Regressão logística binária com fator de cura para dados em conglomerados: uma aplicação em traumatismo dentário

Abstract

Cross-sectional studies in the health area usually have a binary outcome and logistic regression is the first option to answer the researcher’s questions. However, some conditions lead to the model not being adequate, in its standard form, for the treatment of the binary outcome. The presence of a cure, that is, when we know that an unknown portion of the population is no longer at risk of developing the event of interest, is an example of this type of situation. This work was developed in the line of research "Methodology and statistics in research on dental trauma", a partnership established since 2015 between the Dental Trauma Program of the UFMG School of Dentistry (PTD FAO UFMG) and the ICEx-Statistics Department. UFMG. The researchers’ main interest was to establish risk factors for the presence of Inflammatory External Root Resorption (IRR). Logistic regression was the methodology indicated for the study of the association between clinical and radiographic factors, measured in the patient’s first consultation at the PTD FAO UFMG, and the outcome of interest, the RREI. However, RREI is only expected in those cases in which there is pulp necrosis and root canal infection, that is, teeth whose pulp healing is favorable are not at risk of developing RREI. As this definition is not possible in the initial consultation, that is, at the time of data collection, the presence of a latent cure fraction is characterized, which can lead to the inadequacy of the usual logistic model. Diop et al. (2011) claim that the binary response healing problem can be seen as a ZIB (Zero-inflated Binomial) model. Considering that in the project’s casuistry, the same individual may have more than one traumatized tooth, the project challenge was to adjust a binary logistic model with a cure factor in the presence of conglomerates. For this purpose, the methodology presented by Hall e Zhang (2004), in which the authors make the EM algorithm more flexible to accommodate more than one measurement per individual in zero-inflated models. In this work, we present the logistic regression model with latent cure factor, which has the same shape as the zero-inflated binomial. Then, we extend the model to accommodate clusters, which represent one or more teeth per patient, and, finally, we present the application of thisCross-sectional studies in the health area usually have a binary outcome and logistic regression is the first option to answer the researcher’s questions. However, some conditions lead to the model not being adequate, in its standard form, for the treatment of the binary outcome. The presence of a cure, that is, when we know that an unknown portion of the population is no longer at risk of developing the event of interest, is an example of this type of situation. This work was developed in the line of research "Methodology and statistics in research on dental trauma", a partnership established since 2015 between the Dental Trauma Program of the UFMG School of Dentistry (PTD FAO UFMG) and the ICEx-Statistics Department. UFMG. The researchers’ main interest was to establish risk factors for the presence of Inflammatory External Root Resorption (IRR). Logistic regression was the methodology indicated for the study of the association between clinical and radiographic factors, measured in the patient’s first consultation at the PTD FAO UFMG, and the outcome of interest, the RREI. However, RREI is only expected in those cases in which there is pulp necrosis and root canal infection, that is, teeth whose pulp healing is favorable are not at risk of developing RREI. As this definition is not possible in the initial consultation, that is, at the time of data collection, the presence of a latent cure fraction is characterized, which can lead to the inadequacy of the usual logistic model. Diop et al. (2011) claim that the binary response healing problem can be seen as a ZIB (Zero-inflated Binomial) model. Considering that in the project’s casuistry, the same individual may have more than one traumatized tooth, the project challenge was to adjust a binary logistic model with a cure factor in the presence of conglomerates. For this purpose, the methodology presented by Hall e Zhang (2004), in which the authors make the EM algorithm more flexible to accommodate more than one measurement per individual in zero-inflated models. In this work, we present the logistic regression model with latent cure factor, which has the same shape as the zero-inflated binomial. Then, we extend the model to accommodate clusters, which represent one or more teeth per patient, and, finally, we present the application of this methodology to analyze the case series at FO-UFMG m