Marginal logistic regression with a cure fraction in a cluster design: An application in dental traumatology

Main Article Content

Enrico Antônio Colosimo
Eduardo Fernandes e Silva
Juliana Vilela Bastos

Abstract

 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.

Article Details

How to Cite
Colosimo, E. A., Eduardo Fernandes e Silva, & Juliana Vilela Bastos. (2022). Marginal logistic regression with a cure fraction in a cluster design: An application in dental traumatology. Brazilian Journal of Biometrics, 40(4), 382–392. https://doi.org/10.28951/bjb.v40i4.622
Section
Articles

References

Andersen, M, Lund, A, Andreasen, J. & Andreasen, F. In vitro solubility of human pulp tissuein calcium hydroxide and sodium hypochlorite. Dental Traumatology 8,104–108 (1992).

Cario, M. C. & Nelson, B. L. Modeling and generating random vectors with arbitrary marginal distributions and correlation matrixtech. rep. (Citeseer, 1997).

Coste, S. C., e Silva, E. F., Santos, L. C. M., Ferreira, D. A. B., de Souza Côrtes, M. I., Colosimo,E. A. & Bastos, J. V. Survival of replanted permanent teeth after traumatic avulsion. Journal of Endodontics 46, 370–375 (2020).

Dempster, A. P.et al.Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society: Series B (Methodological) 39,1–22 (1977).

Diop, A.et al.Maximum likelihood estimation in the logistic regression model with a curefraction. Electronic journal of statistics 5,460–483 (2011).

Follmann, D. A. & Lambert, D. Identifiability of finite mixtures of logistic regression models. Journal of Statistical Planning and Inference 27, 375–381 (1991).

Hall, D. B. Zero-inflated Poisson and binomial regression with random effects: a case study. Biometrics 56, 1030–1039 (2000).

Hall, D. B. & Zhang, Z. Marginal models for zero inflated clustered data. Statistical Modelling 4,161–180 (2004).

Kelley, M. E. & Anderson, S. J. Zero inflation in ordinal data: incorporating susceptibility to response through the use of a mixture model. Statistics in medicine 27, 3674–3688 (2008).

Li, S. T. & Hammond, J. L. Generation of pseudorandom numbers with specified univariate distributions and correlation coefficients. IEEE Transactions on Systems, Man, and Cybernetics, 557–561 (1975).

Louis, T. A. Finding the observed information matrix when using the EM algorithm. Journalof the Royal Statistical Society: Series B (Methodological)44,226–233 (1982).

Sy, J. & Taylor, J. Standard errors for the Cox proportional hazards cure model. Mathematical and computer modelling 33, 1237–1251 (2001).

Touloumis, A. Simulating Correlated Binary and Multinomial Responses under Marginal Model Specification: The SimCorMultRes Package. The R Journal 8, 79–91. https://journal.r-project.org/archive/2016/RJ-2016-034/index.html (2016).

Xu, S. Generalized estimating equation based zero-inflated models with application to exam-ining the relationship between dental caries and fluoride exposures. (2013).

Yamaguchi, M.et al. Preliminary criteria for classification of adult Still’s disease. The Journal of rheumatology 19, 424 (1992).