In this paper, we derive copula-based and empirical dependency models (DMs) for simulating non-independent variables, and then propose a new way for determining the distribution of the model outputs conditional on every subset of inputs. Our approach relies on equivalent representations of the model outputs using DMs, and an algorithm is provided for selecting the representations that are necessary and sufficient for deriving the distribution of the model outputs given each subset of inputs. In sensitivity analysis, the selected representations allow for assessing the main, total and interactions effects of each subset of inputs. We then introduce the first-order and total indices of every subset of inputs with the former index less than the latter. Consistent estimators of such indices are provided, including their asymptotic distributions. Analytical and numerical results are provided using single and multivariate response models.