We describe a first principles methodology to evaluate statistically the hazard related to non-stationary seismic sources like induced seismicity. We use time-dependent Gutenberg-Richter parameters, which leads to a time-varying rate of earthquakes. This is achieved by deriving analytic expressions for occurrence rates which are verified using Monte Carlo simulations. We show two examples: (1) a synthetic case with two seismic sources (background and induced seismicity); and (2) a recent case of induced seismicity, the Horn River Basin, Northeast British Columbia. In both cases, the statistics from the Monte Carlo simulations agree with the analytical quantities. The results show that induced seismicity can change seismic hazard rates but that this greatly depends on both the duration and intensity of the non-stationary sequence as well as the chosen evaluation period. Further studies will include extensions to handle spatial source distributions as well as ground motion analysis in order to generate a complete methodology for non-stationary probabilistic seismic hazard analysis.