SEATTLE — When Andrew Farnum used to speak about work with his wife, a program officer focused on global health at the Bill & Melinda Gates Foundation, he would ask himself how he might use his background in finance to have an impact on global health issues. Farnum started out at Goldman Sachs, then moved to a group at TPG Capital focused on investments in developing countries, then joined the Children’s Investment Fund Foundation, which was started by a billionaire hedge fund manager focused on combating disease and reducing child mortality.