$$\ell _2$$ ℓ 2 -penalized approximate likelihood inference in logit mixed models for regional prevalence estimation under covariate rank-deficiency

Joscha Krause (), Jan Pablo Burgard and Domingo Morales
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Joscha Krause: Trier University
Jan Pablo Burgard: Trier University
Domingo Morales: University Miguel Hernández de Elche

Metrika: International Journal for Theoretical and Applied Statistics, 2022, vol. 85, issue 4, No 3, 459-489

Abstract: Abstract 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 $$\ell _2$$ ℓ 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.

Keywords: Generalized linear mixed models; Laplace approximation; Multiple sclerosis; Prevalence mapping; Small area estimation (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s00184-021-00837-y

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