# Registered secondary-analysis plan: missing responses and long-term recovery in PRINCIPLE

Question: What do the published aggregate counts alone identify about the direction of the unadjusted long-term fully-recovered proportion difference between ivermectin and concurrent eligible usual care, and which assumptions about unavailable binary responses change that direction?

This is a targeted secondary sensitivity analysis of Table 3 of Butler et al., Journal of Infection 2024, DOI 10.1016/j.jinf.2024.106130, using the public Europe PMC fullTextXML for PMC10981761. The paper, outcome definitions, all six pairs of counts and its reported adjusted effects have already been read. Registration freezes the calculations before they run. It is not outcome-blind, a prospective trial, a systematic review, or a replication of the original adjusted mixed model. Searches on October 16, 2026 found the original trial and general missing-outcome methodology; the ledger search found the earlier hospitalization audit but no long-COVID claim. Search absence does not establish novelty. The value sought is a transparent exact sensitivity map for these specific reported margins.

Primary endpoint: feeling fully recovered at the nominal six-month follow-up in the primary long-term analysis population. Include the nominal three- and twelve-month outcomes as secondary checks, and all three corresponding rows from the paper's larger sensitivity population. Each time point is analyzed separately, without summing participants or combining correlated follow-up outcomes. The primary long-term cohort is conditional on participation in the acute primary analysis; the larger cohort is kept separate. Both use concurrent eligible controls. These outcomes are patient-reported recovery, not clinician-diagnosed long COVID, hospitalization, or mortality. The source describes broad response windows, so nominal month labels do not imply exact follow-up dates.

Use the factual counts and denominator totals in the table: primary cohort N_T=2157, N_C=1806; sensitivity cohort N_T=2250, N_C=1869. For each row retain recovered e, observed response n, and cohort N separately. Fail unless 0<=e<=n<=N and all cells match an independent reading of the pinned XML table. Preserve source URL, retrieval date, byte length and SHA-256. Do not distribute the article text or figures; the bundle contains only extracted facts, original code and prose. No participant-level data are accessed.

Define unavailable count m=N-n. For hypothetical binary record completions x_T in {0,...,m_T} and x_C in {0,...,m_C}, compute D=(e_T+x_T)/N_T-(e_C+x_C)/N_C. This is a finite-table completion contrast, not an identified causal effect or recovered intention-to-treat estimand. It assumes the unspecified records can be given a binary recovery code; the source does not supply reasons for unavailable responses or participant-level information about death/intercurrent events. The bounds condition only on the supplied margins and do not assert that every extreme completion is clinically possible.

Report observed-response recovery proportions and unadjusted difference, availability proportions, the exact minimum/maximum of D under unrestricted completions, and whether the resulting identification interval contains zero. These bounds are not confidence intervals and do not quantify sampling uncertainty. Preserve exact rational values for checks and rounded values for reading.

For a transparent continuous-rate sensitivity map, write D(q_T,q_C)=(e_T+m_T*q_T)/N_T-(e_C+m_C*q_C)/N_C, with q in [0,1]. This interpolation represents hypothetical proportions, not observed people or fitted missingness probabilities. Report the range when both arms share any common q; do not call common q 'missing at random'. Report the complete null frontier q_C(q_T), its feasible domain, and a declared anchor: q_C=e_C/n_C, with the tipping q_T solving D=0. Report q_C-q_T in percentage points, and whether the anchor tipping value is feasible. Separately enumerate every integer x_T and compute the smallest integer x_C making D<=0, preserving infeasible rows. No p-value threshold is called a tipping point here; it is only reversal of the crude point-estimate direction.

Validate extrema and all integer thresholds by independent exact cross-multiplication, exhaustive small-population fixtures and all actual integer completion pairs where feasible. Check arm reversal, endpoints, monotonicity, no-missing fixtures and impossible-input guards. Do not import the main calculation into the independent validator. Record all six rows whether or not they support a common pattern.

Interpretation: unequal response availability alone does not prove bias. A feasible reversal does not show that its missingness mechanism occurred or is plausible. Conversely, equal response rates do not identify missing outcomes. This analysis neither reproduces nor refutes the trial's covariate-adjusted repeated-measures model. It cannot address open-label reporting effects, individual trajectories, general clinical efficacy, treatment advice or biological mechanism. Any new endpoint or analysis beyond this plan is labeled exploratory in deviations.json.