Whilst most surgeons are reluctant to approve of running as they are concerned about being blamed for acute hardware failure, if you ask them what is the most frequent cause leading to revision surgery they will admit that it is not injuries/acute trauma/sudden failure. Rather, it is recurrent pain/progression of arthritis/degeneration of the biological interface. In the absence of large studies (a few small studies suggest that running does not result in worse outcomes of THJR at least after 5 years or longer) the next best available evidence (from larger studies) is that running does not accelerate arthritis (in fact there is a good chance it may stave it off). Biologically, mobilisation and weight bearing results in stronger bone structure/density, so to me it make sense to run. Additionally, one needs to put on the scale the long term cardiovascular benefits of running as aerobic, weight-loss exercise. I have been running more than 4,000 km on my artificial hips now, and 3 years after surgery my mobility, strength and running times are still improving (parkrun in 21:45 today, age grade 70.02%).