Establishing reference interval bounds for censored and contaminated data

Abstract

Reference intervals are essential across the medical and environmental fields. A reference interval (for example, the $95\text{\%}$ central prediction interval) defines the normal range of measurements for a specific physiological parameter in healthy individuals. Inappropriate reference interval bounds may occur because of censored measurements (due to instrument limitations) or contaminated data (by accidentally sampling nonhealthy individuals). To address this, we propose using the regression-on-order-statistics (ROS) method combined with an optimal Box–Cox transformation. The ROS method involves regressing Gaussian scores based on ranks from ordered noncensored Box–Cox transformed measurements. To find the optimal Box–Cox transformation, we maximize the adjusted $R^2$ when estimating the mean and standard deviation through regression of empirical Gaussian quantiles on measurements. We demonstrate how to identify contamination and introduce a new command, ros. Real-life data illustrate the effectiveness of the ROS method.