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Logistic regression model is the first option to deal with binary outcomes in cross-sectional health studies. However, some conditions, such as the presence of a cure fraction, characterized when an unknown portion of the population is no longer at risk of developing the event of interest, can lead to the non-adequacy of the model. Therefore, the presence of a cure fraction requires an extension in the standard form of the logistic regression model or the use of an alternative one. The present work aims to identify risk factors for the presence of External Inflammatory Root Resorption (EIRR) using a real application. The data set consisted in replanted permanent teeth referred to treatment at the Dental Trauma Clinic of the School of Dentistry from the Federal University of Minas Gerais (DTC-SD-UFMG) after emergency care at the Metropolitan Hospital Odilon Beherns in Belo Horizonte, Brazil. A logistic regression type model is considered to study the association between clinical and radiographic factors and the presence/absence of EIRR, measured radiographically at the first patient appointment at DTC-SD-UFMG. Considering that EIRR is only expected in those cases where the root canal become infected following pulp necrosis, those teeth whose pulp healing is favorable are not at risk of developing EIRR. However, pulpal status usually can only be defined in the long term, such that information is not available at the time of data collection, characterizing the presence of a latent cure fraction. Moreover, in the present sample some patients contributed with more than one replanted tooth, forming clusters of correlated measurements. In the present work we followed the methodology proposed by Hall & Zhang (2004) in which they used an adaption of the EM (expectation-maximization) algorithm, called ES (Expectation-Solution) algorithm combined with GEE (Generalized Estimation Equations) to accommodate the cluster (individual) multivariate response in a logistic cure fraction model.
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