Models with Errors due to Misreported Measurements

Measurement error and misclassification models feature prominently in the literature. This paper describes misreporting error, which can be considered to fall somewhere between these two broad types of model. Misreporting is concerned with situations where a continuous random variable X is measured with error and only reported as the discrete random variable Z. Data grouping or rounding are the simplest examples of this, but more generally X may be reported as a value z of Z which refers to a different interval from the one in which X lies. The paper discusses a method for handling misreported data and draws links with measurement error and misclassification models. A motivating example is considered from a prenatal Down's syndrome screening, where the gestational age at which mothers present for screening is a true continuous variable but is misreported because it is only ever observed as a discrete whole number of weeks which may in fact be in error. The implications this misreporting might have for the screening are investigated.