Sensitivity of fetal anomaly detection as a function of time

In this paper, we show that the ratio of the number of fetal anomalies detected by ultrasounds (US) to the total number of cases is not a consistent estimator of the US sensitivity. As Eddy pointed out, when the disease evolves over time, the sensitivity of a test also varies over time according to the development of the disease. To assess correctly the detection capability of a test, it is therefore necessary to estimate a time continuous function (sensitivity function) instead of a single parameter. From a methodological point of view, by considering the "detectability" time of a fetal anomaly as a random variable and parametrizing its distribution function, we estimate the probability that an anomaly is detected conditional upon the precise timing of actually performed US during pregnancy. We fit this model with Eurofetus data (about 7,300 abnormal fetuses), and we compare estimations for different kinds of anomalies (classification based on the system involved and/or severity of the handicap). To allow for heterogeneity of anomalies regarding the detectability time, we generally adopt mixture models. For instance, we select a bi-gamma distribution for major malformations and estimate that 63% of such anomalies are detectable quite early in pregnancy (conditional mean: 15.2 weeks of amenorrhea (WA) +/- 4.2 WA), the others becoming detectable later (30.3 WA +/- 6.4 WA). Such results are then integrated in a cost-effectiveness analysis.