Reference curves of radiographic damage in patients with rheumatoid arthritis: application of quantile regression and fractional polynomials

OBJECTIVE: To (1) introduce the methodology of quantile regression and fractional polynomials; (2) test the application of this methodology to develop, conditional on disease duration, preliminary reference curves of radiographic damage in patients with rheumatoid arthritis (RA); and (3) prove the importance of the definition and selection of the reference group when developing reference curves. METHODS: The study design was cross sectional. The main study factors were disease duration and radiographic damage using the Larsen score. The 2 study samples were 98 patients from a multicenter trial of cyclosporine and 203 patients with RA from a teaching hospital clinic. RESULTS: Using disease duration as the time dependent covariate we constructed quantile regression reference curves of radiographic damage. The reference curves for the 2 samples differed in shape, location, and slope. CONCLUSION: Quantile regression and fractional polynomials simplify the construction of reference curves when data cannot be easily modified to meet assumptions of normality, linearity, and constant variance. Quantile reference curves provide clinicians with a useful clinical tool to measure outcome at arbitrary timepoints, to interpret change, and to set treatment objectives. However, the definition and selection of the reference used to construct the reference curves is of critical importance.