Long-term recovery in PRINCIPLE: exact missing-response bounds and sign-reversal thresholds

Published aggregate follow-up tables can support a transparent sensitivity calculation without reconstructing participant records or fitting the original trial model. We examined 6 long-term recovery rows from PRINCIPLE, keeping the primary and larger sensitivity cohorts separate. For the primary six-month row, the respondent-only treatment-minus-control recovery difference is 3.071 percentage points. Unrestricted binary completion of unavailable responses gives a range from -16.54 to 21.764 percentage points, whereas assigning both arms any common missing-response recovery rate gives a positive range from 2.329 to 2.896 percentage points. These are conditional bounds, not confidence intervals. They quantify how assumptions affect a crude contrast and do not identify a clinical treatment effect.