A two-part model for reference curve estimation subject to a limit of detection

Abstract

Reference curves are commonly used to identify individuals with extreme values of clinically relevant variables or stages of progression which depend naturally on age or maturation. Estimation of reference curves can be complicated by a technical limit of detection (LOD) that censors the measurement from the left, as is the case in our study of reproductive hormone levels in boys around the time of the onset of puberty. We discuss issues with common approaches to the LOD problem in the context of our pubertal hormone study, and propose a two-part model that addresses these issues. One part of the proposed model specifies the probability of a measurement exceeding the LOD as a function of age. The other part of the model specifies the conditional distribution of a measurement given that it exceeds the LOD, again as a function of age. Information from the two parts can be combined to estimate the identifiable portion (i.e. above the LOD) of a reference curve and to calculate the relative standing of a given measurement above the LOD. Unlike some common approaches to LOD problems, the two-part model is free of untestable assumptions involving unobservable quantities, flexible for modeling the observable data, and easy to implement with existing software. The method is illustrated with hormone data from the Third National Health and Nutrition Examination Survey.