title: An alternative classification to mixture modeling for longitudinal counts or binary measures.
abstract: Classifying patients according to longitudinal measures, or trajectory classification, has become frequent in clinical research. The k-means algorithm is increasingly used for this task in case of continuous variables with standard deviations that do not depend on the mean. One feature of count and binary data modeled by Poisson or logistic regression is that the variance depends on the mean; hence, the within-group variability changes from one group to another depending on the mean trajectory level. Mixture modeling could be used here for classification though its main purpose is to model the data. The results obtained may change according to the main objective. This article presents an extension of the k-means algorithm that takes into account the features of count and binary data by using the deviance as distance metric. This approach is justified by its analogy with the classification likelihood. Two applications are presented with binary and count data to show the differences between the classifications obtained with the usual Euclidean distance versus the deviance distance.
authors.affiliation: 1 Université de Lyon, Lyon, France.|2 Université Lyon 1, Villeurbanne, France.|3 CNRS, UMR5558, Laboratoire de Biométrie et Biologie Evolutive, Villeurbanne, France.|4 Hospices Civils de Lyon, Service de Biostatistique, Lyon, France.
authors.forename: Fabien
authors.initials: F
authors.lastname: Subtil
authors.affiliation: 1 Université de Lyon, Lyon, France.|2 Université Lyon 1, Villeurbanne, France.|3 CNRS, UMR5558, Laboratoire de Biométrie et Biologie Evolutive, Villeurbanne, France.|4 Hospices Civils de Lyon, Service de Biostatistique, Lyon, France.|5 International Chair in Mathematical Physics and Applications, Université d'Abomey-Calavi, Abomey-Calavi, Bénin.
authors.forename: Olayidé
authors.initials: O
authors.lastname: Boussari
authors.affiliation: 6 Epicentre, Paris, France.
authors.forename: Mathieu
authors.initials: M
authors.lastname: Bastard
authors.affiliation: 6 Epicentre, Paris, France.|7 UMI 233 TransVIHMI, Institut de Recherche pour le Développement, Université Montpellier 1, Montpellier, France.
authors.forename: Jean-François
authors.initials: JF
authors.lastname: Etard
authors.affiliation: 1 Université de Lyon, Lyon, France.|2 Université Lyon 1, Villeurbanne, France.|3 CNRS, UMR5558, Laboratoire de Biométrie et Biologie Evolutive, Villeurbanne, France.|4 Hospices Civils de Lyon, Service de Biostatistique, Lyon, France.
authors.forename: René
authors.initials: R
authors.lastname: Ecochard
authors.affiliation: 8 INSERM, UMR 1027, Research Unit on Perinatal Epidemiology and Childhood Disabilities, Adolescent Health, Toulouse, France.|9 Université Paul Sabatier, UMR 1027, Toulouse, France.|1 0CeRSM (EA 2931), UFR STAPS, Université de Paris Ouest-Nanterre-La Défense, France.
authors.forename: Christophe
authors.initials: C
authors.lastname: Génolini
mesh_terms: D000349:Africa; D000465:Algorithms; D000818:Animals; D000852:Anopheles; D023241:Antiretroviral Therapy, Highly Active; D015658:HIV Infections / Q000188:drug therapy; D006801:Humans; D016013:Likelihood Functions; D016015:Logistic Models; D008137:Longitudinal Studies; D011891:Rain; D012675:Senegal; D016903:Drug Monitoring
keywords: binary data; cluster analysis; count data; k-means; likelihood; longitudinal data