We discuss the analysis of molecular dynamics calculations where we simulate the kinetics of the breaking and forming of hydrogen bonds in distinctly different environments: liquid water and concentrated aqueous solution of DMSO. In our analysis, we consider reactive flux correlation functions computed for a variety of specific conditions and identify rate constants for bond making and breaking in terms of the liquid's molecular dynamics. According to the proposed mechanism of hydrogen-bond kinetics, hydrogen bonds most frequently break during a process of switching allegiance with a newly formed bond replacing the broken one. Simulations reveal bond dynamics in the mixture to be significantly slower than in pure water. This is interpreted in terms of reduced likelihood of fluctuations in the hydrogen-bond network, related to the presence of free hydrogen-bonding sites, which participate in the process of switching allegiances. Implications of our analysis for future experimental work are briefly discussed.