A comparison of statistical methods for age-specific reference values of discrete scales

Age-specific reference values are important in medical science to evaluate the normal ranges of subjects and to help physicians signal potential disorders as early as possible. They are applied to many types of measurements, including discrete measures obtained from questionnaires and clinical tests. These discrete measures are typically skewed to the left and bounded by a maximum score of one (or 100%). This article investigates the performances of various statistical methods, including quantile regression, the Lambda-Mu-Sigma (LMS) method and its extensions, and the generalized additive models for location, scale, and shape with zero and one-inflated distributions implemented with either fractional polynomials or splines, for age-specific reference values on discrete measures. Their large-sample performances were investigated using Monte-Carlo simulations, and the consistency of splines and fractional polynomials age profiles with quantile regression had been demonstrated as well. The advantages and disadvantages of these methods were illustrated with data on the Infant Motor Profile, a test score on motor behavior in children of 3-18 months. We concluded that quantile regression with fractional polynomials approach is a robust and computationally efficient method for setting age-specific reference values for discrete measures.