癌 is a phono-semantic compound: semantic 疒 'to be ill' + phonetic 嵒 (yán); 嵒 (yán) is a variant of 岩 (yán).

In Mandarin, this character used to be pronounced identically as 岩 (yán). Its pronunciation was changed to ái in December 1962 to avoid the homophony between 癌 (yán, “cancer”) and 炎 (yán, “inflammation”) (compare 肺炎 (fèiyán, “pneumonia”) and 肺癌 (fèi'ái, “lung cancer”)). The new pronunciation ái stems from dialectal pronunciations of 岩 (“rock; cliff”) /ŋai/, influenced by 崖 (yá, yái, “cliff”).

https://humanum.arts.cuhk.edu.hk/Lexis/lexi-mf/search.php?word=%E7%99%8C