A measurement error Rao–Yu model for regional prevalence estimation over time using uncertain data obtained from dependent survey estimates

• Published in: Test (Madrid, Spain) Vol. 31; no. 1; pp. 204 - 234
• Main Authors: Burgard, Jan Pablo, Krause, Joscha, Morales, Domingo
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2022; Springer Nature B.V
• Subjects: Economics; Error analysis; Estimates; Finance; Hypertension; Insurance; Management; Mathematics and Statistics; Maximum likelihood estimation; Original Paper; Parameter estimation; Public health; Statistical Theory and Methods; Statistics; Statistics for Business; Uncertainty; Empirical best prediction; Parametric bootstrap; 62P10; 62F40; Dependent errors; 62F86; Hierarchical model; Temporal data; 62F10; Small area estimation; 62F35
• ISSN: 1133-0686; 1863-8260
• DOI: 10.1007/s11749-021-00776-w

The assessment of prevalence on regional levels is an important element of public health reporting. Since regional prevalence is rarely collected in registers, corresponding figures are often estimated via small area estimation using suitable health data. However, such data are frequently subject to uncertainty as values have been estimated from surveys. In that case, the method for prevalence estimation must explicitly account for data uncertainty to allow for reliable results. This can be achieved via measurement error models that introduce distribution assumptions on the noisy data. However, these methods usually require target and explanatory variable errors to be independent. This does not hold when data for both have been estimated from the same survey, which is sometimes the case in official statistics. If not accounted for, prevalence estimates can be severely biased. We propose a new measurement error model for regional prevalence estimation that is suitable for settings where target and explanatory variable errors are dependent. We derive empirical best predictors and demonstrate mean-squared error estimation. A maximum likelihood approach for model parameter estimation is presented. Simulation experiments are conducted to prove the effectiveness of the method. An application to regional hypertension prevalence estimation in Germany is provided.