In spite of their complex geometry, cable in conduit conductors (CICCs) have to be modelled with a rather simple description for coupling losses when operating in transient regime. Difficulties to predict ac losses in superconducting cable have already been shown in previous models such as the new analytical one developed at CEA named COLISEUM (after Coupling Losses analytical Staged cables Unified Model) and CEA heuristic one multi partial shielding (MPAS). In this paper, we present a parametric analysis for coupling losses in superconducting strands and cables subjected to time-varying transverse magnetic field by using the recently developed COLISEUM. This analysis aims at understanding trends of the model in a broad domain of investigation and their associated limits of application. We show that for a wide range of parameters, it is possible to reduce this model of four time constants to a smaller subset. This reduction brings simplifications to the current COLISEUM and enables it to be consistent with the number of time constants considered in the MPAS model from CEA.