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$$\ell _2$$ ℓ 2 -penalized approximate likelihood inference in logit mixed models for regional prevalence estimation under covariate rank-deficiency
Metrika ( IF 0.7 ) Pub Date : 2021-08-17 , DOI: 10.1007/s00184-021-00837-y
Joscha Krause 1 , Jan Pablo Burgard 1 , Domingo Morales 2
Affiliation  

Regional prevalence estimation requires the use of suitable statistical methods on epidemiologic data with substantial local detail. Small area estimation with medical treatment records as covariates marks a promising combination for this purpose. However, medical routine data often has strong internal correlation due to diagnosis-related grouping in the records. Depending on the strength of the correlation, the space spanned by the covariates can become rank-deficient. In this case, prevalence estimates suffer from unacceptable uncertainty as the individual contributions of the covariates to the model cannot be identified properly. We propose an area-level logit mixed model for regional prevalence estimation with a new fitting algorithm to solve this problem. We extend the Laplace approximation to the log-likelihood by an \(\ell _2\)-penalty in order to stabilize the estimation process in the presence of covariate rank-deficiency. Empirical best predictors under the model and a parametric bootstrap for mean squared error estimation are presented. A Monte Carlo simulation study is conducted to evaluate the properties of our methodology in a controlled environment. We further provide an empirical application where the district-level prevalence of multiple sclerosis in Germany is estimated using health insurance records.



中文翻译:

$$\ell _2$$ ℓ 2 - 在协变量秩亏条件下用于区域流行率估计的 logit 混合模型中的惩罚近似似然推断

区域流行率估计需要对具有大量局部细节的流行病学数据使用合适的统计方法。以医疗记录作为协变量的小区域估计标志着为此目的的有希望的组合。然而,由于记录中的诊断相关分组,医疗常规数据通常具有很强的内部相关性。根据相关性的强度,协变量跨越的空间可能会出现秩亏。在这种情况下,流行率估计存在不可接受的不确定性,因为无法正确识别协变量对模型的个体贡献。我们提出了一种区域级 logit 混合模型用于区域流行度估计,并使用新的拟合算法来解决这个问题。我们将拉普拉斯近似扩展到对数似然\(\ell _2\) -惩罚,以便在存在协变量秩不足的情况下稳定估计过程。介绍了模型下的经验最佳预测器和均方误差估计的参数引导程序。进行蒙特卡罗模拟研究以评估我们的方法在受控环境中的特性。我们进一步提供了一个实证应用,其中使用健康保险记录估计德国多发性硬化症的地区级患病率。

更新日期:2021-08-19
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