Sensitivity analysis is becoming one of the key tools of systems biology. Sensitivity analysis has been used to integrate model identification and discrimination with optimal experimental design and knowledge discovery. For example, first-order sensitivity coefficients are the basis for the diagnosis of robust and fragile mechanisms and D-optimal experimental planning. However, it is not generally possible to calculate sensitivity coefficients analytically, thus numerical techniques must be used to solve the auxiliary matrix differential equation which governs the time behavior of first-order sensitivity coefficients. In this study we explore the working hypothesis that qualitative conclusions drawn from sensitivity analysis, such as those obtained by computing Overall State Sensitivity Coefficients (OSSC) to diagnose robustness and fragility, are robust to the choice of numerical solution technique. We test our working hypothesis by analyzing a mechanistic model of the human complement cascade. Complement is a key component of the immune system that destroys invading microorganisms and eliminates immune complexes. Complement consists of more than 30 plasma and cell surface proteins and is activated by three pathways, the classical, alternative and lectin pathways; in this study, we explore only the alternative activation pathway. The alternative pathway consists of complement proteins numbered C3-C9, plasma factors B, D, H and I and several regulatory proteins restraining activation. The complement model used in this study consisted of 86 differential equations and 57 protein-protein interactions, where all protein-protein and catalytic interactions were modeled using mass action kinetics. Five different numerical techniques were applied to the compute sensitivity coefficients of the complement model using 100 randomly generated parameter sets to account for parametric uncertainty; forward finite-difference, a third order fixed step-size backward difference formulation, a fifth-order variable step-size scheme (ODE15s, Matlab, The Mathworks, Natick, MA), a variational method (collocation) that employed lagragian-interpolating trial functions, and a semi-analytical method which assumed a constant Jacobian over an integration time-step. While the quantitative OSSC values varied between all methods, the qualitative conclusion drawn concerning the robustness and fragility of mechanisms in the cascade were similar between the ODE15s, the semi-analytical technique and collocation methods as determined by the Spearman rank. However, the forward-finite difference and third-order fixed step-size backward difference scheme showed qualitatively different fragility results. We hypothesize these differences follow from model stiffness. To this end, we demonstrated that particular structural motifs common to cascades such as complement can, in part, be responsible for system stiffness and that the presence of these motifs could be used to inform the choice of numerical sensitivity method.