Cohort-level discrepancy between observed and model-based pedicle screw loosening risk: an exploratory aggregate-data evaluation of the explanatory gap index

Abstract

Published pedicle screw loosening (PSL) cohorts differ substantially in observed event rates, predictor measurement, surgical context, and outcome ascertainment. We evaluated whether an aggregate discrepancy index can describe how far an observed cohort result lies from a common model-derived linear-predictor reference when individual participant data are unavailable. The derivation cohort comprised 221 patients undergoing open transforaminal lumbar interbody fusion (TLIF), with 80 patient-level PSL events confirmed on routine 24-month computed tomography. A prespecified five-predictor L2-penalized logistic model included Posterior Functional Muscle Unit lean cross-sectional area (PFMU-lCSA), DEXA T-score, instrumentation extent, body mass index (BMI), and age. Internal validation used 2,000 bootstrap resamples; 10-fold cross-validation was retained as a secondary descriptive analysis. The Explanatory Gap Index (EGI) was defined as the observed cohort log-odds minus the model linear predictor evaluated at the available cohort-level predictor vector. Published-cohort analyses used reported aggregate values and explicitly labeled conversions or literature-based substitutions; individual participant data were not available. Apparent AUC was 0.850; mean bootstrap optimism was 0.013, yielding an optimism-corrected AUC of 0.837. The apparent calibration slope was 1.054 and the optimism-corrected slope was 0.964; Brier score was 0.144 (scaled Brier 0.376). At the original Youden threshold of 0.421, sensitivity was 75.0% (95% CI 64.5–83.2%) and specificity 83.0% (95% CI 75.9–88.3%). Aggregate EGI point estimates were +0.244 for the derivation benchmark, −0.072 for Zou 2020, −0.272 for Huang 2025, +0.495 for Marie-Hardy 2020, and +1.487 for Hu 2025. These estimates were not pooled. An exploratory ecological regression across the five cohort observations produced a slope of 0.369 (95% CI −1.413 to 2.151) and was considered inconclusive because of the very small number of cohort-level observations. EGI is a descriptive aggregate model–cohort discrepancy, not a conventional calibration statistic, a measure of statistical uncertainty, or a mechanism-identification tool. Discrepancies may reflect biological or clinical differences, surgical or institutional factors, measurement and outcome domains, case-mix, predictor substitution, aggregate-data approximation, model transportability, sampling variation, or data/reporting characteristics. Close agreement indicates aggregate concordance rather than proof of generalizability. Independent patient-level external validation is required before claims of transportability or clinical utility can be made.