The concentration of radiation-induced point defects in general materials under irradiation is commonly described by the point defect kinetics equations based on rate theory. However, the parametric uncertainty in describing the rate constants of competing physical processes, such as recombination and loss to sinks, can lead to a large uncertainty in predicting the time-evolving point defect concentrations. Here, based on perturbation theory, we derive up to the third-order correction to the solution of point defect kinetics equations. This new set of equations enables a full description of continuously changing rate constants and can accurately predict the solution up to 50% deviation in these rate constants. These analyses can also be applied to reveal the sensitivity of the solution to input parameters and aggregated uncertainty from multiple rate constants.