The Collinearity Problem: Implication Testing of Sclerodactyly in Systemic Sclerosis

Sclerodactyly — skin thickening and tightening of the fingers — affects approximately 83% of SSc patients and scores 4 points in the 2013 ACR/EULAR classification criteria, the single highest-scoring item. Four implications are commonly stated: that diffuse cutaneous SSc (dcSSc) subtype, anti-Scl70 antibody, high modified Rodnan Skin Score (mRSS >14), and sclerodactyly itself imply digital pitting scars. Using the PAC-bound implication testing framework (Ritschel & Claude, 2026), we evaluated these implications in a synthetic SSc cohort (n=800) calibrated to Khanna et al. (2017) and the EUSTAR database. All four implications were REJECTED — but for methodologically distinct reasons. Three implications (dcSSc, Scl70, high mRSS ⇒sclerodactyly) showed very low violation rates (0–3.6%) and received REJECTED verdicts solely because the PC algorithm could not orient causal edges between these collinear phenotypic markers of the same fibrotic process. Anti-Scl70 sclerodactyly achieved a violation rate of exactly 0.0% (PAC