Comorbid Atlas

Of 104 evaluable symptom-by-direction combinations, 23 (22.1%) place more than a quarter of their posterior mass outside the Fréchet–Hoeffding feasible region (ι > 0.25). 20 of these 23 violate the upper bound and would pass a one-sided screen unnoticed. A separate sufficiency rule (each symptom prevalence resting on at least two studies) excludes 42 combinations; the two sets overlap, so 56 fail at least one criterion and 48 are usable. Excluded combinations are omitted from the panels entirely, not clipped.

The 23/104 headline is one defensible point: across the screen's own conventions (r_min ∈ {0.01, 0.02, 0.05}, cutoff ∈ {0.15–0.50}) the infeasible count ranges from 13 to 39 of 104 (Table 6).

• Not a diagnosis, and not a general-population screening estimate — every input is a within-referred-population probability.
• The paper treats symptom-conditioned prediction as exploratory: it additionally depends on the approximation Pr(S | A,B) ≈ Pr(S | B), on λ, and on the construction of the four-symptom panel. The feasibility finding does not depend on any of these.
• λ is an unidentified sensitivity parameter, not a calibrated correction; the gap between λ=0.5 and λ=1 is a lower bound on dependence-related uncertainty.
• This client-side prototype approximates the paper's Monte Carlo propagation (M = 3,000 draws) with a closed-form log-odds calculation. Per-symptom contributions are derived from the published cumulative trajectory (Fig. 4, panel symptoms added in order of |log Λ|) and anchored to the exact published endpoints (Table 2); it reproduces the Table 3 sweep to within about one percentage point. Intermediate trajectory points are read from the figure.
• Credible intervals for partial panels are interpolated on the logit scale between the published prior interval and the published full-panel interval; they are approximate.
• Symptom absence is not modelled: the paper estimates likelihood ratios for presence only.
• Pooled estimates are dominated by self-selected surveys with self-reported comorbidity; only one included source (a claims-database cohort) has ascertainment independent of patient report.
• Hereditary alpha-tryptasemia is a candidate common cause of part of the hEDS–MCAS association; no included study reports tryptase genotype.
• Referral/collider bias is not modelled: all pooled cohorts are diagnosis-selected, so even a perfectly calibrated version of this tool would estimate risk within a referred population, not the general population.