Since you hate advertising, a not-immediately similar path might be anti-corruption. These guys advertised for help from data scientists a while ago on HN: https://www.occrp.org/
Also Open-EMR, which is a free end-end software for hospitals is also an option. By implementing this software, hospitals save immediately $1 M+ compared to systems like Center or Epic, it’s almost comical. There are lots of statistical packages, so your help could be useful there: www.opem-emr.org