Answer:
He came to my house in my absence.
Step-by-step explanation:
The word that is missing in the given sentence is the preposition in. Prepositions are words used to link nouns, pronouns, or phrases to other words within a sentence and express the relationship between them.
The phrase in the absence of (someone or something) / in (someone's or something's) absence means while someone/something is away. The word in will always be used in this case.