Model-based screening by risk with application to Down's syndrome

Screening for a disorder may be carried out by assessing the risk that an individual is affected given the values of variables whose distributions alter when the disorder is present. An optimal screening policy is obtained by identifying those individuals whose risk is greater than some cut-off value. This paper summarizes the way in which risk is derived from the likelihood ratio of being affected by the disorder, and compares three different methods of estimating the likelihood ratio, namely direct estimation, logistic regression and distribution modelling. For continuous variables that have a multivariate normal distribution, screening by risk is equivalent to the use of quadratic discrimination. The paper shows how estimates of the risk and associated detection and false positive rates can be derived for a screening policy which uses specified risk cut-offs. Screening by risk has the counter-intuitive property that as the separation in the distribution of screening variables between affected and unaffected individuals increases, the detection and false positive rates may both increase. The approach is explored using data on antenatal screening for Down's syndrome. The method of choice is model-based; the model is described and tested for goodness of fit. Complications arising from outliers and non-normality must be overcome before an appropriate assessment of risk can be made. The concept of shrinkage is used to estimate the detection of false positive rates that may be expected in a new data set.