Global Sensitivity Analysis (GSA) is an important tool to better understand the behavior of black box models. Among the numerous methods for GSA, variance-based approaches have received much attention. Only a few papers focus on Quantile Oriented Sensitivity Analysis (QOSA), which can help in analysing the behavior of the response at different quantile levels. Moreover, existing QOSA estimation methods have flaws: bias when input variables are dependent, loss of accuracy and efficiency as input space dimension increases. In this paper, we propose a new estimation procedure of QOSA indices based on the notion of projected random forest, with the initial random forest built from a criterion designed for quantiles: the pinball loss also known as quantile loss.