Missing data that are missing at random and not supposed to be imputed

I’m using Stan to run an item response tree model. There are some data missing at random that are supposed to be missing instead of imputed given the research assumption. In this case, can I just specify the number of missing data, the number of observed data, and rows corresponding to those observed data in the data section, but not treat missing data as part of unknown parameters or model them in the model section? That is, I just tell Stan that there are some missing data, but I won’t do any things (such as imputation or modeling) to those missing data.

Could you please let me know if this model estimation is legit? Thank you!

A long time ago I was taught that if data is missing completely at random, then a complete case analysis will be unbiased: When is complete case analysis unbiased? – The Stats Geek

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