¹Institut für Medizinische Statistik, Informatik und Datenwissenschaften (IMSID), Universitätsklinikum Jena, Jena, Germany

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Heterogeneity is a common challenge in meta-analysis, where differences in study design, populations, and measurement methods often violate the assumption of homogeneity, a violation that can substantially impact the validity, precision, and interpretation of pooled effect estimates [1], [2]. In order to address heterogeneity a bivariate linear mixed model can be used to jointly analyze estimated pairs of sensitivity (Se) and specificity (Sp) from a meta-analysis of diagnostic tests [1]. This bivariate statistical approach does not transform pairs of sensitivity and specificity of individual studies into a single indicator of diagnostic accuracy, but preserves the two-dimensional nature of the data, taking into account any correlation between the two. Chu and Cole (2006) proposed an exact binomial rendition of the bivariate mixed-effects regression model using the binomial distribution for sensitivity and specificity and a bivariate normal distribution for the corresponding random effects [3]. The assumption of a normal distribution for the random effects may be too strong. To overcome this, we propose a semiparametric mixture model based on a nonparametric distribution of the random effects which allows for flexible modeling of heterogeneity across studies, enabling the joint estimation of sensitivity and specificity. Finite mixture models, though not yet standard in meta-analysis, offer a flexible and principled framework for uncovering latent subgroups and capturing multimodal heterogeneity, as demonstrated in related work (see [4], [5]). To implement this approach in the context of diagnostic accuracy, we assume a bivariate binomial distribution for sensitivity and specificity, in the sense that marginally each of the two random variables has a binomial distribution. We then consider the corresponding likelihood to characterize the probability distribution function (pdf) of the mixture model, allowing for the joint modeling of these correlated diagnostic measures across latent subpopulations. This leads to a finite mixture of bivariate logistic regression models, which allows for the classification of the studies into latent subgroups with distinct diagnostics profiles. Model parameters are then estimated using the EM algorithm [6], from which sensitivity and specificity are obtained by applying the logit transformation to the estimated parameters. The method is presented using data from a meta-analysis investigating the diagnostic accuracy of Procalcitonin (PCT) for diagnosis of sepsis in critically ill patients [7].

The authors declare that they have no competing interests.

The authors declare that an ethics committee vote is not required.

Literatur

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