The box containing the first 4,875 COVID-19 vaccine doses to arrive at MD Anderson was much larger than I’d expected. It only had five small trays of vials inside, but with all of the insulation and dry ice needed to keep them frozen, it weighed about 80 pounds.

I remember being very nervous as the delivery truck backed up to our loading dock on Dec. 14, 2020. MD Anderson was the first hospital in the Texas Medical Center to get...