Covariate-adjusted Nonlinear Quantile Regression Fitting for GFR and SCr

The glomerular filtration rate (GFR) is traditionally considered as the best overall index of renal function in health and disease. Because GFR is difficult to be measured in clinical practices, most clinicians estimate the GFR from the serum creatinine (SCr) concentration. There are a variety of models to estimate the relationship between GFR and SCr. These models typically rely on covariate-adjusted nonlinear regression methods([1]), and these methods still rely on nonlinear least-square regression methods (NLSRs) to estimate parameter. However, NLSRs are not robust. When outliers or strong influential points exist, the accuracy of estimating will be influenced among patient groups. But, the quantile regression (QR) can provide a robust alternative to NLSR methods and has been used successfully in many fields. In this paper, we propose a new method which is covariate-adjusted nonlinear quantile regression. We apply the method of covariate-adjusted nonlinear quantile regression to study the relationship between GFR and SCr, and this new method can evidently and more accurately assess and predict their relationship. This new method possesses robust fitting and overcomes some outliers than covariate-adjusted nonlinear regression.