This is a jukugo word, which usually means on'yomi readings from the kanji. Since 大 has two on'yomi readings, here's a mnemonic to help you remember which one to use:
Your local medical university really prides itself on its eagle dye (いだい). It's the only dye in the world made straight out of eagles. A bit strange for a medical university, but impressive nonetheless!
I’m studying to get into medical school.
I pretended to be a med student and snuck into med school to find a future doctor boyfriend.
I paid my tuition for med school by selling my Pokémon collection.