Measurement error, not aggregation, limits symmetry-weighted indices of mandibular kinematics: a simulation study

Simulation code, configuration files, and analyses supporting the article: "Measurement error, not aggregation, limits symmetry-weighted indices of mandibular kinematics: a simulation study". Abstract: Objective: To characterise the measurement properties of a composite index that weights mandibular range of motion by a left-to-right symmetry term, a construction transferred from gait analysis and obtainable from the standard clinical examination. Design: Monte Carlo parameter sweep. Restriction (0.20 to 1.00) and true excursive symmetry (0.10 to 1.00) were swept across 323 cells, with 20,000 measurement pairs per cell from published reference values under Gaussian errors of 0.5, 1.0, and 2.0 mm. Three symmetry operators and four aggregation rules were compared for bias, precision, and minimum detectable change. Sensitivity analyses relaxed independent and magnitude-independent error and proportional restriction. Results: The min/max ratio was biased downward near symmetry (mean bias −0.108 at 9.7 mm excursions and −0.243 at 3.9 mm under 1.0 mm error). A 0.85 threshold flagged 26.6% of perfectly symmetric unrestricted jaws. The three operators ranked jaws identically at equivalent cut-offs, being monotone transformations of the same ratio. Embedding the symmetry term inside a geometric mean halved the smallest detectable change in index points, but the ranking reversed in invariant units of true symmetry (0.24, 0.33, and 0.43), and maximum opening outperformed every composite in restriction units (0.06 versus ≥0.13). Conclusions: Aggregation architecture trades symmetry sensitivity for amplitude sensitivity, and index-scale comparisons reward compression rather than precision. At manual precision, no formulation separates the targeted symmetry change from measurement noise. The precision of the inputs, not the arrangement of the formula, is the binding constraint, and this held under correlated and proportional error and selective restriction. Keywords: Temporomandibular joint; Mandible; Range of motion; Measurement error; Monte Carlo method; Symmetry