of RA, individually and through their interactions. Using cross-sectional data from the National Health and Nutrition Examination Survey (NHANES), a set of 11 well-known RA risk factors such as age, gender, ethnicity, body mass index (BMI), and depression were selected to predict RA. We considered up to third-order interactions between the risk factors and implemented factor analysis of mixed data (FAMD) to account for both the continuous and categorical natures of these variables. The model was further optimized over the area under the receiver operating characteristic curve (AUC) using a genetic algorithm (GA) with the optimal predictive model having a smoothed AUC of 0.826 (95% CI: 0.801-0.850) on a validation dataset and 0.805 (95% CI: 0.781-0.829) on a holdout test dataset. Apart from corroborating the influence of individual risk factors on RA, our model identified a strong association of RA with multiple second- and third-order interactions, many of which involve age or BMI as one of the factors. This observation suggests a potential role of risk-factor interactions in RA disease mechanism. Furthermore, our findings on the contribution of RA risk factors and their interactions to disease prediction could be useful in developing strategies for early diagnosis of RA.