Abstract
In Down's syndrome screening using biochemical markers, the marker concentrations are adjusted for the gestational age of the fetus, since they are known to change with gestational age. This adjustment is performed by referring to the population median of each marker for the appropriate gestational age group. The measurement of gestational age is subject to error, whatever method is used, and the population median used is actually the median of a mixture of distributions for different true gestational ages. We show how the proportions in this mixture can be estimated and how the true median corresponding to a given true gestational age can be estimated. For simplicity, we consider the case of using a single marker, namely maternal serum α-fetoprotein, and show that the usual estimation method has considerable bias. The effect of this mixture on the calculation of patient-specific risks is discussed and we show that detection rates can be improved by allowing for this error in the dating process. The overall detection rate is increased by about 1%. The increase in detection rate is age-dependent and for some maternal ages the increase is of the order of 5%. The comparative effects of different methods for dating are discussed.