Abstract
The present study presents binary data modeling regarding 1.6% of neonatal deaths in 3,448 newborns from an epidemiological and observational study with a cross-sectional design, involving the retrospective analysis of 4,293 medical records of high-risk pregnant women followed in a gestational outpatient clinic from September 2012 to September 2017. Different symmetric and asymmetric link functions were considered by means of Bayesian inference. The support of more accurate inferences regarding the parameters of the model will provide biological interpretations that are more reliable and consistent with the reality. The model that presented, significantly, the lowest value for the deviance information criterion (DIC = 398.8), was the binomial with power logit (PL) link function, whose median posterior value estimated and significant for the parameter asymmetry was l = 0.25 (0.14;1.17). This significance is observed in all other models of the power family, however with very different values and significantly higher DIC values, indicating less parsimonious models. The Bayesian methodology proved to be flexible. Additionally, the results show that such model shows an accuracy = 97.4% and area under the ROC curve AUC = 89.4% in the prediction of neonatal deaths based on the weight of children at birth. Specifically, for 2.500g, a value predicted in the medical literature for low weight, the model predicts a probability of 1.43%.
Highlights
Mathematical models that seek to relate variables from biological events are commonly used in different areas of knowledge for the adjustment of observed data
After analysis of convergence in the chains and tests of adherence to the binomial distribution of HosmerLemeshow (H-L), we observed in all the models analyzed negative and significant values (0 ⊄ HPD95%) for β1, parameter that influences the rate of increase/decrease in probability of occurrence of the event of interest, death as a function of the weight (g) of newborns
The PL and PCLL models presented significantly the lowest DIC's (398.8 and 400.7, respectively), with processing times 48.5 and 75.9 minutes, respectively, leading to the choice of the model with a power logit link function (p-value H-L = 0.998 and a good fit), whose estimated value for the asymmetry parameter was = 0.25 (0.14;1.17) and significant, since the zero value is not contained in its respective HPD95% range
Summary
Mathematical models that seek to relate variables from biological events are commonly used in different areas of knowledge for the adjustment of observed data. Regression models with linear or nonlinear predictors, whose parameters provide biological explanations, are of greater interest. Among the situations of data analysis in which the answers, being dichotomic (success '1' and failure '0'), besides the presence of explanatory (co)variable(s), a binomial regression model is the proper choice. The uncritical choice of an appropriate link function may cause differences in the model settings, as well as in decision-making related to the research objective. The method of estimation of the parameters is an important point to be considered, since each one has its assumptions that allow or not a greater flexibility in the modeling in the data analysis
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