In component-based safety-critical systems, when a system safety property is violated, it is necessary to analyze which components are the cause. Given a system execution trace that exhibits component faults leading to a property violation, our causality analysis formalizes a notion of counterfactual reasoning ("what would the system behavior be if a component had been correct?") and algorithmically derives such alternative system behaviors, without re-executing the system itself. In this paper, we show that we can improve precision of the analysis if 1) we can emulate execution of components instead of relying on their contracts, and 2) take into consideration input/output dependencies between components to avoid blaming components for faults induced by other components. We demonstrate the utility of the extended analysis with a case study for a closed-loop patient-controlled analgesia system.