= Solution
Because the measurement can cross the threshold in both directions while the model declares dementia irreversible, one needs the diagnostic rule's sensitivity
$$
\mathbb P(X<10\mid\text{true dementia})
$$
and specificity
$$
\mathbb P(X\geq10\mid\text{no true dementia}).
$$
These quantify false negative and false positive state classifications and permit a hidden-state or misclassification model instead of treating every threshold crossing as the true irreversible onset.
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