<p>This paper centers on estimating the turning point (or mode) of the hazard function in survival studies, particularly in health-related research. The hazard function represents the instantaneous risk of an event, like death, and it often follows a unimodal pattern in these contexts. Identifying the turning point is important because it reveals when the risk is highest, which helps in developing more targeted treatment plans and determining the best times for interventions. Additionally, considering that some patients may be cured, estimating cure rates provides a fuller picture of survival outcomes. To tackle these issues, the paper introduces a cure rate regression model based on the Dagum distribution. A key feature of this model is that it reparameterizes the Dagum distribution to include the mode of the hazard function, which is linked to covariates through a logarithmic function. For estimating the proportion of cured patients, a logistic regression model is used to capture the effects of different covariates. The parameters of the model are estimated using the maximum likelihood method, and its performance is tested through extensive Monte Carlo simulations. The paper also illustrates the practical benefits of the model by applying it to a dataset on COVID-19 in maternal populations.</p>