The stronger the electric power, district heating and gas system are linked in an integrated energy system (IES) the larger their flexibility potential but also their complexity. To ensure a secure system operation, the effect of a coupling unit's power change on the overall system state must be analyzed before the power change is carried out. Otherwise, coupling units can unintentionally cause limit violations in one energy system. Currently, for such analyses a power flow calculation must be performed, which is computational expensive and timeconsuming. This paper presents sensitivity factors extending Power Transfer Distribution Factors from electric power system analysis to IES. The sensitivity factors include the dynamic behavior of district heating and gas systems as we derive the sensitivity factors from a joined quasi-steady-state power flow calculation. In two case studies we profoundly test the applicability of the IES sensitivity factors, their accuracy, and limitations. We show that the sensitivity factors are on average ten times faster in estimating a new system state after a unit's power change compared to a power flow calculation. Also, the sensitivity factors can provide good estimates and have a higher accuracy than sensitivity factors which are derived from a steadystate power flow calculation.