As it turns out, the parameter term_id_or_unknown can be combined with without_term_value_id to get observations which either have no value set for a specific annotation, or they have a value but it’s something other than the one specified. For example, term_id_or_unknown=17&without_term_value_id=19 calls for observations which either do not have Alive or Dead filled out (the value is null), or which do have it filled out, but it’s filled with anything other than Dead (so either Alive or Cannot be determined). That is, you can exclude only observations marked Dead, while keeping those that are null, Alive, or Cannot be determined.
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