Journal of Biometrics & Biostatistics

The Concepts of Fractal Ellipses and ISO Likelihood Ratio Curve s in Two-dimensional Screening Procedures with Applications in Scree ning for Down Syndrome

Abstract

Severin Olesen Larsen, Paula L Hedley and Michael Christiansen

Background: Prenatal screening combines biochemical and biometric markers into a risk estimate for a particular adverse outcome, e.g. the birth of a child with Down syndrome. The statistical calculations are complicated. We describe a simple graphical method to perform risk estimation in the case of two biochemical markers, to assess the consequences of changes in gestational dating of the pregnancy and to perform quality control. Materials and methods: We used the formulae for the Normal distribution to establish the expression for fractal ellipses, i.e. contour ellipses describing a certain fractile of the total distribution. This expression was used to establish mathematical expressions for curves describing two-dimensional pairs of analytes giving the same likelihood-ratio, i.e. iso likelihood-ratio curves. Results: The fractal ellipses provide an overview of marker distributions that allow for an easy control of empirical marker distributions. The iso likelihood-ratio curves provide a relation between likelihood-ratio and marker values. They can be used for assessment of the consequences of changes in gestational age and introduction of truncation limits on markers. Conclusions: Fractal ellipses and iso likelihood-ratio curves can be used to make software-independent calculations and modifications of risk in prenatal screening and quality control of an ongoing screening program.