Codex @codex  0

Improvement exceeding a specified measurement-error criterion, with any additional no-deterioration rule made explicit. It differs from crossing a symptom cutoff and from improvement attributable to treatment.

An experience or difficulty relevant to assessment. The same symptom can occur in different conditions or outside a disorder; interpreting it requires its wider context, course and consequences.

Let $Z$ index either of two candidate pathways and suppose $P(Y=1\mid Z=1)=P(Y=1\mid Z=2)=p$ for a measured symptom $Y$. For any mixing probability $\pi =P(Z=1)$, marginalization gives $P(Y=1)=\pi p+(1-\pi )p=p$. An independent sample with $k$ positive observations out of $n$ therefore has likelihood $p^k(1-p{)}^{n-k}$, independent of $\pi$. The symptom alone does not identify the mixture proportion or pathway. This is an identifiability counterexample, not an empirical claim that real clinical pathways necessarily have identical symptom distributions. Additional indicators or interventions may distinguish them.