In this paper, we propose a defective model induced by a frailty term for modeling the proportion of cured. Unlike most of the cure rate models, defective models have advantage of modeling the cure rate without adding any extra parameter in model. The introduction of an unobserved heterogeneity among individuals has bring advantages for the estimated model. The influence of unobserved covariates is incorporated using a proportional hazard model. The frailty term assumed to follow a gamma distribution is introduced on the hazard rate to control the unobservable heterogeneity of the patients. We assume that the baseline distribution follows a Gompertz and inverse Gaussian defective distributions. Thus we propose and discuss two defective distributions: the defective gamma-Gompertz and gamma-inverse Gaussian regression models. Simulation studies are performed to verify the asymptotic properties of the maximum likelihood estimator. Lastly, in order to illustrate the proposed model, we present three applications in real data sets, in which one of them we are using for the first time, related to a study about breast cancer in the A.C.Camargo Cancer Center, São Paulo, Brazil.

To analyze the influence of lying in prone position on a specially designed stretcher on the maternal-fetal hemodynamic parameters and comfort of pregnant women. A randomized, controlled trial with 33 pregnant women divided into 2 groups: pregnant group sequence 1 and pregnant group sequence 2. The order of positions used in sequence 1 was Fowler's position, prone position, supine position, left lateral, Fowler's position 2, supine position 2, prone position 2 and left lateral 2. The order of positions used in sequence 2 was Fowler's position, prone position, left lateral, supine position, Fowler's position 2, left lateral 2, prone position 2 and supine position 2. Each woman remained in each position for 6 minutes. For the statistical analyses, we used Wilcoxon's test for 2 paired samples when comparing the prone position with the other positions. The variables are presented in graphs showing the means and 95% confidence intervals. Trial Registration: Clinical Trial No. ISRCTN41359519. All the parameters were within the standards of normality. There were no differences between positions in terms of maternal heart rate, diastolic blood pressure, oxygen saturation and fetal heart rate. However, there were significant decreases in respiratory rate and systolic blood pressure in prone position 2 compared with left lateral 2. There was an increase in oxygen saturation in prone position compared with Fowler's position and supine position 2 in both sequences. All the women reported feeling comfortable in the prone position. The prone position was considered safe and comfortable and could be advantageous for improving oxygen saturation and reducing the systolic blood pressure and respiratory rate.

The coronavirus disease 2019 (COVID-19) pandemic has had deleterious effects among the obstetric population. Pregnant and postpartum women constitute a high-risk group for severe COVID-19. Vaccination reduces the risk of infection, but it is not known whether women who become infected despite vaccination have a milder course of disease than those who had not been vaccinated. This retrospective cohort study evaluated whether vaccination reduces the severity of COVID-19 infection, as measured by severe maternal morbidity and mortality among hospitalized pregnant and postpartum individuals. A total of 2284 pregnant and postpartum women hospitalized with severe COVID-19 were included. Those who did and who did not receive COVID-19 vaccination were compared. The rates of intensive care unit admission, intubation, and mortality were significantly lower among subjects in the vaccinated group (p < 0.001, p < 0.001 and p < 0.001, respectively). The numbers of patients who needed to be vaccinated to avoid one case of intensive care unit admission, intubation, or death due to COVID-19 were 7, 7, and 9, respectively. The COVID-19 vaccine offers protective effects against intensive care unit admission, intubation, and death in hospitalized pregnant and postpartum women with severe SARS-CoV-2-induced SARS.