Archimedean Copulas: A Useful Approach in Biomedical Data—A Review with an Application in Pediatrics

Giulia Risca, Stefania Galimberti, Paola Rebora, Alessandro Cattoni, Maria Grazia Valsecchi and Giulia Capitoli ()
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Giulia Risca: Bicocca Bioinformatics Biostatistics and Bioimaging Centre-B4, School of Medicine and Surgery, University of Milano-Bicocca, 20900 Monza, Italy
Stefania Galimberti: Bicocca Bioinformatics Biostatistics and Bioimaging Centre-B4, School of Medicine and Surgery, University of Milano-Bicocca, 20900 Monza, Italy
Paola Rebora: Bicocca Bioinformatics Biostatistics and Bioimaging Centre-B4, School of Medicine and Surgery, University of Milano-Bicocca, 20900 Monza, Italy
Alessandro Cattoni: Pediatrics, Fondazione IRCCS San Gerardo dei Tintori, 20900 Monza, Italy
Maria Grazia Valsecchi: Bicocca Bioinformatics Biostatistics and Bioimaging Centre-B4, School of Medicine and Surgery, University of Milano-Bicocca, 20900 Monza, Italy
Giulia Capitoli: Bicocca Bioinformatics Biostatistics and Bioimaging Centre-B4, School of Medicine and Surgery, University of Milano-Bicocca, 20900 Monza, Italy

Stats, 2025, vol. 8, issue 3, 1-19

Abstract: Many applications in health research involve the analysis of multivariate distributions of random variables. In this paper, we review the basic theory of copulas to illustrate their advantages in deriving a joint distribution from given marginal distributions, with a specific focus on bivariate cases. Particular attention is given to the Archimedean family of copulas, which includes widely used functions such as Clayton and Gumbel–Hougaard, characterized by a single association parameter and a relatively simple structure. This work differs from previous reviews by providing a focused overview of applied studies in biomedical research that have employed Archimedean copulas, due to their flexibility in modeling a wide range of dependence structures. Their ease of use and ability to accommodate rotated forms make them suitable for various biomedical applications, including those involving survival data. We briefly present the most commonly used methods for estimation and model selection of copula’s functions, with the purpose of introducing these tools within the broader framework. Several recent examples in the health literature, and an original example of a pediatric study, demonstrate the applicability of Archimedean copulas and suggest that this approach, although still not widely adopted, can be useful in many biomedical research settings.

Keywords: copula model; Archimedean family; clinical research; dependence structure; joint distribution; surrogate endpoint (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2025
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