Two bivariate geometrically defined reference regions with applications to male reproductive hormones and human...

Two conceptually simple two-dimensional reference charts are described. The charts are characterized analytically, but also by geometric properties that are easily communicated to subject-matter researchers--the users of such charts. For both charts, the proposed estimators are non-parametric, so no distributional assumptions are needed about the two-dimensional response. An important example that will serve to motivate and illustrate one of the charts is the study of the human reproductive hormones Inhibin B and FSH. A low Inhibin B concentration combined with a high FSH concentration is an indication that something may be wrong in the seminal cells which produce semen, and such measurements help in the process of distinguishing between different reasons for infertility. The aim in the study of the human reproductive hormones was to give a two-dimensional reference curve for the non-normally distributed hormone measurements while taking into account that some measurements were left-censored because of a detection limit in the assay used to measure the concentrations.