Cox model and decision trees: an application to breast cancer data.

Objective: To evaluate, using semiparametric methodologies of survival analysis, the relationship between covariates and time to death of patients with breast cancer, as well as the determination discriminatory power in the conditional inference tree of patients who had cancer. Methods: A retrospective cohort study was conducted using data collected from medical records of women who had breast cancer and underwent treatment between 2005 and 2015 at the Hospital da Fundação de Assistencial da Paraíba in Campina Grande, State of Paraiba, Brazil. Survival curves were estimated using the Kaplan-Meier method, Cox regression, and conditional decision tree. Results: Women with triple-negative molecular subtypes had a shorter survival time compared to women with positive hormone receptors. The addition of hormone therapy reduced the risk of a patient dying by 5.5%, and the risk of a HER2-positive patient dying was 34.5% lower compared to those who were negative for this gene. Patients undergoing hormone therapy had a median survival time of 4 753 days. Conclusions: This paper shows a favorable scenario for the use of immunotherapy for patients with HER2 overexpression. Further studies could assess the effectiveness of immunotherapy in patients with other conditions, to favor the prognosis and better quality of life for the patient.

Modeling hormesis using multivariate nonlinear regression in plant biology: A comprehensive approach to understanding dose-response relationships.

For over a century, ecotoxicological studies have reported the occurrence of hormesis as a significant phenomenon in many areas of science. In plant biology, hormesis research focuses on measuring morphological, physiological, biochemical, and productivity changes in plants exposed to low doses of herbicides. These studies involve multiple features that are often correlated. However, the multivariate aspect and interdependencies among components of a plant system are not considered in the adopted modeling framework. Therefore, a multivariate nonlinear modeling approach for hormesis is proposed, where information regarding correlations among response variables is taken into account through a variance-covariance matrix obtained from univariate residuals. The proposed methodology is evaluated through a Monte Carlo simulation study and an application to experimental data from safflower (Carthamus tinctorius L.) cultivation. In the simulation study, the multivariate model outperformed the univariate models, exhibiting higher precision, lower bias, and greater accuracy in parameter estimation. These results were also confirmed in the analysis of the experimental data. Using the delta method, mean doses of interest can be derived along with their associated standard errors. This is the first study to address hormesis in a multivariate context, allowing for a better understanding of the biphasic dose-response relationships by considering the interrelationships among various measured characteristics in the plant system, leading to more precise parameter estimates.

Cox model and decision trees: an application to breast cancer data / El modelo de regresión de Cox y los árboles de decisiones: su aplicación a los datos sobre cáncer de mama / Modelo de Cox e árvores de decisão: utilização com dados de câncer de mama

ABSTRACT Objective. To evaluate, using semiparametric methodologies of survival analysis, the relationship between covariates and time to death of patients with breast cancer, as well as the determination discriminatory power in the conditional inference tree of patients who had cancer. Methods. A retrospective cohort study was conducted using data collected from medical records of women who had breast cancer and underwent treatment between 2005 and 2015 at the Hospital da Fundação de Assistencial da Paraíba in Campina Grande, State of Paraiba, Brazil. Survival curves were estimated using the Kaplan-Meier method, Cox regression, and conditional decision tree. Results. Women with triple-negative molecular subtypes had a shorter survival time compared to women with positive hormone receptors. The addition of hormone therapy reduced the risk of a patient dying by 5.5%, and the risk of a HER2-positive patient dying was 34.5% lower compared to those who were negative for this gene. Patients undergoing hormone therapy had a median survival time of 4 753 days. Conclusions. This paper shows a favorable scenario for the use of immunotherapy for patients with HER2 overexpression. Further studies could assess the effectiveness of immunotherapy in patients with other conditions, to favor the prognosis and better quality of life for the patient.

RESUMEN Objetivo. Evaluar, mediante métodos semiparamétricos del análisis de supervivencia, la relación entre las covariables y el tiempo hasta la muerte de las pacientes con cáncer de mama, así como la determinación del poder discriminatorio en el árbol de inferencia condicional de las pacientes con cáncer. Métodos. Se llevó a cabo un estudio retrospectivo de cohortes con datos recogidos de los expedientes médicos de mujeres con cáncer de mama que recibieron tratamiento entre los años 2005 y 2015 en el Hospital da Fundação de Assistencial da Paraíba en Campina Grande, en el estado de Paraíba (Brasil). Se calcularon las curvas de supervivencia mediante el método Kaplan-Meier, el modelo de regresión de Cox y un árbol de decisiones condicionales. Resultados. Las mujeres con subtipos moleculares triple negativos tuvieron un período de supervivencia más corto en comparación con las mujeres con receptores hormonales positivos. La adición del tratamiento hormonal redujo en 5,5 % el riesgo de muerte de la paciente y en un 34,5% el riesgo de muerte de pacientes con cáncer HER2-positivo en comparación con las pacientes negativas para este gen. Las pacientes en tratamiento hormonal tuvieron un tiempo medio de supervivencia de 4 753 días. Conclusiones. Este estudio muestra un escenario favorable para el uso de la inmunoterapia en las pacientes con sobreexpresión del HER2. En futuros estudios se podría evaluar la eficacia de la inmunoterapia en pacientes con otras enfermedades, con el fin de favorecer el pronóstico y mejorar la calidad de vida de la paciente.

RESUMO Objetivo. Avaliar, por meio de métodos semiparamétricos de análise de sobrevida, a relação entre covariáveis e tempo até a morte em pacientes com câncer de mama e determinar o poder discriminatório na árvore de inferência condicional em pacientes que tiveram câncer. Métodos. Estudo de coorte retrospectivo realizado a partir de dados coletados de prontuários médicos de mulheres com câncer de mama, tratadas entre 2005 e 2015 no Hospital da Fundação Assistencial da Paraíba em Campina Grande, no estado da Paraíba, Brasil. As curvas de sobrevida foram estimadas pelo método de Kaplan-Meier, regressão de Cox e árvore de decisão condicional. Resultados. As pacientes com subtipos moleculares de tumor triplo-negativo tiveram uma sobrevida menor em comparação com as que apresentavam tumor com receptores hormonais. O acréscimo de hormonioterapia reduziu o risco de morte em 5,5%. O risco de morte foi 34,5% menor em pacientes com HER2+ quando comparadas às que tinham tumores sem a expressão desse gene. A mediana de sobrevida das pacientes tratadas com hormonioterapia foi de 4 753 dias. Conclusões. A presente análise revela um cenário favorável para o uso de imunoterapia em pacientes com superexpressão de HER2. Outros estudos devem ser realizados para avaliar a eficácia da imunoterapia em outras doenças e os fatores que favorecem o prognóstico e melhoram a qualidade de vida dessas pessoas.