Abstract

In this work, we address the problem of assessing prognostic factors on the specific survival times of pregnant and postpartum women hospitalized with severe acute respiratory syndrome confirmed by COVID-19 when cure is a possibility, where there is also the interest in explaining the factors' impact on different quantiles of the survival times and in estimating the unobservable heterogeneity given by considering the prognostic factors that are not observed (as smoke status). Besides, the hazard function presents a unimodal form. To this end, we propose a quantile regression model for survival data in the presence of long-term survivors based on the defective Dagum distribution model with a power variance function (PVF) frailty term introduced in the hazard function to control for unobservable heterogeneity in patient populations, which is conveniently reparametrized in terms of the q-th quantile and then linked to covariates via a logarithm link function. We consider Markov Chain Monte Carlo (MCMC) methods to develop a Bayesian analysis in the proposed model and we evaluate its performance through a Monte Carlo simulation study. This study is part of the Brazilian Obstetric Observatory, a multidisciplinary project that aims to monitor and analyze public data from Brazil in order to disseminate relevant information in the area of maternal and child health.