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.

区域一级的流行率评估是公共卫生报告的重要组成部分。由于很少在寄存器中收集区域患病率，因此通常使用适当的健康数据通过小面积估算来估算相应的数字。但是，由于从调查中估算出这些值，因此这些数据经常会受到不确定性的影响。在这种情况下，患病率估算方法必须明确考虑数据不确定性，以确保结果可靠。这可以通过引入误差数据的分布假设的测量误差模型来实现。但是，这些方法通常要求目标变量和解释变量错误是独立的。当从同一次调查中估计了两者的数据时，这并不成立，在官方统计中有时就是这种情况。如果不考虑，患病率估计值可能会严重偏差。我们提出了一种用于区域患病率估计的新的测量误差模型，该模型适用于目标误差和解释变量误差相关的设置。我们推导出经验最佳的预测变量，并证明均方误差估计。提出了一种用于模型参数估计的最大似然方法。仿真实验证明了该方法的有效性。提供了在德国地区高血压患病率估算中的应用。提出了一种用于模型参数估计的最大似然方法。仿真实验证明了该方法的有效性。提供了在德国地区高血压患病率估算中的应用。提出了一种用于模型参数估计的最大似然方法。仿真实验证明了该方法的有效性。提供了在德国地区高血压患病率估算中的应用。