Interval-valued variables have become very common in data analysis. Up until now, symbolic regression mostly approaches this type of data from an optimization point of view, considering neither the probabilistic aspects of the models nor the nonlinear relationships between the interval response and the interval predictors. In this article, we formulate interval-valued variables as bivariate random vectors and introduce the bivariate symbolic regression model based on the generalized linear models theory which provides much-needed exibility in practice. Important inferential aspects are investigated. Applications to synthetic and real data illustrate the usefulness of the proposed approach.

This study analyzes the factors contributing to the duration of severe oral mucositis in oncopediatric patients. A longitudinal study was conducted in the pediatric department of a cancer referral hospital between 2013 and 2017. Seventy-three patients diagnosed with cancer undergoing chemotherapy protocols were analyzed. Oral evaluations were performed using the Modified Oral Assessment Guide criteria, and the data were collected from the patients’ records. The Kaplan-Meier method was used to estimate survival curves. Most patients were males (52.1%), of mixed race (“pardo”) (49.3%), with a mean age of 7.56 years (±5.34). There was a predominance of patients diagnosed with solid tumors (52.1%), with no metastasis (86.3%), using natural product chemotherapeutics (56.2%), who had not undergone a bone marrow transplant (97.3%); amputation was observed in 35.6% of patients, while death rates were as high as 8.2%. The survival analysis estimated a mean time of 30.6 days until complete remission of severe oral mucositis. The regression analysis showed that patients over 10 years old had a median mucositis duration 1.4 times greater than those at the age of 10 years or younger. Patients without metastasis had a median mucositis duration 1.7 times greater than those with metastasis (p-value ≤ 0.10). Increasing age and the absence of metastasis were conditions that prolonged the duration of severe oral mucositis.

This study aimed to evaluate the factors associated with the occurrence of severe oral mucositis (SOM) in pediatric oncology patients during the chemotherapeutic treatment. This is a nested case-control to a prospective cohort that monitored 105 patients for 10 consecutive weeks after the beginning of the chemotherapy treatment. Logistic regression was used to identify the factors associated with SOM, by group of malignancy (hematologic or solid tumors) (Sig.=5%). To patients with hematologic tumors were found factors associated with SOM in two weeks of treatment: in the 6th week (increase in frequency of chemotherapy doses (OR=3.02)) and in the 7th week (female sex (OR=21.28); and increase in frequency of chemotherapy doses (OR=2.51)); and to patients with solid tumors were found factors associated with SOM in five weeks of treatment: in the 1st week (female sex (OR=14.43); age increase (OR=1.24)); in the 2nd week (Miscellany (OR=6.39)); in the 5th week (Antimetabolites (OR=17.44); Miscellany (OR=45.42); and platelets reduction (OR=1.12)); in the 6th week (creatinine increase (OR=1.63)); and in the 7th week (creatinine increase (OR=2.39)). For patients with hematologic tumors, to be female, and the increase in the frequency of chemotherapy doses increased the risk for SOM and for patients with solid tumors, to be female, the increase in age and in level blood concentration of creatinine, the reduction in number of platelets and the use of chemotherapy with miscellany and antimetabolites agents were associated with an increase in risk for occurrence of SOM.

In real problems, it is usual to have the available data presented as intervals. Therefore, different approaches have been proposed to obtain a regression model for this new type of data. In this paper, we represent the interval-valued response variable $Z=[Y_{\mathrm{L}},Y_{\mathrm{U}}]$ as a bivariate random vector and we consider the copula's theory to propose a general bivariate distribution for Z, creating a more flexible random component to the model. Inference techniques and a residual definition based on deviance are considered, as well as applications to synthetic and real data sets that demonstrate the usefulness of the proposed approach. The new method is also compared with other methods reported in the literature.