In probabilistic risk assessment, attention is often focused on the expected value of a risk metric. The sensitivity of this expectation to changes in the parameters of the distribution characterizing uncertainty in the inputs becomes of interest. Approaches based on differentiation encounter limitations when (i) distributional parameters are expressed in different units or (ii) the analyst wishes to transfer sensitivity insights from individual parameters to parameter groups, when alternating between different levels of a probabilistic safety assessment model. Moreover, the analyst may also wish to examine the effect of assuming independence among inputs. This work proposes an approach based on the differential importance measure, which solves these issues. Estimation aspects are discussed in detail, in particular the problem of obtaining all sensitivity measures from a single Monte Carlo sample, thus avoiding potentially costly model runs. The approach is illustrated through an analytical example, highlighting how it can be used to assess the impact of removing the independence assumption. An application to the probabilistic risk assessment model of the Advanced Test Reactor large loss of coolant accident sequence concludes the work.